Solar Install Math Cheat Sheet: Series vs Parallel, the 1.25 Factor, Bifacial Gain, and Fridge Runtime

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 1.25 (that’s 125%, not “1.25 percent”), bifacial gain without fairy dust, and how long a fridge will actually survive on 5 kWh vs 15 kWh.

Grab a calculator (there’s one built into this page). Then hire a licensed electrician for panel, service, and high-voltage work—these formulas help you buy smarter, not rewire your main breaker like a YouTube dare.

Quick-reference formulas

• Power: watts = volts × amps (AC or DC).
• Energy: watt-hours = watts × hours. Kilowatt-hours = Wh ÷ 1,000.
• Series string: voltages add; current stays about one panel’s current.
• Parallel strings: currents add; voltage stays about one string’s voltage.
• Battery energy: Wh ≈ V_nominal × Ah (use the chemistry’s real nominal voltage).
• Array Wh/day (rough): array watts × peak sun hours × performance ratio.
• Continuous current sizing (NEC idea): often × 1.25 (125%). Two continuous factors stacked → about 1.56 (1.25 × 1.25).

Series vs parallel (with real numbers)

Imagine four 400 W panels. Label them roughly like many modern 400 W modules (check your datasheet):

• Vmp ≈ 37 V, Imp ≈ 10.81 A
• Voc ≈ 45 V, Isc ≈ 11.5 A

Four in series (one string)

• Vmp ≈ 37 × 4 = 148 V
• Voc ≈ 45 × 4 = 180 V at 25°C STC
• Imp still ≈ 10.81 A; Isc ≈ 11.5 A
• Power ≈ 400 × 4 = 1,600 W

Series is how you climb into an MPPT’s happy voltage window without dragging monstrous wire ampacity. It’s also how you accidentally outrun the inverter’s max Voc on a cold morning.

Four in parallel

• Vmp still ≈ 37 V; Voc ≈ 45 V
• Imp ≈ 10.81 × 4 = 43.24 A; Isc ≈ 11.5 × 4 = 46 A
• Power still ≈ 1,600 W

Parallel keeps voltage low and current high—thicker cable, fussier fusing, and “why is my charge controller warm?” energy. Most home arrays mix both: series strings, then paralleled at a combiner.

Cold-weather Voc: the MPPT’s least favorite surprise

Panel Voc rises as cells get colder. Datasheets list a Voc temperature coefficient—often around −0.25% to −0.30%/°C (negative because Voc falls as temperature rises). From 25°C STC down to −20°C is a 45°C drop.

Example with Voc = 45 V and −0.27%/°C: cold Voc per panel ≈ 45 × (1 + 45 × 0.0027) ≈ 50.5 V. Ten in series ≈ 505 V cold vs 450 V at 25°C. If your inverter max Voc is 500 V, that “perfect” 10-panel string is a winter landmine. Nine panels ≈ 454 V cold—still verify against your coefficient and record cold.

Always size string length to the inverter’s Voc limit at the coldest temperature your site actually sees—not the brochure photo taken in July.

The “1.25 percent” myth (it’s 125%, and sometimes 156%)

People say “add 1.25 percent.” What installers mean is the 1.25 multiplier—125% of continuous current—a 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’s mood.

• One 1.25: continuous current × 1.25 for many conductor/OCPD sizing steps. Example: Isc 11.5 A → 11.5 × 1.25 = 14.4 A.
• Two 1.25s (≈1.56): some PV calculations effectively stack factors (for example continuous-current treatment that lands near 125% × 125% = 156%). Example: 11.5 × 1.5625 ≈ 18.0 A; three paralleled strings of that module → 34.5 × 1.5625 ≈ 53.9 A before you pick wire and breakers from ampacity tables.
• Temperature: hot attics and rooftop conduits can require extra ampacity correction on top of those multipliers. Cold raises Voc (above); heat derates wire.

On the AC side, a 6,000 W inverter at 240 V is 6,000 ÷ 240 = 25 A. Continuous-load thinking often points near 25 × 1.25 = 31.25 A, so people shop a 35 A or 40 A breaker only after checking the inverter manual and Code—not vibes.

Tools that help you verify numbers (not replace an electrician): Fluke 117 multimeter, Klein NCVT-3P, Klein 11063W stripper, Klein 85076INS insulated drivers, TEKTON 24330 torque wrench, IWISS MC4 tool kit.

Some links are affiliate links, including Amazon and Signature Solar, and I may earn a commission at no extra cost to you. As an Amazon Associate I earn from qualifying purchases. Full affiliate disclosure.

Array watts → daily kWh (peak sun hours)

Nameplate watts are laboratory bragging rights (STC). Daily energy is messier:

Wh/day ≈ array watts × peak sun hours × performance ratio

Example: 10 × 400 W = 4,000 W array, 4.5 peak sun hours, PR 0.80 → 4,000 × 4.5 × 0.80 = 14,400 Wh/day (14.4 kWh).

Peak sun hours are “equivalent full-sun hours,” 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.

System losses / performance ratio

A honest PR (often 0.75–0.85 for many homes) folds in dirt, wiring drop, mismatch, inverter efficiency, snow, and “the tree grew.” Rough product of common factors: inverter 0.98 × DC wiring/mismatch 0.96 × soiling 0.98 × temperature/other 0.92 × availability 0.98 ≈ 0.83—close to that 0.80 rule of thumb. Don’t stack fantasy 0.95s until your roof proves it.

Bifacial panel math (without overpromising)

Bifacial modules can make extra power from light hitting the rear. Manufacturers publish a bifaciality factor—often roughly 70–90%—meaning the rear is that fraction as effective as the front for the same irradiance.

Rear irradiance depends on ground albedo (grass ~0.2, light gravel/white roof higher, fresh snow higher still), height, tilt, and shade under the rack. A simplified planning estimate:

Extra fraction ≈ bifaciality × (rear irradiance ÷ front irradiance)

Example: bifaciality 0.80 and rear/front ≈ 0.10 → about 8% extra. On a 400 W front-side rating that’s ~432 W effective in that condition—not a permanent 432 W nameplate. Dull ground and low racks can land nearer 3–5%; 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.

Interactive solar math calculator

Use the tabs below for array energy, battery sizing, and appliance runtime. Everything runs locally in your browser.

Battery Ah, Wh, and 12V vs 24V vs 48V

Wh ≈ volts × amp-hours. A “100 Ah” battery is not a universal gas tank:

• 12 V lead-ish 100 Ah ≈ 12 × 100 = 1,200 Wh nameplate
• 12.8 V LiFePO₄ 100 Ah ≈ 1,280 Wh
• 51.2 V LiFePO₄ 100 Ah server rack ≈ 5,120 Wh (5.12 kWh)

Same 3,000 W load through a 92% efficient inverter: DC power ≈ 3,000 ÷ 0.92 ≈ 3,261 W. Current ≈ 3,261 ÷ V → about 272 A at 12 V, 136 A at 24 V, 68 A at 48 V. That’s why home solar grew up and moved to 48 V—wire size and lug temperatures prefer it.

Usable DoD: LiFePO₄ vs lead-acid

• LiFePO₄: many owners plan ~80–90% usable (leave a floor for longevity and BMS manners). 5.12 kWh × 0.90 = 4.61 kWh usable.
• Lead-acid / AGM: routinely plan ~50% DoD for lifespan. Same 5.12 kWh nameplate → ~2.56 kWh usable.

Comparing nameplates without DoD is how lead-acid “wins” on spreadsheet and loses on Tuesday night.

Inverter efficiency, surge, and 120/240V

Inverters waste a slice as heat—often ~90–97% 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.

Motors surge: a fridge that runs at 150 W may kick 3–7× for a second. Your inverter’s surge rating must clear that, and so must the battery’s discharge limit.

U.S. homes are split-phase 120/240 V. Power is still V × 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—see our off-grid, hybrid, and grid-tie inverter guides.

Solar → battery recharge time

Rough charge time (hours) ≈ battery Wh to replace ÷ (PV charge power × charge efficiency). Example: restore 80% of 5.12 kWh = 4,096 Wh from a 1,600 W effective PV charge at 95% → 4,096 ÷ (1,600 × 0.95) ≈ 2.7 hours of equivalent full sun. Weather stretches that into “maybe tomorrow.”

Worked example: standard refrigerator runtime

Assumptions (edit them for your sticker):

• Running power while the compressor is on: 150 W
• Duty cycle: 35% (compressor runs 35% of the day in a mild kitchen)
• Door-open / defrost fudge: 400 W × 0.4 h = 160 Wh/day
• Inverter efficiency: 90%
• Inverter idle: 30 W continuous → 30 × 24 = 720 Wh/day from the battery bus
• LiFePO₄ usable: 90% of nameplate

Compressor energy: 150 × 24 × 0.35 = 1,260 Wh/day AC. Plus 160 Wh fudge → 1,420 Wh/day AC.

Battery-side for the fridge path: 1,420 ÷ 0.90 ≈ 1,578 Wh. Add idle 720 Wh → ~2,298 Wh/day DC total for “fridge + sleepy inverter.”

• 5.12 kWh LiFePO₄ (usable 4.61 kWh): 4,608 ÷ 2,298 ≈ 2.0 days (~48 hours)
• 15.36 kWh LiFePO₄ (usable 13.82 kWh): 13,824 ÷ 2,298 ≈ 6.0 days (~144 hours)
• Same 5.12 kWh if it were lead at 50% DoD (2.56 kWh usable): ≈ 1.1 days

Open the door like it’s a TV, park the fridge in a hot garage, or skip the idle term and your “two days” becomes an awkward evening. Surge still needs an inverter that won’t fold when the compressor starts.

Whole-home sketch (2 days of autonomy)

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 ≈ 8.05 kWh AC/day.

At 92% inverter efficiency plus 0.72 kWh idle: DC ≈ 8.05 ÷ 0.92 + 0.72 ≈ 9.47 kWh/day. Two days ≈ 18.9 kWh usable → nameplate at 90% DoD ≈ 21.0 kWh (a 20.48 kWh bank is close; 25.6 kWh is more comfortable). Array to refill one day in summer at 4.5 PSH × 0.80 PR: 9.47 ÷ (4.5 × 0.80) ≈ 2.6 kW STC; winter at 3.0 PSH wants closer to 4.0 kW.

Breakers and wire (high level only)

Voltage drop ≈ 2 × length × current × ohms/ft (copper charts). Long low-voltage DC runs punish you; raising system voltage or shortening cable fixes more sins than buying “bigger hopes.” Overcurrent devices must match conductor ampacity and equipment ratings. Grounding, disconnects, rapid shutdown, and service interconnects are licensed-electrician territory—full stop.

Common mistakes

• Sizing strings to 25°C Voc and discovering January is colder than marketing.
• Confusing 1.25% with the 1.25× continuous-current factor (and ignoring the ~1.56 stack).
• Counting lead-acid and LiFePO₄ nameplates as equal usable energy.
• Using fridge nameplate watts all day instead of duty-cycle averages—or forgetting surge.
• Ignoring inverter idle on “tiny” overnight loads.
• Promising bifacial 20% gains on dark dirt two feet off the ground.
• Skipping a meter: {AMZ(“B000O3LUEI”,”measure twice”)} still beats explaining scorch marks to the inspector.

Safety disclaimer

This article is educational. Electrical codes, utility rules, and equipment manuals win every argument. Do not work in live panels. Have a licensed electrician handle service equipment, transfer switches, and anything that can backfeed the grid.

Related reading

Inverter deep dives: off-grid · hybrid · grid-tie. Gear notes on the solar equipment hub and our DIY install story. Shop EG4-class hardware via Signature Solar (affiliate) when you’re ready to match math to metal.

Prefer the short version? Catch solar and tech explainers on YouTube.

Pages of Wisdom — plain-English solar math.