This page documents every formula and constant the calculator uses. It exists so you can reproduce the result by hand, check it against another tool, or tell us we have got something wrong.
1. Where the sunlight data comes from
Irradiance is taken from the NASA POWER project — specifically the monthly
climatology of ALLSKY_SFC_SW_DWN, all-sky surface shortwave downward irradiance, for the Renewable Energy
community, in kWh/m²/day. Air temperature comes from T2M in the same request.
POWER derives these from satellite observation and reanalysis, and the climatology values are multi-year averages. That matters: they describe a typical year, not next year. A single year will land above or below them.
We chose POWER over the alternatives deliberately. It covers the entire globe, needs no API key and no billing account, and works equally well in Quetta, Lagos and Lahore — unlike roof-level services that cover a short list of wealthy countries. The trade-off is that POWER does not see your individual roof planes, which is why the calculator asks you for the mounting and the facing instead of inferring them.
If POWER cannot be reached, the calculator falls back to a clear-sky approximation computed from your latitude and the day of year, with a fixed clearness index of 0.52. Results from the fallback are labelled in red. Do not rely on them for a purchase decision.
2. Tilt and orientation
POWER reports irradiance on a horizontal surface. Real panels are tilted, which changes how much they receive. A full transposition model (Perez, Hay-Davies) needs hourly direct and diffuse components; the calculator instead applies an annual plane-of-array factor by latitude band:
| |Latitude| | Gain at optimal tilt |
|---|---|
| 0–10° | 1.02 |
| 10–20° | 1.05 |
| 20–30° | 1.09 |
| 30–40° | 1.14 |
| 40–50° | 1.20 |
| 50–60° | 1.26 |
| above 60° | 1.30 |
Flush mounting on an existing pitched roof receives 55% of that gain. Panels laid flat receive none — the factor is
1.00. Optimal tilt is reported as min(40°, 0.87 × |latitude| + 3°).
Facing is applied as a multiplier, interpolated between: 0° off the equator-facing direction = 1.00, 45° = 0.955, 90° (due east or west) = 0.85, 180° = 0.60.
This is a simplification and we say so plainly. It is accurate enough to choose between a 9 kWp and a 10 kWp array; it is not a substitute for a shading survey or a full hourly simulation.
3. The yield model
Each month is computed separately and multiplied by its length, then summed for the annual figure.
Temperature derate is handled on its own rather than being folded into the system efficiency, so the
two cannot double-count. Cell temperature is approximated as air temperature plus 25 K at full sun, and the derate
is 1 − 0.004 × (cell temperature − 25), floored at 0.6. The 0.4 %/K figure is typical of
modern crystalline silicon.
System efficiency (default 85%) covers inverter conversion, DC and AC wiring, mismatch and availability. Soiling (default 4%) and shading (default 3%) are separate so you can set them from what you actually see on your roof.
4. Array sizing
Panel count is that figure divided by the chosen panel wattage and rounded up, which is why the reported offset usually lands slightly above your target. The final array size is recomputed from the whole-panel count, and all downstream numbers use the recomputed figure rather than the fractional one.
Roof area assumes the panel's physical area for the wattage chosen, multiplied by 1.12 for a pitched roof or 1.85 for a flat roof, where row spacing is needed to prevent inter-row shading.
5. Inverter sizing
The result is rounded up to the next real product rating from a standard ladder (1, 1.5, 2, 2.5, 3, 3.6, 4, 5, 6, 8, 10, 12, 15, 20, 25, 30, 40, 50, 60, 75, 100 kW). The calculator reports which of the two constraints decided the answer, because when backup drives it the resulting DC/AC ratio can fall below 1 and that looks like an error when it is not.
6. Battery sizing
The square root of round-trip efficiency charges roughly half the loss to the discharge leg, which is the convention for sizing against a discharge requirement. Day fraction is 0.25 for essential backup and 0.60 for evening shifting.
| Chemistry | Depth of discharge | Round-trip | Continuous C-rate | Nominal voltage |
|---|---|---|---|---|
| Lithium LFP | 0.90 | 0.94 | 0.5C | 51.2 V |
| Lithium NMC | 0.85 | 0.93 | 0.5C | 51.2 V |
| Sealed lead-acid | 0.50 | 0.82 | 0.2C | 48 V |
| Flooded lead-acid | 0.50 | 0.80 | 0.1C | 48 V |
Amp-hours are nameplate kWh × 1000 ÷ nominal voltage. The calculator then checks that
nameplate kWh × C-rate is at least your essential load, and warns if it is not — a bank can hold plenty
of energy and still be unable to deliver it fast enough.
7. Economics
Year-one saving splits generation between self-consumption, valued at your import tariff, and export, valued at the export rate:
Self-consumption is capped at your actual consumption — you cannot save more than you spend.
The 25-year model applies tariff escalation compounding annually and panel degradation compounding annually:
Payback is the year the cumulative saving crosses the installed cost, interpolated within the year. Two lifetime figures are reported: a nominal sum, and a present value discounted at a rate you set (default 10%). Use the discounted one when comparing against other uses of the money. The nominal figure looks enormous purely because compounding tariff escalation over 25 years makes everything look enormous.
8. What this model does not do
- It does not simulate hour by hour, so it cannot model your actual load profile against your actual generation curve. Self-consumption is an input you set, not something it derives.
- It does not know your tariff slabs. If your rate steps up with consumption, solar that cuts your top slab is worth more per unit than the flat tariff suggests, and the calculator will understate your saving.
- It does not model subsidies, tax credits, feed-in contracts, or capital financing.
- It does not see your roof. Shade, obstructions, structural capacity and usable area are yours to assess.
- It does not do string design, cable sizing, protection coordination or earthing. Those need a qualified engineer.
9. Default cost and tariff figures
The regional defaults in the currency selector are rough order-of-magnitude starting points so the form is not empty. They are not researched quotes, they go out of date, and they vary enormously within a single country. Replace them. Take the tariff from your own bill and the installed cost from a written quote. Every economic number the calculator produces is only as good as those two inputs.
10. Corrections
If you think a constant is wrong or a formula is misapplied, we would genuinely like to know. The contact page explains how to reach us.