Three-Phase Power Calculator
Compute real, apparent, and reactive power in a balanced three-phase load.
What it does
A balanced three-phase circuit moves power through three conductors at once, and the arithmetic collapses into one clean formula: apparent power equals the square root of three times line-to-line voltage times line current.
Real power, the part that actually does work, is apparent power scaled by the power factor. The gap between them is reactive power, current that shuttles back and forth into magnetic fields and capacitors without ever turning a motor.
The defaults show the trio together. At 480 V and 100 A the load draws 83.1 kVA, a common utility service size. With a power factor of 0.9 the real power is 74.8 kW, and the missing 36.2 kVAR is what a capacitor bank would trim.
The power triangle keeps the three straight: kW and kVAR form the legs, kVA the hypotenuse, and the power factor is the cosine of the angle between them. That is why correcting power factor shrinks current without changing useful output.
The formulas assume a balanced, sinusoidal load. Unbalanced panels, harmonics, and single-phase taps need per-phase bookkeeping. For motors, transformers, and feeder sizing, this page covers the standard case.
How to use
- Enter the line-to-line voltage, 480 V for example.
- Enter the line current the meter shows.
- Enter the power factor as a decimal.
- Read real power in kW.
- Read apparent power in kVA for equipment sizing.
- Read reactive power in kVAR for correction planning.
Formula
- V
- Line-to-line RMS voltage in volts, like 208, 480, or 600.
- I
- Line current in amperes through each phase conductor.
- S
- Apparent power in volt-amperes; divide by 1000 for kVA.
- PF
- Power factor = cos(angle) = P / S, from 0 up to 1.
- Q
- Reactive power in VAR; the unused magnetic exchange.
Line-to-line voltage with line current is the industry convention, so 480 V feeds use those ratings directly whether the load is wye or delta. For a single-phase circuit the √3 disappears. At unity power factor kVAR is zero and kW equals kVA. The square root of three is about 1.732, which is why 480 V and 100 A multiply to 83.1 kVA rather than a rounder number.
Worked example
Example: 480 V, 100 A at 0.9 PF
Line voltage 480 V, line current 100 A, power factor 0.9 (defaults).
- Apparent power: 1.732 x 480 x 100 = 83,138 VA = 83.1 kVA.
- Real power: 83.1 x 0.9 = 74.8 kW.
- Reactive power: sqrt(83.1² - 74.8²) = 36.2 kVAR.
- A capacitor bank rated near 36 kVAR would bring the factor close to unity.
- The feeder still sizes on 83.1 kVA, not the 74.8 kW billed as work.
Reference table
| Voltage | Current | PF | kW / kVA / kVAR |
|---|---|---|---|
| 208 V | 30 A | 0.9 | 9.7 / 10.8 / 4.7 |
| 240 V | 50 A | 0.85 | 17.7 / 20.8 / 10.9 |
| 480 V | 100 A | 0.9 | 74.8 / 83.1 / 36.2 |
| 600 V | 200 A | 0.8 | 166.3 / 207.8 / 124.7 |
| 400 V | 63 A | 0.95 | 41.5 / 43.6 / 13.6 |
Limits
- Balanced loads only; unequal phases need per-phase analysis.
- Sinusoidal steady state; harmonics distort the simple products.
- Single power factor for the whole load, not per motor.
- Voltage is line-to-line by convention here, not phase voltage.
Common mistakes
- Using phase voltage and expecting the √3 result to still hold.
- Entering 90 instead of 0.9 for power factor.
- Sizing conductors from kW while kVA is the number that heats them.
- Forgetting the √3 factor and computing single-phase power.
- Treating low power factor as lost energy; it is circulating current, not consumed watts.
Try it yourself
Quick checks. Answers sit tucked under each question.
480 V, 100 A, power factor 0.9?
74.8 kW, 83.1 kVA, 36.2 kVAR.
240 V, 50 A, power factor 0.85?
17.7 kW, 20.8 kVA, 10.9 kVAR.
400 V, 63 A, power factor 0.95?
41.5 kW, 43.6 kVA, 13.6 kVAR.
Questions
What is power factor?
The ratio of real power to apparent power, equal to the cosine of the phase angle between voltage and current. A purely resistive load sits at 1.
Why does the formula use the square root of three?
Three phases share the load at 120 degree spacing, and the geometry of that arrangement leaves a factor of √3 between line quantities and the total power.
What is kVAR?
Reactive power: current that charges magnetic fields or capacitors but does no net work. It still occupies capacity in transformers and cables.
Should I use line or phase voltage?
This tool expects line-to-line voltage, the 208, 480, or 600 V on equipment nameplates. Phase voltage in a wye is line voltage divided by √3.
Why do utilities bill for low power factor?
Poor power factor forces the utility to supply more current for the same useful power, requiring larger equipment. Many rate schedules add a penalty below 0.9.
How do I fix a low power factor?
Add capacitor banks sized in kVAR near the load. The target is usually 0.95 to 0.98, chosen against the penalty and the cost of the capacitors.