WiremanWireman · Formulas and conversions · 2023 NEC ·
Reference
Formulas and conversions
The everyday math of the trade, each with a worked example. To solve one, use the Ohm's law and power calculator.
Ohm's law and power
V is voltage in volts (some books write E or U), I is current in amps, R is resistance in ohms and P is power in watts.
| To find | From V and I | From I and R | From V and R | Using P |
|---|---|---|---|---|
| Voltage (V) | — | I × R | — | P ÷ I, or √(P × R) |
| Current (I) | — | — | V ÷ R | P ÷ V, or √(P ÷ R) |
| Resistance (R) | V ÷ I | — | — | V² ÷ P, or P ÷ I² |
| Power (P) | V × I | I² × R | V² ÷ R | — |
Worked example
A 1500 W heater on 120 V draws 1500 ÷ 120 = 12.5 A. Its resistance is 120² ÷ 1500 = 9.6 Ω. On 240 V the same element would draw 25 A and make 6000 W: power goes with the square of the voltage.
These hold exactly for DC and resistive loads (heaters, incandescent lamps). Motors, transformers and electronics also have power factor: use the AC formulas below.
Single- and three-phase power
| Find | Single-phase | Three-phase |
|---|---|---|
| Amps from kVA | kVA × 1000 ÷ V | kVA × 1000 ÷ (V × 1.732) |
| Amps from kW | kW × 1000 ÷ (V × PF) | kW × 1000 ÷ (V × 1.732 × PF) |
| kVA | V × I ÷ 1000 | V × I × 1.732 ÷ 1000 |
| kW | V × I × PF ÷ 1000 | V × I × 1.732 × PF ÷ 1000 |
- Three-phase V is line-to-line (208, 240, 480). 1.732 is √3.
- Power factor (PF) = kW ÷ kVA, between 0 and 1. Resistive loads are 1.0; motors run about 0.8 to 0.9 at full load and lower when lightly loaded.
- kVAR (reactive power) = √(kVA² − kW²). Capacitors supply kVAR to raise PF.
Worked examples
A 50 kW three-phase load at 480 V and 0.85 PF draws 50,000 ÷ (480 × 1.732 × 0.85) = 70.8 A.
A 75 kVA three-phase transformer at 208 V delivers 75,000 ÷ (208 × 1.732) = 208 A at full load.
A 4.5 kW, 240 V single-phase water heater element draws 4500 ÷ 240 = 18.75 A.
Horsepower and efficiency
1 hp = 746 W of output
Efficiency = output ÷ input
Input kW = hp × 0.746 ÷ efficiency
Worked example
A 10 hp motor at 90% efficiency takes 10 × 0.746 ÷ 0.90 = 8.29 kW in. At 480 V three-phase and 0.85 PF that's 8290 ÷ (480 × 1.732 × 0.85) ≈ 11.7 A.
For sizing motor conductors and protection, don't use this math or the nameplate: use the full-load current tables (430.6(A)(1)). The motor calculator does it for you.