Quick answer
Three-phase real power P = √3 × V_LL × I × power factor, and apparent power S = √3 × V_LL × I. At 400 V and 20 A with a power factor of 0.85, P = 11.78 kW, S = 13.86 kVA and Q = 7.30 kvar.
Enter line-to-line voltage, line current and power factor. The calculator returns real, apparent and reactive power.
Related tools: Wattage Calculator: Solve power, voltage or current for a DC or resistive load.
How to use the Three-Phase Power Calculator
- Enter line-to-line voltage (V) (above 0).
- Enter line current (A) (above 0).
- Enter power factor (between 0 and 1).
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Line-to-line voltage | A number, in V | > 0 |
| Line current | A number, in A | > 0 |
| Power factor | A number | > 0, ≤ 1 |
Formula and method
Formula
P = √3 × V_LL × I × pf; S = √3 × V_LL × I
IEEE-754 double precision; shown to the decimals indicated.
Balanced load.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Line-to-line voltage = 400; Line current = 20; Power factor = 0.85.
| Result | Value |
|---|---|
| Real power | 11.7779 kW |
| Apparent power | 13.8564 kVA |
| Reactive power | 7.2993 kvar |
Example 2
Inputs: Line-to-line voltage = 208; Line current = 35; Power factor = 0.9.
| Result | Value |
|---|---|
| Real power | 11.3484 kW |
| Apparent power | 12.6093 kVA |
| Reactive power | 5.4963 kvar |
Example 3
Inputs: Line-to-line voltage = 480; Line current = 10; Power factor = 1.
| Result | Value |
|---|---|
| Real power | 8.3138 kW |
| Apparent power | 8.3138 kVA |
| Reactive power | 0 kvar |
The first line is the headline result (real power). Below it the three-Phase Power Calculator lists apparent power and reactive power, which describe the same case from other angles. IEEE-754 double precision; shown to the decimals indicated.
The √3 factor
In a balanced three-phase system the line voltage is √3 times the phase voltage. So power is √3 × V_LL × I × pf. For 400 V and 20 A, S = 1.732 × 400 × 20 = 13,856 VA.
Balanced loads only
The formula assumes the three phases carry equal currents. For unbalanced loads calculate each phase and add. Reactive power Q = √(S² − P²) = 7.30 kvar.
How the result changes with line-to-line voltage
Holding every other input at the first worked example, this table changes only line-to-line voltage. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Line-to-line voltage | Real power | Apparent power | Reactive power |
|---|---|---|---|
| 200 | 5.889 kW | 6.9282 kVA | 3.6497 kvar |
| 400 | 11.7779 kW | 13.8564 kVA | 7.2993 kvar |
| 800 | 23.5559 kW | 27.7128 kVA | 14.5986 kvar |
| 1600 | 47.1118 kW | 55.4256 kVA | 29.1973 kvar |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Line-to-line voltage: entering "0" shows "Line-to-line voltage must be greater than 0." beside that field and no result.
- Power factor: entering "1.5" shows "Power factor must be at most 1." beside that field and no result.
Choosing between the Three-Phase Power Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Wire Size Calculator](/engineering/wire-size/) | current, one-way length and supply voltage | Smallest AWG for the voltage drop |
| [Voltage Drop Calculator](/engineering/voltage-drop-calculator/) | current, one-way length and wire gauge | Voltage drop |
| [Wattage Calculator](/engineering/wattage/) | Power | |
| [Ohm's Law Calculator](/engineering/ohm-s-law-calculator/) | Current | |
| [Power Converter](/converters/power-converter/) | value, from and to | Horsepower (mechanical) → Watt (W) |
Background: structural and wiring estimates
Structural and electrical results are only as good as their assumptions. Bending stress is the bending moment divided by the section modulus, and an allowable stress is the yield strength divided by a safety factor that depends on the governing design code and the type of load. For a single-phase or DC run the voltage drop uses the round-trip length: V = 2 × L × R per unit length × I.
Recommended limits, such as keeping branch-circuit voltage drop around 3%, differ between sources and code editions. These pages are estimates: follow the applicable code and a qualified engineer or electrician for real work.
Assumptions and limitations
- Unbalanced loads need per-phase calculation
Use results as engineering estimates and check them against the governing standards, safety factors and a qualified engineer's judgement before relying on them.
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for line-to-line voltage and power factor to confirm this.
Frequently asked questions
What is a good power factor?
A power factor above about 0.9 is considered good; the example's 0.85 means 15% of the apparent power is reactive.
Is voltage line-to-line or line-to-neutral?
Line-to-line, the voltage between two phases. For 400 V line-to-line, each phase to neutral is 400 ÷ √3 = 231 V.
How many amps for 15 kW?
About 25.5 A at 400 V and pf 0.85.
What does the Three-Phase Power Calculator calculate?
Real, apparent and reactive power of a balanced three-phase load. It returns Real power, Apparent power and Reactive power.
What formula does the Three-Phase Power Calculator use?
P = √3 × V_LL × I × pf; S = √3 × V_LL × I. Balanced load.
What do I need to enter in the three-Phase Power Calculator?
You enter Line-to-line voltage (V), Line current (A) and Power factor.
How is the result rounded or limited?
IEEE-754 double precision; shown to the decimals indicated. Unbalanced loads need per-phase calculation.
What is an example of a three-Phase Power result?
With line-to-line voltage 400, line current 20 and power factor 0.85, the real power is 11.7779 kW.
Can I rely on this calculator for a decision?
Use results as engineering estimates and check them against the governing standards, safety factors and a qualified engineer's judgement before relying on them. For this calculator in particular: Unbalanced loads need per-phase calculation.
Related calculators
- Wattage Calculator — Solve power, voltage or current for a DC or resistive load.
- Ohm's Law Calculator — Solve voltage, current or resistance.
- Power Converter — Convert watts, kilowatts, horsepower and BTU per hour.
- Transformer Turns Ratio Calculator — Secondary voltage from primary voltage and turns.
- Power-to-Weight Ratio Calculator — Power per unit weight of a vehicle.
- Power of 2 Calculator — Compute 2 raised to an integer power exactly.
Sources
- OpenStax, University Physics Volume 2 (Rice University): electricity, circuits and thermodynamics
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.