{"id":693,"date":"2026-11-06T09:30:13","date_gmt":"2026-11-06T15:30:13","guid":{"rendered":"https:\/\/pagesofwisdom.com\/?p=693"},"modified":"2026-11-06T09:43:32","modified_gmt":"2026-11-06T15:43:32","slug":"solar-install-math-series-parallel-batteries-fridge","status":"publish","type":"post","link":"https:\/\/pagesofwisdom.com\/index.php\/2026\/11\/06\/solar-install-math-series-parallel-batteries-fridge\/","title":{"rendered":"Solar Install Math Cheat Sheet: Series vs Parallel, the 1.25 Factor, Bifacial Gain, and Fridge Runtime"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">Solar shopping without math is how you end up with a beautiful array that politely refuses to charge a battery bank sized for optimism. This is the plain-English cheat sheet: series vs parallel, the famous <strong>1.25<\/strong> (that\u2019s <em>125%<\/em>, not \u201c1.25 percent\u201d), bifacial gain without fairy dust, and how long a fridge will actually survive on 5 kWh vs 15 kWh.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Grab a calculator (there\u2019s one built into this page). Then hire a <strong>licensed electrician<\/strong> for panel, service, and high-voltage work\u2014these formulas help you buy smarter, not rewire your main breaker like a YouTube dare.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1600\" height=\"1065\" src=\"https:\/\/pagesofwisdom.com\/wp-content\/uploads\/2026\/11\/solar-rooftop-inverter-guide.jpg\" alt=\"Rooftop solar panels on a residential home under blue sky\" class=\"wp-image-680\" srcset=\"https:\/\/pagesofwisdom.com\/wp-content\/uploads\/2026\/11\/solar-rooftop-inverter-guide.jpg 1600w, https:\/\/pagesofwisdom.com\/wp-content\/uploads\/2026\/11\/solar-rooftop-inverter-guide-300x200.jpg 300w, https:\/\/pagesofwisdom.com\/wp-content\/uploads\/2026\/11\/solar-rooftop-inverter-guide-1024x682.jpg 1024w, https:\/\/pagesofwisdom.com\/wp-content\/uploads\/2026\/11\/solar-rooftop-inverter-guide-768x511.jpg 768w, https:\/\/pagesofwisdom.com\/wp-content\/uploads\/2026\/11\/solar-rooftop-inverter-guide-1536x1022.jpg 1536w\" sizes=\"auto, (max-width: 1600px) 100vw, 1600px\" \/><figcaption class=\"wp-element-caption\">Panel math starts on the roof\u2014series, parallel, and cold Voc decide what your inverter can swallow. Photo: Unsplash.<\/figcaption><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">Quick-reference formulas<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n\n<li><strong>Power:<\/strong> watts = volts \u00d7 amps (AC or DC).<\/li>\n\n\n<li><strong>Energy:<\/strong> watt-hours = watts \u00d7 hours. Kilowatt-hours = Wh \u00f7 1,000.<\/li>\n\n\n<li><strong>Series string:<\/strong> voltages add; current stays about one panel\u2019s current.<\/li>\n\n\n<li><strong>Parallel strings:<\/strong> currents add; voltage stays about one string\u2019s voltage.<\/li>\n\n\n<li><strong>Battery energy:<\/strong> Wh \u2248 V<sub>nominal<\/sub> \u00d7 Ah (use the chemistry\u2019s real nominal voltage).<\/li>\n\n\n<li><strong>Array Wh\/day (rough):<\/strong> array watts \u00d7 peak sun hours \u00d7 performance ratio.<\/li>\n\n\n<li><strong>Continuous current sizing (NEC idea):<\/strong> often \u00d7 <strong>1.25<\/strong> (125%). Two continuous factors stacked \u2192 about <strong>1.56<\/strong> (1.25 \u00d7 1.25).<\/li>\n\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">Series vs parallel (with real numbers)<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Imagine four 400 W panels. Label them roughly like many modern 400 W modules (check <em>your<\/em> datasheet):<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n\n<li>Vmp \u2248 37 V, Imp \u2248 10.81 A<\/li>\n\n\n<li>Voc \u2248 45 V, Isc \u2248 11.5 A<\/li>\n\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Four in series (one string)<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n\n<li>Vmp \u2248 37 \u00d7 4 = <strong>148 V<\/strong><\/li>\n\n\n<li>Voc \u2248 45 \u00d7 4 = <strong>180 V<\/strong> at 25\u00b0C STC<\/li>\n\n\n<li>Imp still \u2248 <strong>10.81 A<\/strong>; Isc \u2248 <strong>11.5 A<\/strong><\/li>\n\n\n<li>Power \u2248 400 \u00d7 4 = <strong>1,600 W<\/strong><\/li>\n\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Series is how you climb into an MPPT\u2019s happy voltage window without dragging monstrous wire ampacity. It\u2019s also how you accidentally outrun the inverter\u2019s <strong>max Voc<\/strong> on a cold morning.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Four in parallel<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n\n<li>Vmp still \u2248 <strong>37 V<\/strong>; Voc \u2248 <strong>45 V<\/strong><\/li>\n\n\n<li>Imp \u2248 10.81 \u00d7 4 = <strong>43.24 A<\/strong>; Isc \u2248 11.5 \u00d7 4 = <strong>46 A<\/strong><\/li>\n\n\n<li>Power still \u2248 <strong>1,600 W<\/strong><\/li>\n\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Parallel keeps voltage low and current high\u2014thicker cable, fussier fusing, and \u201cwhy is my charge controller warm?\u201d energy. Most home arrays mix both: series strings, then paralleled at a combiner.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1600\" height=\"1065\" src=\"https:\/\/pagesofwisdom.com\/wp-content\/uploads\/2026\/11\/solar-panels-closeup-guide.jpg\" alt=\"Close-up of blue solar photovoltaic panels outdoors\" class=\"wp-image-682\" srcset=\"https:\/\/pagesofwisdom.com\/wp-content\/uploads\/2026\/11\/solar-panels-closeup-guide.jpg 1600w, https:\/\/pagesofwisdom.com\/wp-content\/uploads\/2026\/11\/solar-panels-closeup-guide-300x200.jpg 300w, https:\/\/pagesofwisdom.com\/wp-content\/uploads\/2026\/11\/solar-panels-closeup-guide-1024x682.jpg 1024w, https:\/\/pagesofwisdom.com\/wp-content\/uploads\/2026\/11\/solar-panels-closeup-guide-768x511.jpg 768w, https:\/\/pagesofwisdom.com\/wp-content\/uploads\/2026\/11\/solar-panels-closeup-guide-1536x1022.jpg 1536w\" sizes=\"auto, (max-width: 1600px) 100vw, 1600px\" \/><figcaption class=\"wp-element-caption\">Bifacial panels can gain a little from the rear\u2014treat manufacturer bifaciality as a range, not a promise. Photo: Unsplash.<\/figcaption><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">Cold-weather Voc: the MPPT\u2019s least favorite surprise<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Panel Voc rises as cells get colder. Datasheets list a Voc temperature coefficient\u2014often around <strong>\u22120.25% to \u22120.30%\/\u00b0C<\/strong> (negative because Voc falls as temperature rises). From 25\u00b0C STC down to \u221220\u00b0C is a <strong>45\u00b0C<\/strong> drop.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Example with Voc = 45 V and \u22120.27%\/\u00b0C: cold Voc per panel \u2248 45 \u00d7 (1 + 45 \u00d7 0.0027) \u2248 <strong>50.5 V<\/strong>. Ten in series \u2248 <strong>505 V<\/strong> cold vs 450 V at 25\u00b0C. If your inverter max Voc is 500 V, that \u201cperfect\u201d 10-panel string is a winter landmine. Nine panels \u2248 <strong>454 V<\/strong> cold\u2014still verify against <em>your<\/em> coefficient and record cold.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Always size string length to the inverter\u2019s Voc limit at the coldest temperature your site actually sees\u2014not the brochure photo taken in July.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">The \u201c1.25 percent\u201d myth (it\u2019s 125%, and sometimes 156%)<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">People say \u201cadd 1.25 percent.\u201d What installers mean is the <strong>1.25 multiplier<\/strong>\u2014<strong>125% of continuous current<\/strong>\u2014a long-standing National Electrical Code approach for conductors and overcurrent devices serving continuous loads (loads expected for three hours or more). Solar PV source and output circuits get special continuous-current treatment in the Code; this is the idea in plain English, not a substitute for reading the current NEC edition or your inspector\u2019s mood.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n\n<li><strong>One 1.25:<\/strong> continuous current \u00d7 1.25 for many conductor\/OCPD sizing steps. Example: Isc 11.5 A \u2192 11.5 \u00d7 1.25 = <strong>14.4 A<\/strong>.<\/li>\n\n\n<li><strong>Two 1.25s (\u22481.56):<\/strong> some PV calculations effectively stack factors (for example continuous-current treatment that lands near 125% \u00d7 125% = <strong>156%<\/strong>). Example: 11.5 \u00d7 1.5625 \u2248 <strong>18.0 A<\/strong>; three paralleled strings of that module \u2192 34.5 \u00d7 1.5625 \u2248 <strong>53.9 A<\/strong> before you pick wire and breakers from ampacity tables.<\/li>\n\n\n<li><strong>Temperature:<\/strong> hot attics and rooftop conduits can require extra ampacity correction on top of those multipliers. Cold raises Voc (above); heat derates wire.<\/li>\n\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">On the AC side, a 6,000 W inverter at 240 V is 6,000 \u00f7 240 = <strong>25 A<\/strong>. Continuous-load thinking often points near 25 \u00d7 1.25 = <strong>31.25 A<\/strong>, so people shop a 35 A or 40 A breaker only after checking the inverter manual and Code\u2014not vibes.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Tools that help you verify numbers (not replace an electrician): <a href=\"https:\/\/www.amazon.com\/dp\/B000O3LUEI?tag=pagesofwisdom-20\" rel=\"noopener noreferrer sponsored\">Fluke 117 multimeter<\/a>, <a href=\"https:\/\/www.amazon.com\/dp\/B08DQMX7YF?tag=pagesofwisdom-20\" rel=\"noopener noreferrer sponsored\">Klein NCVT-3P<\/a>, <a href=\"https:\/\/www.amazon.com\/dp\/B00BC39YFQ?tag=pagesofwisdom-20\" rel=\"noopener noreferrer sponsored\">Klein 11063W stripper<\/a>, <a href=\"https:\/\/www.amazon.com\/dp\/B0BF76JDCC?tag=pagesofwisdom-20\" rel=\"noopener noreferrer sponsored\">Klein 85076INS insulated drivers<\/a>, <a href=\"https:\/\/www.amazon.com\/dp\/B00FMPKAD0?tag=pagesofwisdom-20\" rel=\"noopener noreferrer sponsored\">TEKTON 24330 torque wrench<\/a>, <a href=\"https:\/\/www.amazon.com\/dp\/B00W4WRQVI?tag=pagesofwisdom-20\" rel=\"noopener noreferrer sponsored\">IWISS MC4 tool kit<\/a>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Some links are affiliate links, including Amazon and <a href=\"https:\/\/signaturesolar.com\/?ref=6GBwB-d9rAtRIn\">Signature Solar<\/a>, and I may earn a commission at no extra cost to you. As an Amazon Associate I earn from qualifying purchases. <a href=\"https:\/\/pagesofwisdom.com\/index.php\/affiliate-disclosure\/\">Full affiliate disclosure<\/a>.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1600\" height=\"1067\" src=\"https:\/\/pagesofwisdom.com\/wp-content\/uploads\/2026\/11\/tools-workbench-solar-guide.jpg\" alt=\"Hand tools arranged on a workbench in a workshop\" class=\"wp-image-686\" srcset=\"https:\/\/pagesofwisdom.com\/wp-content\/uploads\/2026\/11\/tools-workbench-solar-guide.jpg 1600w, https:\/\/pagesofwisdom.com\/wp-content\/uploads\/2026\/11\/tools-workbench-solar-guide-300x200.jpg 300w, https:\/\/pagesofwisdom.com\/wp-content\/uploads\/2026\/11\/tools-workbench-solar-guide-1024x683.jpg 1024w, https:\/\/pagesofwisdom.com\/wp-content\/uploads\/2026\/11\/tools-workbench-solar-guide-768x512.jpg 768w, https:\/\/pagesofwisdom.com\/wp-content\/uploads\/2026\/11\/tools-workbench-solar-guide-1536x1024.jpg 1536w\" sizes=\"auto, (max-width: 1600px) 100vw, 1600px\" \/><figcaption class=\"wp-element-caption\">A meter and a torque wrench beat guessing. Photo: Unsplash.<\/figcaption><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">Array watts \u2192 daily kWh (peak sun hours)<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Nameplate watts are laboratory bragging rights (STC). Daily energy is messier:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Wh\/day \u2248 array watts \u00d7 peak sun hours \u00d7 performance ratio<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Example: 10 \u00d7 400 W = 4,000 W array, 4.5 peak sun hours, PR 0.80 \u2192 4,000 \u00d7 4.5 \u00d7 0.80 = <strong>14,400 Wh\/day (14.4 kWh)<\/strong>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Peak sun hours are \u201cequivalent full-sun hours,\u201d not clock hours of daylight. A cloudy winter week can halve your summer average. Use a local solar resource map or PVWatts-style data for your zip code when money is on the line.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">System losses \/ performance ratio<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">A honest PR (often 0.75\u20130.85 for many homes) folds in dirt, wiring drop, mismatch, inverter efficiency, snow, and \u201cthe tree grew.\u201d Rough product of common factors: inverter 0.98 \u00d7 DC wiring\/mismatch 0.96 \u00d7 soiling 0.98 \u00d7 temperature\/other 0.92 \u00d7 availability 0.98 \u2248 <strong>0.83<\/strong>\u2014close to that 0.80 rule of thumb. Don\u2019t stack fantasy 0.95s until your roof proves it.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Bifacial panel math (without overpromising)<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Bifacial modules can make extra power from light hitting the rear. Manufacturers publish a <strong>bifaciality factor<\/strong>\u2014often roughly <strong>70\u201390%<\/strong>\u2014meaning the rear is that fraction as effective as the front for the same irradiance.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Rear irradiance depends on <strong>ground albedo<\/strong> (grass ~0.2, light gravel\/white roof higher, fresh snow higher still), height, tilt, and shade under the rack. A simplified planning estimate:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Extra fraction \u2248 bifaciality \u00d7 (rear irradiance \u00f7 front irradiance)<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Example: bifaciality 0.80 and rear\/front \u2248 0.10 \u2192 about <strong>8%<\/strong> extra. On a 400 W front-side rating that\u2019s ~<strong>432 W effective<\/strong> in that condition\u2014not a permanent 432 W nameplate. Dull ground and low racks can land nearer <strong>3\u20135%<\/strong>; snow and bright roofs can do better for a while. Size MPPT current with bifacial boost in mind if the manufacturer says to, and never sell yourself a 30% gain because a brochure glowed.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Interactive solar math calculator<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Use the tabs below for array energy, battery sizing, and appliance runtime. Everything runs locally in your browser.<\/p>\n\n\n\n<div class=\"pow-solar-calc\" id=\"pow-solar-calc\" style=\"border:1px solid #d0d7de;border-radius:12px;padding:16px;margin:1.5rem 0;background:#f8fafc;max-width:720px;\">\n<style>\n.pow-solar-calc *{box-sizing:border-box;font-family:inherit}\n.pow-solar-calc .tabs{display:flex;flex-wrap:wrap;gap:8px;margin:0 0 12px}\n.pow-solar-calc .tabs button{flex:1 1 140px;padding:10px 12px;border:1px solid #cbd5e1;border-radius:8px;background:#fff;cursor:pointer;font-weight:600}\n.pow-solar-calc .tabs button.active{background:#0f766e;color:#fff;border-color:#0f766e}\n.pow-solar-calc .pane{display:none}\n.pow-solar-calc .pane.active{display:block}\n.pow-solar-calc label{display:block;font-size:14px;margin:10px 0 4px;color:#334155}\n.pow-solar-calc input{width:100%;padding:10px;border:1px solid #cbd5e1;border-radius:8px;font-size:16px}\n.pow-solar-calc .row{display:grid;grid-template-columns:1fr 1fr;gap:12px}\n@media(max-width:560px){.pow-solar-calc .row{grid-template-columns:1fr}}\n.pow-solar-calc .out{margin-top:14px;padding:12px;border-radius:8px;background:#ecfdf5;border:1px solid #99f6e4;font-size:15px;line-height:1.45}\n.pow-solar-calc .err{background:#fef2f2;border-color:#fecaca;color:#991b1b}\n.pow-solar-calc .hint{font-size:13px;color:#64748b;margin:8px 0 0}\n.pow-solar-calc .go{margin-top:12px;padding:10px 14px;border:0;border-radius:8px;background:#0f766e;color:#fff;font-weight:700;cursor:pointer;width:100%}\n<\/style>\n<p style=\"margin:0 0 8px;font-weight:700;\">Solar math calculator (runs in your browser\u2014nothing is uploaded)<\/p>\n<div class=\"tabs\" role=\"tablist\">\n<button type=\"button\" class=\"active\" data-tab=\"array\">Array kWh\/day<\/button>\n<button type=\"button\" data-tab=\"battery\">Battery size<\/button>\n<button type=\"button\" data-tab=\"runtime\">Appliance runtime<\/button>\n<\/div>\n<div class=\"pane active\" id=\"pane-array\">\n<div class=\"row\"><div><label for=\"sc-panels\">Number of panels<\/label><input id=\"sc-panels\" type=\"number\" min=\"1\" step=\"1\" value=\"10\"><\/div>\n<div><label for=\"sc-watts\">Watts per panel (STC)<\/label><input id=\"sc-watts\" type=\"number\" min=\"1\" step=\"1\" value=\"400\"><\/div><\/div>\n<div class=\"row\"><div><label for=\"sc-sun\">Peak sun hours \/ day<\/label><input id=\"sc-sun\" type=\"number\" min=\"0.1\" step=\"0.1\" value=\"4.5\"><\/div>\n<div><label for=\"sc-pr\">Performance ratio (0.7\u20130.9 typical)<\/label><input id=\"sc-pr\" type=\"number\" min=\"0.5\" max=\"1\" step=\"0.01\" value=\"0.80\"><\/div><\/div>\n<button type=\"button\" class=\"go\" id=\"sc-array-go\">Calculate array energy<\/button>\n<div class=\"out\" id=\"sc-array-out\">Enter values and calculate.<\/div>\n<p class=\"hint\">Formula: panels \u00d7 watts \u00d7 peak sun hours \u00d7 performance ratio = Wh\/day. Default matches the 10\u00d7400W \u00d7 4.5 h \u00d7 0.80 example (14,400 Wh\/day).<\/p>\n<\/div>\n<div class=\"pane\" id=\"pane-battery\">\n<div class=\"row\"><div><label for=\"sc-daily\">Daily DC Wh needed<\/label><input id=\"sc-daily\" type=\"number\" min=\"1\" step=\"1\" value=\"3000\"><\/div>\n<div><label for=\"sc-days\">Days of autonomy<\/label><input id=\"sc-days\" type=\"number\" min=\"0.25\" step=\"0.25\" value=\"2\"><\/div><\/div>\n<div class=\"row\"><div><label for=\"sc-dod\">Usable fraction \/ DoD (0\u20131)<\/label><input id=\"sc-dod\" type=\"number\" min=\"0.1\" max=\"1\" step=\"0.01\" value=\"0.90\"><\/div>\n<div><label for=\"sc-eff\">Round-trip \/ inverter path efficiency<\/label><input id=\"sc-eff\" type=\"number\" min=\"0.5\" max=\"1\" step=\"0.01\" value=\"0.92\"><\/div><\/div>\n<button type=\"button\" class=\"go\" id=\"sc-batt-go\">Calculate battery nameplate<\/button>\n<div class=\"out\" id=\"sc-batt-out\">Enter values and calculate.<\/div>\n<p class=\"hint\">Formula: bank Wh \u2248 (daily Wh \u00d7 days) \u00f7 (DoD \u00d7 efficiency). Default: 3,000 Wh \u00d7 2 \u00f7 (0.90 \u00d7 0.92) \u2248 7,246 Wh nameplate.<\/p>\n<\/div>\n<div class=\"pane\" id=\"pane-runtime\">\n<div class=\"row\"><div><label for=\"sc-kwh\">Battery nameplate Wh<\/label><input id=\"sc-kwh\" type=\"number\" min=\"1\" step=\"1\" value=\"5120\"><\/div>\n<div><label for=\"sc-usable\">Usable fraction<\/label><input id=\"sc-usable\" type=\"number\" min=\"0.1\" max=\"1\" step=\"0.01\" value=\"0.90\"><\/div><\/div>\n<div class=\"row\"><div><label for=\"sc-load\">Average load watts<\/label><input id=\"sc-load\" type=\"number\" min=\"1\" step=\"1\" value=\"150\"><\/div>\n<div><label for=\"sc-inv\">Inverter efficiency<\/label><input id=\"sc-inv\" type=\"number\" min=\"0.5\" max=\"1\" step=\"0.01\" value=\"0.90\"><\/div><\/div>\n<button type=\"button\" class=\"go\" id=\"sc-run-go\">Calculate runtime<\/button>\n<div class=\"out\" id=\"sc-run-out\">Enter values and calculate.<\/div>\n<p class=\"hint\">Usable Wh = nameplate \u00d7 usable fraction. Hours \u2248 usable Wh \u00f7 (load W \u00f7 inverter eff). For a cycling fridge, use average watts (duty cycle \u00d7 running watts), not just nameplate.<\/p>\n<\/div>\n<\/div>\n<script>\n(function(){\n  var root=document.getElementById('pow-solar-calc');\n  if(!root) return;\n  function num(id){var el=document.getElementById(id); return el?parseFloat(el.value):NaN;}\n  function show(id, html, err){var el=document.getElementById(id); if(!el) return; el.className='out'+(err?' err':''); el.innerHTML=html;}\n  function ok(){for(var i=0;i<arguments.length;i++){var v=arguments[i]; if(!(v>0) || !isFinite(v)) return false;} return true;}\n  root.querySelectorAll('.tabs button').forEach(function(btn){\n    btn.addEventListener('click', function(){\n      root.querySelectorAll('.tabs button').forEach(function(b){b.classList.remove('active');});\n      root.querySelectorAll('.pane').forEach(function(p){p.classList.remove('active');});\n      btn.classList.add('active');\n      var pane=document.getElementById('pane-'+btn.getAttribute('data-tab'));\n      if(pane) pane.classList.add('active');\n    });\n  });\n  document.getElementById('sc-array-go').addEventListener('click', function(){\n    var n=num('sc-panels'), w=num('sc-watts'), s=num('sc-sun'), pr=num('sc-pr');\n    if(!ok(n,w,s) || !(pr>0 && pr<=1)){show('sc-array-out','Check inputs: panels, watts, sun hours must be &gt; 0; performance ratio between 0 and 1.',true); return;}\n    var stc=n*w, wh=stc*s*pr, kwh=wh\/1000;\n    show('sc-array-out','<strong>Array STC:<\/strong> '+Math.round(stc).toLocaleString()+' W<br><strong>Estimated energy:<\/strong> '+Math.round(wh).toLocaleString()+' Wh\/day ('+kwh.toFixed(2)+' kWh\/day)<br><span style=\"font-size:13px;color:#475569\">Assumes flat peak-sun-hour model; real weather, shade, and soiling change the answer.<\/span>');\n  });\n  document.getElementById('sc-batt-go').addEventListener('click', function(){\n    var d=num('sc-daily'), days=num('sc-days'), dod=num('sc-dod'), eff=num('sc-eff');\n    if(!ok(d,days) || !(dod>0&&dod<=1) || !(eff>0&&eff<=1)){show('sc-batt-out','Check inputs: daily Wh and days &gt; 0; DoD and efficiency between 0 and 1.',true); return;}\n    var need=d*days, bank=need\/(dod*eff);\n    show('sc-batt-out','<strong>Energy to cover:<\/strong> '+Math.round(need).toLocaleString()+' Wh<br><strong>Nameplate battery:<\/strong> about '+Math.round(bank).toLocaleString()+' Wh ('+(bank\/1000).toFixed(2)+' kWh)<br><span style=\"font-size:13px;color:#475569\">Add inverter idle and HVAC separately\u2014those eat the bank quietly.<\/span>');\n  });\n  document.getElementById('sc-run-go').addEventListener('click', function(){\n    var wh=num('sc-kwh'), u=num('sc-usable'), load=num('sc-load'), inv=num('sc-inv');\n    if(!ok(wh,load) || !(u>0&&u<=1) || !(inv>0&&inv<=1)){show('sc-run-out','Check inputs: Wh and load &gt; 0; usable fraction and inverter efficiency between 0 and 1.',true); return;}\n    var usable=wh*u, dcW=load\/inv, hours=usable\/dcW, days=hours\/24;\n    show('sc-run-out','<strong>Usable energy:<\/strong> '+Math.round(usable).toLocaleString()+' Wh<br><strong>DC draw at inverter:<\/strong> '+dcW.toFixed(0)+' W<br><strong>Runtime:<\/strong> '+hours.toFixed(1)+' hours ('+days.toFixed(2)+' days)<br><span style=\"font-size:13px;color:#475569\">Example: 5,120 Wh \u00d7 0.90 \u00f7 (150 W \u00f7 0.90) \u2248 27.6 h if the load were a steady 150 W\u2014cycling fridges need average watts instead.<\/span>');\n  });\n})();\n<\/script>\n\n\n\n<h2 class=\"wp-block-heading\">Battery Ah, Wh, and 12V vs 24V vs 48V<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Wh \u2248 volts \u00d7 amp-hours. A \u201c100 Ah\u201d battery is not a universal gas tank:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n\n<li>12 V lead-ish 100 Ah \u2248 12 \u00d7 100 = <strong>1,200 Wh<\/strong> nameplate<\/li>\n\n\n<li>12.8 V LiFePO\u2084 100 Ah \u2248 <strong>1,280 Wh<\/strong><\/li>\n\n\n<li>51.2 V LiFePO\u2084 100 Ah server rack \u2248 <strong>5,120 Wh (5.12 kWh)<\/strong><\/li>\n\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Same 3,000 W load through a 92% efficient inverter: DC power \u2248 3,000 \u00f7 0.92 \u2248 3,261 W. Current \u2248 3,261 \u00f7 V \u2192 about <strong>272 A at 12 V<\/strong>, <strong>136 A at 24 V<\/strong>, <strong>68 A at 48 V<\/strong>. That\u2019s why home solar grew up and moved to 48 V\u2014wire size and lug temperatures prefer it.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1600\" height=\"1083\" src=\"https:\/\/pagesofwisdom.com\/wp-content\/uploads\/2026\/11\/solar-battery-storage-wall.jpg\" alt=\"Home energy storage battery cabinet next to electrical equipment\" class=\"wp-image-681\" srcset=\"https:\/\/pagesofwisdom.com\/wp-content\/uploads\/2026\/11\/solar-battery-storage-wall.jpg 1600w, https:\/\/pagesofwisdom.com\/wp-content\/uploads\/2026\/11\/solar-battery-storage-wall-300x203.jpg 300w, https:\/\/pagesofwisdom.com\/wp-content\/uploads\/2026\/11\/solar-battery-storage-wall-1024x693.jpg 1024w, https:\/\/pagesofwisdom.com\/wp-content\/uploads\/2026\/11\/solar-battery-storage-wall-768x520.jpg 768w, https:\/\/pagesofwisdom.com\/wp-content\/uploads\/2026\/11\/solar-battery-storage-wall-1536x1040.jpg 1536w\" sizes=\"auto, (max-width: 1600px) 100vw, 1600px\" \/><figcaption class=\"wp-element-caption\">Battery Wh and DoD turn \u201chow big is the bank?\u201d into hours of fridge time. Photo: Unsplash.<\/figcaption><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">Usable DoD: LiFePO\u2084 vs lead-acid<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n\n<li><strong>LiFePO\u2084:<\/strong> many owners plan ~<strong>80\u201390%<\/strong> usable (leave a floor for longevity and BMS manners). 5.12 kWh \u00d7 0.90 = <strong>4.61 kWh usable<\/strong>.<\/li>\n\n\n<li><strong>Lead-acid \/ AGM:<\/strong> routinely plan ~<strong>50%<\/strong> DoD for lifespan. Same 5.12 kWh nameplate \u2192 ~<strong>2.56 kWh usable<\/strong>.<\/li>\n\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Comparing nameplates without DoD is how lead-acid \u201cwins\u201d on spreadsheet and loses on Tuesday night.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Inverter efficiency, surge, and 120\/240V<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Inverters waste a slice as heat\u2014often ~90\u201397% depending on load. A 150 W AC load at 90% efficiency pulls ~167 W from the battery bus. Idle draw (tens of watts) adds up over a quiet night; include it.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Motors surge: a fridge that runs at 150 W may kick 3\u20137\u00d7 for a second. Your inverter\u2019s <strong>surge rating<\/strong> must clear that, and so must the battery\u2019s discharge limit.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">U.S. homes are split-phase <strong>120\/240 V<\/strong>. Power is still V \u00d7 A: a 20 A\/120 V circuit is 2,400 W; a 30 A\/240 V dryer circuit is 7,200 W. Pick inverters that speak the voltages your appliances need\u2014see our <a href=\"https:\/\/pagesofwisdom.com\/index.php\/2026\/11\/06\/off-grid-solar-inverter-pros-cons-guide\/\">off-grid<\/a>, <a href=\"https:\/\/pagesofwisdom.com\/index.php\/2026\/11\/06\/hybrid-solar-inverter-pros-cons-guide\/\">hybrid<\/a>, and <a href=\"https:\/\/pagesofwisdom.com\/index.php\/2026\/11\/06\/grid-tie-solar-inverter-pros-cons-guide\/\">grid-tie<\/a> inverter guides.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Solar \u2192 battery recharge time<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Rough charge time (hours) \u2248 battery Wh to replace \u00f7 (PV charge power \u00d7 charge efficiency). Example: restore 80% of 5.12 kWh = 4,096 Wh from a 1,600 W effective PV charge at 95% \u2192 4,096 \u00f7 (1,600 \u00d7 0.95) \u2248 <strong>2.7 hours of equivalent full sun<\/strong>. Weather stretches that into \u201cmaybe tomorrow.\u201d<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Worked example: standard refrigerator runtime<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Assumptions (edit them for your sticker):<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n\n<li>Running power while the compressor is on: <strong>150 W<\/strong><\/li>\n\n\n<li>Duty cycle: <strong>35%<\/strong> (compressor runs 35% of the day in a mild kitchen)<\/li>\n\n\n<li>Door-open \/ defrost fudge: <strong>400 W \u00d7 0.4 h = 160 Wh\/day<\/strong><\/li>\n\n\n<li>Inverter efficiency: <strong>90%<\/strong><\/li>\n\n\n<li>Inverter idle: <strong>30 W continuous<\/strong> \u2192 30 \u00d7 24 = 720 Wh\/day from the battery bus<\/li>\n\n\n<li>LiFePO\u2084 usable: <strong>90%<\/strong> of nameplate<\/li>\n\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Compressor energy: 150 \u00d7 24 \u00d7 0.35 = <strong>1,260 Wh\/day AC<\/strong>. Plus 160 Wh fudge \u2192 <strong>1,420 Wh\/day AC<\/strong>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Battery-side for the fridge path: 1,420 \u00f7 0.90 \u2248 <strong>1,578 Wh<\/strong>. Add idle 720 Wh \u2192 <strong>~2,298 Wh\/day DC<\/strong> total for \u201cfridge + sleepy inverter.\u201d<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n\n<li><strong>5.12 kWh LiFePO\u2084<\/strong> (usable 4.61 kWh): 4,608 \u00f7 2,298 \u2248 <strong>2.0 days (~48 hours)<\/strong><\/li>\n\n\n<li><strong>15.36 kWh LiFePO\u2084<\/strong> (usable 13.82 kWh): 13,824 \u00f7 2,298 \u2248 <strong>6.0 days (~144 hours)<\/strong><\/li>\n\n\n<li><strong>Same 5.12 kWh if it were lead at 50% DoD<\/strong> (2.56 kWh usable): \u2248 <strong>1.1 days<\/strong><\/li>\n\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Open the door like it\u2019s a TV, park the fridge in a hot garage, or skip the idle term and your \u201ctwo days\u201d becomes an awkward evening. Surge still needs an inverter that won\u2019t fold when the compressor starts.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Whole-home sketch (2 days of autonomy)<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Sample daily AC loads: fridge path 1.42 kWh + freezer 1.0 + lights 0.45 + internet\/IT 0.48 + well controls 0.4 + phones\/misc 0.3 + laundry occasional average 1.0 + cooking average 3.0 \u2248 <strong>8.05 kWh AC\/day<\/strong>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">At 92% inverter efficiency plus 0.72 kWh idle: DC \u2248 8.05 \u00f7 0.92 + 0.72 \u2248 <strong>9.47 kWh\/day<\/strong>. Two days \u2248 18.9 kWh usable \u2192 nameplate at 90% DoD \u2248 <strong>21.0 kWh<\/strong> (a 20.48 kWh bank is close; 25.6 kWh is more comfortable). Array to refill one day in summer at 4.5 PSH \u00d7 0.80 PR: 9.47 \u00f7 (4.5 \u00d7 0.80) \u2248 <strong>2.6 kW<\/strong> STC; winter at 3.0 PSH wants closer to <strong>4.0 kW<\/strong>.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Breakers and wire (high level only)<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Voltage drop \u2248 2 \u00d7 length \u00d7 current \u00d7 ohms\/ft (copper charts). Long low-voltage DC runs punish you; raising system voltage or shortening cable fixes more sins than buying \u201cbigger hopes.\u201d Overcurrent devices must match conductor ampacity and equipment ratings. Grounding, disconnects, rapid shutdown, and service interconnects are licensed-electrician territory\u2014full stop.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Common mistakes<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n\n<li>Sizing strings to 25\u00b0C Voc and discovering January is colder than marketing.<\/li>\n\n\n<li>Confusing 1.25% with the 1.25\u00d7 continuous-current factor (and ignoring the ~1.56 stack).<\/li>\n\n\n<li>Counting lead-acid and LiFePO\u2084 nameplates as equal usable energy.<\/li>\n\n\n<li>Using fridge nameplate watts all day instead of duty-cycle averages\u2014or forgetting surge.<\/li>\n\n\n<li>Ignoring inverter idle on \u201ctiny\u201d overnight loads.<\/li>\n\n\n<li>Promising bifacial 20% gains on dark dirt two feet off the ground.<\/li>\n\n\n<li>Skipping a meter: {AMZ(&#8220;B000O3LUEI&#8221;,&#8221;measure twice&#8221;)} still beats explaining scorch marks to the inspector.<\/li>\n\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">Safety disclaimer<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">This article is educational. Electrical codes, utility rules, and equipment manuals win every argument. Do not work in live panels. Have a <strong>licensed electrician<\/strong> handle service equipment, transfer switches, and anything that can backfeed the grid.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Related reading<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Inverter deep dives: <a href=\"https:\/\/pagesofwisdom.com\/index.php\/2026\/11\/06\/off-grid-solar-inverter-pros-cons-guide\/\">off-grid<\/a> \u00b7 <a href=\"https:\/\/pagesofwisdom.com\/index.php\/2026\/11\/06\/hybrid-solar-inverter-pros-cons-guide\/\">hybrid<\/a> \u00b7 <a href=\"https:\/\/pagesofwisdom.com\/index.php\/2026\/11\/06\/grid-tie-solar-inverter-pros-cons-guide\/\">grid-tie<\/a>. Gear notes on the <a href=\"https:\/\/pagesofwisdom.com\/index.php\/solar-equipment-for-diy\/\">solar equipment hub<\/a> and our <a href=\"https:\/\/pagesofwisdom.com\/index.php\/2024\/03\/22\/our-solar-power-system-install-diy-2024\/\">DIY install story<\/a>. Shop EG4-class hardware via <a href=\"https:\/\/signaturesolar.com\/?ref=6GBwB-d9rAtRIn\">Signature Solar<\/a> (affiliate) when you\u2019re ready to match math to metal.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Prefer the short version? Catch solar and tech explainers on <a href=\"https:\/\/www.youtube.com\/channel\/UCDn23q274Scgpr-wrpKV1-Q\">YouTube<\/a>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>Pages of Wisdom \u2014 plain-English solar math.<\/em><\/p>\n\n","protected":false},"excerpt":{"rendered":"<p>Plain-English solar math: series\/parallel, 125% and 1.56 factors, bifacial estimates, battery Wh, and how long 5\u201315 kWh runs a fridge\u2014plus a built-in calculator.<\/p>\n","protected":false},"author":1,"featured_media":682,"comment_status":"closed","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[180],"tags":[196,220,218,198,195,224,221,222,223,219,225,217],"class_list":["post-693","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-solar","tag-120v-vs-240v","tag-battery-sizing","tag-bifacial-solar","tag-diy-solar","tag-lifepo4","tag-mppt","tag-nec-1-25","tag-peak-sun-hours","tag-refrigerator-runtime","tag-series-vs-parallel","tag-solar-calculator","tag-solar-math"],"aioseo_notices":[],"aioseo_head":"\n\t\t<!-- All in One SEO 5.0.5 - aioseo.com -->\n\t<meta name=\"description\" content=\"Worked solar math for series vs parallel, cold Voc, 125%\/1.56 current factors, bifacial gain, battery sizing, and refrigerator runtime on 5\u201315 kWh\u2014with a free calculator.\" \/>\n\t<meta name=\"robots\" content=\"max-image-preview:large\" \/>\n\t<meta name=\"author\" content=\"pagesofwisdom.com\"\/>\n\t<link rel=\"canonical\" href=\"https:\/\/pagesofwisdom.com\/index.php\/2026\/11\/06\/solar-install-math-series-parallel-batteries-fridge\/\" \/>\n\t\t<meta name=\"generator\" content=\"All in One SEO (AIOSEO) 5.0.5\" \/>\n\t\t<meta property=\"og:locale\" content=\"en_GB\" \/>\n\t\t<meta property=\"og:site_name\" content=\"Pages of Wisdom - The Practical Insights of Andrew on Tech, Self-Reliance, and Home Business\" \/>\n\t\t<meta property=\"og:type\" content=\"article\" \/>\n\t\t<meta property=\"og:title\" content=\"Solar Install Math: Series\/Parallel, 1.25 Factor, Bifacial, Fridge Runtime\" \/>\n\t\t<meta property=\"og:description\" content=\"Worked solar math for series vs parallel, cold Voc, 125%\/1.56 current factors, bifacial gain, battery sizing, and refrigerator runtime on 5\u201315 kWh\u2014with a free calculator.\" \/>\n\t\t<meta property=\"og:url\" content=\"https:\/\/pagesofwisdom.com\/index.php\/2026\/11\/06\/solar-install-math-series-parallel-batteries-fridge\/\" \/>\n\t\t<meta property=\"article:published_time\" content=\"2026-11-06T15:30:13+00:00\" \/>\n\t\t<meta property=\"article:modified_time\" content=\"2026-11-06T15:43:32+00:00\" \/>\n\t\t<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n\t\t<meta name=\"twitter:title\" content=\"Solar Install Math: Series\/Parallel, 1.25 Factor, Bifacial, Fridge Runtime\" \/>\n\t\t<meta name=\"twitter:description\" content=\"Worked solar math for series vs parallel, cold Voc, 125%\/1.56 current factors, bifacial gain, battery sizing, and refrigerator runtime on 5\u201315 kWh\u2014with a free calculator.\" \/>\n\t\t<script type=\"application\/ld+json\" class=\"aioseo-schema\">\n\t\t\t{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"BlogPosting\",\"@id\":\"https:\\\/\\\/pagesofwisdom.com\\\/index.php\\\/2026\\\/11\\\/06\\\/solar-install-math-series-parallel-batteries-fridge\\\/#blogposting\",\"name\":\"Solar Install Math: Series\\\/Parallel, 1.25 Factor, Bifacial, Fridge Runtime\",\"headline\":\"Solar Install Math Cheat Sheet: Series vs Parallel, the 1.25 Factor, Bifacial Gain, and Fridge Runtime\",\"author\":{\"@id\":\"https:\\\/\\\/pagesofwisdom.com\\\/index.php\\\/author\\\/pagesofwisdom-com\\\/#author\"},\"publisher\":{\"@id\":\"https:\\\/\\\/pagesofwisdom.com\\\/#organization\"},\"image\":{\"@type\":\"ImageObject\",\"url\":\"https:\\\/\\\/pagesofwisdom.com\\\/wp-content\\\/uploads\\\/2026\\\/11\\\/solar-panels-closeup-guide.jpg\",\"width\":1600,\"height\":1065,\"caption\":\"Panels make DC power. 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