The circuit and energy formulas behind the electrical calculators, each worked and checked against them. Keep units consistent: volts, amps, ohms and watts, or convert milliamps and kilohms first.
Formulas
| Quantity | Formula | Example |
|---|---|---|
| Ohm's law | V = I × R |
12 V across 4 Ω: 3 A |
| Electrical power | P = V × I = I² × R = V² / R |
12 V at 3 A: 36 W |
| Resistors in series | R = R₁ + R₂ + … |
100 + 220 + 330 = 650 Ω |
| Resistors in parallel | 1/R = 1/R₁ + 1/R₂ + … |
Two 100 Ω: 50 Ω; 100, 220 and 330 Ω: 56.9 Ω |
| Voltage divider | Vout = Vin × R₂ / (R₁ + R₂) |
9 V, 10 kΩ over 5 kΩ: 3.0 V |
| LED series resistor | R = (Vsupply − Vforward) / I |
5 V supply, 2 V LED, 20 mA: 150 Ω |
| Cable voltage drop (single phase) | VD = 2 × K × L × I / CM |
Copper (K = 12.9), 12 AWG (6,530 CM), 50 ft, 15 A: 2.96 V, 2.47% of 120 V |
| Energy cost | kWh = kW × hours, cost = kWh × rate |
1,500 W for 4 h a day over 30 days at $0.15: 180 kWh, $27.00 |
| Battery runtime | hours = capacity (mAh) × usable / load (mA) |
2,000 mAh, 80% usable, 100 mA: 16 hours |
| Solar payback | years = net cost / yearly savings |
$12,000 and $1,500 saved a year: 8 years |
Try them
The Ohm's Law Calculator and Electrical Power Calculator solve the first two rows from any two known values. The Resistor Calculator reads colour bands, the Voltage Divider Calculator and LED Resistor Calculator pick standard values, and the Voltage Drop Calculator and Wire Size Calculator size cables. For running costs use the Electricity Calculator, Battery Life Calculator and Solar Panel Payback Calculator.
Common mistakes
- Forgetting the return path. A cable's voltage drop counts the round trip, which is why the formula has the factor 2.
- Using the nominal resistor value for power. Check that the resistor's wattage rating exceeds
I² × R, with a safety margin of two or more. - Mixing mAh and Wh. Battery energy is capacity times voltage; two cells of the same mAh at different voltages store different energy.
- Treating these as safety advice. For mains wiring follow your local electrical code or ask a licensed electrician.