Methodology

Every calculator on this site runs in your browser on one shared, tested formula library. This page lists the formulas, the defaults and where the numbers come from.

Electricity

• Energy: kWh = watts × hours ÷ 1,000.
• Cost: cost = kWh × price per kWh. Months are 30.42 days (365 ÷ 12).
• Default price: 18.2¢/kWh, the US residential average (EIA Electric Power Monthly, August 2026 (18.16¢/kWh US residential average)). Replace it with the rate on your bill.
• Price from a bill: all-in = bill ÷ kWh; energy-only = (bill − fixed charges) ÷ kWh.

EV charging

• Energy added = battery kWh × (end % − start %). Energy from the wall = energy added ÷ charging efficiency (default 90%).
• Range added = energy added × miles per kWh. Tesla presets are approximate usable capacities and efficiencies; check your own car.

Solar

• System size: kW = monthly kWh ÷ 30.42 ÷ peak sun hours ÷ derate (default 80%).
• Tilt: best tilt for a month = latitude − solar declination on the 15th; year-round ≈ latitude; seasonal rule ±15°.
• Declination: δ = 23.45° × sin(360/365 × (284 + day of year)) (Cooper, 1969). Sun position uses the standard spherical-astronomy equations with solar time; accuracy about ±1°.
• Off-grid battery: kWh = daily kWh × days of autonomy ÷ usable depth of discharge ÷ inverter efficiency.
• Charge controller: amps = array watts ÷ battery volts × 1.25.

Wind

• Power: P = ½ × air density × swept area × wind speed³ × Cp, with air density 1.225 kg/m³ at sea level and Cp capped at the Betz limit (16/27).
• Annual energy from an average wind speed assumes a Rayleigh distribution, for which the mean of v³ is 6/π × (mean v)³. Real turbines have cut-in and rated speeds, so treat the result as an upper estimate.

Backup power and conversions

• UPS VA = watts × (1 + headroom) ÷ power factor. Battery runtime = volts × Ah × count × usable fraction × inverter efficiency ÷ load.
• 1 kWh = 3,412.14 BTU; Wh = Ah × V; kW = A × V × PF ÷ 1,000 (× √3 for three phase).

A note on NREL

The US National Renewable Energy Laboratory (NREL) now operates as the National Laboratory of the Rockies (NLR) at nlr.gov. Studies published before the change are cited under the NREL name they carried; links point to their current nlr.gov addresses.

Testing

The formula library has automated unit tests with hand-checked worked examples, and every calculator is tested to render its default inputs without errors. If you find a result that looks wrong, tell us with the inputs you used.