Sizing a solar array looks intimidating until you notice it’s three short multiplications in each direction — one from your bill to a kilowatt target, one from your roof to a panel count, and a sanity check that the two meet in the middle. Here is every step with real numbers.

kW vs kWh — get the units right once

kW (kilowatts) is the system’s size: nameplate power under full sun, the sum of panel ratings. kWh (kilowatt-hours) is what it makes: energy over time, the unit your bill charges for. The translation between them is the sun your location gets — which is why identical 8 kW systems produce ~50% more per year in Phoenix than in Cleveland.

A panel’s watts are measured at Standard Test Conditions (1,000 W/m², 25 °C cell temperature). Real roofs are dirtier, hotter and less perfectly aimed — the difference between nameplate and reality is the loss stack, coming in a moment.

Direction one: bill → kW target

Start from what you use. EIA puts the average US home near 10,500 kWh/year; your bill’s annual total is the honest version.

kW needed = annual kWh ÷ (365 × PSH × orientation × performance)

For 10,500 kWh/yr at 5.0 PSH, ideal orientation (1.00) and 14% combined losses (0.86 factor):

10,500 ÷ (365 × 5.0 × 1.00 × 0.86) = 10,500 ÷ 1,570 ≈ 6.7 kW

At 430 W/panel that’s 16 panels ≈ 6.9 kW. In Seattle (3.9 PSH) the same bill needs ~8.6 kW; in Phoenix (6.4) just ~5.2 kW. Same usage, 65% more hardware — geography is the multiplier.

Two offsets worth knowing: if your utility pays below-retail for exports, sizing to 100% of usage isn’t automatically right (oversized production sells cheap — the ROI guide covers the tariff effect); and if you’re adding an EV or heat pump soon, size for the load you’ll have, not the one you had.

Direction two: roof → panel count

Physical fit is arithmetic too. A modern residential module runs ~2 m² (21–22 sq ft) for 400–450 W at ~21% efficiency. Panel footprint scales with wattage — a 550 W commercial module is a bigger object, roughly 2.6 m².

panels that fit = floor( usable roof area ÷ area per panel )

A 900 sq ft roof plane at 75% usable coverage (fire setbacks, vents, the chimney shadow — see the shade guide) gives 675 sq ft ÷ ~22 sq ft ≈ 30 panels ≈ 12.9 kW at 430 W. That’s a big array; most roofs fit less once you restrict to the good-orientation planes. The calculator’s roof-area mode does this division for you, and the coverage field is where honest shade goes.

The loss stack — why 14% and not 15%

Industry convention (NREL PVWatts) calls total system losses ~14%. It’s not one loss — it’s a product of several, and the order matters to the math even if it doesn’t to the answer:

Stage	Typical	What it covers
Inverter & DC→AC conversion	2–4%	conversion efficiency ~96–98%
Temperature above 25 °C	3–8%	hot cells lose ~0.3–0.4%/°C
Soiling, dust, snow	1–4%	film, pollen, ash, snow cover
Wiring, diodes, connections	1–3%	resistance across runs and junctions
Shading, mismatch, downtime	0–10%	site-specific — the wildcard

Multiply the complements: 0.97 × 0.95 × 0.98 × 0.98 × 0.97 ≈ 0.859 → ~14.1% combined. Adding the percentages instead gives 15% — close here only because each factor is small; at bigger individual losses the gap widens fast (itemize 10% shade and watch the math on the calculator). Each loss always eats the surviving fraction — that’s the compounding the itemized view shows.

Orientation and tilt

Not every roof plane earns the same sun. The calculator’s factor presets, verified against the standard azimuth/tilt derates:

Layout	Factor	Note
Toward the equator at ~latitude tilt	1.00	the reference
SE/SW or tilt off ~15°	~0.95	minor yield cost, better morning/evening shape
Flat or ≤10° tilt	~0.90	loses some winter; gains some summer
Due east or west	~0.84	~15% haircut — often still worthwhile
Away from the equator	~0.70	rarely worth it without a reason

In the southern hemisphere the directions mirror (north is good, south is bad) — the factors are identical.

Sanity check: DC:AC ratio

Proposals quote both a DC array size (sum of panel watts — what this site means by system kW) and an AC inverter rating. A ratio around 1.1–1.4 is normal: panels rarely hit nameplate, so a bit of extra array against a smaller inverter is free capacity. Very high ratios (>1.4) mean midday clipping in good sun — not fatal, just a known trade; very low (<1.0) wastes inverter you’re paying for.

Putting it together — worked example

Household uses 11,800 kWh/yr in New Jersey (~4.4 PSH), mostly west-facing roof (~0.84), 14% losses:

• kW target: 11,800 ÷ (365 × 4.4 × 0.84 × 0.86) ≈ 10.2 kW → 24 × 430 W panels (10.3 kW)
• Year-1 output: 10.3 × 4.4 × 0.84 × 0.86 × 365 ≈ 11,970 kWh — just over the usage mark
• Roof check: 24 × ~22 sq ft ≈ 530 sq ft of panels — needs ~700 sq ft usable west roof

That ~10 kW case is exactly the shape of real residential quotes in the Northeast — and you can reproduce it in the calculator in under a minute to test how the payback moves with every assumption.

Frequently asked questions

Should I size my system to my roof or to my usage?

To your usage, with your roof as the constraint — not the target. Covering ~100% of annual consumption is the economic sweet spot under net metering; oversizing earns reduced export rates in most territories, and undersizing is fine but leaves bill on the table. Run the usage formula, then check it physically fits; if it doesn't, a smaller well-priced system still pays back.

Is a bigger inverter or more panels better?

They're not alternatives — the DC:AC ratio is a design choice, typically 1.1–1.4. Oversizing the panel array relative to the inverter (say 8 kW of panels on a 6.5 kW inverter) is normal and cheap: the array rarely hits nameplate anyway, and clipping the rare peak costs less than a bigger inverter does.

How much roof does a 10 kW system need?

About 23 panels at 430 W ≈ 47 m² (~510 sq ft) of panel footprint — call it 550–650 sq ft of usable roof once setbacks and gaps are included. Enter your roof in the calculator's roof-area mode for the fitted count on your numbers.

Why does my proposal show more kWh than the formula gives?

Check its assumed PSH and losses first — optimistic sun hours and a single-digit loss figure will happily inflate output 15–30%. Then check degradation year numbering: proposals sometimes quote year-1 AC output while marketing materials imply it's the 25-year average. Our peak sun hours guide shows the honest regional ranges.

Do I need batteries for this math?

No — this is generation sizing, which stands alone. Batteries change when your production offsets usage (and its effective value under non-retail tariffs), not how much you make. Size the array first; storage is a separate economics question.