Power Calculator
Calculate electrical power. Convert watts to amps, amps to watts, and volts to watts for DC, single-phase, and three-phase AC circuits.
Enter any two of Voltage, Current, or Power. For AC, provide power factor.
P = V × I × PF
How It Works
- 1
Select phase and solve-for
Choose DC, single-phase AC, or three-phase AC. Then pick which value you want calculated: watts, volts, or amps.
- 2
Enter the two known values and (for AC) power factor
Type the known voltage, current, or power. On AC circuits enter power factor between 0 and 1. Leave it at 1 for resistive loads.
- 3
Read the result and the formula used
The calculator shows the computed value and the exact formula, whether P = V × I for DC or P = √3 × V × I × PF for three-phase.
Power, Watts, Volts, and Amps: What the Utility Actually Sees
A 15-amp household circuit at 120 volts delivers 1,800 watts, and if you plug in an old induction motor the utility still charges you as if you're pulling more. That gap is power factor. On a DC circuit or a purely resistive AC load such as a heater or an incandescent bulb, power is simply P = V × I. On AC circuits with motors, fluorescent ballasts, or switching power supplies, voltage and current fall out of phase. Real power (watts) is what does actual work. Apparent power (volt-amperes) is what the wires and transformers have to carry. Reactive power (VAR) oscillates back and forth without doing useful work, but it still causes I²R losses in the distribution system. Power factor, cos(φ), is the ratio of real to apparent power. Induction motors at rated load typically sit between 0.7 and 0.9. Commercial customers are penalized when their average PF drops too low, which is why power-factor correction capacitors are standard in industrial installations. Three-phase distribution uses the formula P = √3 × V_LL × I_L × cos(φ), where V_LL is the line-to-line voltage and I_L is the line current. The √3 factor comes from the geometry of three voltages spaced 120 degrees apart: V_LL = √3 × V_LN. Common three-phase voltages include 208 V, 240 V, and 480 V line-to-line in North America, and 400 V in most of Europe. The first commercial three-phase transmission ran 400 horsepower over 15 kilometers at 9.5 kV in 1893, and every industrial feeder since has used the same math.
Common pitfalls
Using the single-phase formula on a three-phase circuit. P = V x I works on DC and single-phase AC only. Three-phase balanced systems need the √3 (≈1.732) factor: P = √3 x V_LL x I_L x PF. Drop the √3 and a motor on 480 V 3-phase reads 42% low.
Assuming PF = 1 on inductive loads. Induction motors at full load typically sit between 0.8 and 0.9 PF; at light load PF can fall below 0.6. A 10 kW load at PF 0.7 pulls 14.3 kVA, which is what determines wire gauge, breaker size, and utility demand charges.
Confusing line-to-line and line-to-neutral voltages. In a 208Y/120 V or 480Y/277 V system, V_LL = √3 x V_LN. Plugging 120 V into the three-phase formula for a 208 V circuit gives an answer 42% too low.
Using instantaneous or peak values instead of RMS for AC calculations. V_peak = √2 x V_rms (≈1.414 x). North American 120 V RMS means a 170 V peak and 340 V peak-to-peak. All P = V x I math assumes RMS.
Frequently Asked Questions
How do I convert watts to amps?
For DC or single-phase AC: I = P / (V × PF). Example: a 1200W appliance on a 120V circuit with PF=1 draws 10A. For three-phase AC: I = P / (√3 × V × PF). Power factor defaults to 1 (resistive load); reduce it for motors (~0.8–0.9) or inductive loads.
How do I convert amps to watts?
For DC or single-phase AC: P = V × I × PF. A 10A draw at 120V with PF=1 is 1200W. For three-phase: P = √3 × V_LL × I_L × PF, where V_LL is line-to-line voltage and I_L is line current.
What is power factor and why does it matter?
Power factor (PF = cos φ) is the ratio of real power to apparent power in an AC circuit. PF = 1 for purely resistive loads (heaters, incandescent bulbs). PF < 1 for motors, transformers, and other inductive loads. Utilities bill commercial customers based on real power but size conductors based on apparent power, so low PF costs money in oversized wiring.
Why does three-phase use the √3 factor?
Three-phase power is delivered through three conductors each 120° out of phase. When computing total power from line-to-line voltage (V_LL) and line current (I_L), the balanced three-phase formula P = √3 × V_LL × I_L × PF captures the total real power across all three phases — equivalent to 3 × V_LN × I_L × PF for line-to-neutral voltage.
Can I calculate kVA from watts?
Apparent power in kVA equals real power divided by power factor, then divided by 1000. For 10 kW at PF = 0.8, apparent power is 12.5 kVA. This tool calculates real power (watts); for kVA, divide watts by PF and by 1000.
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