Three Phase Power Calculator
Calculate apparent, active, and reactive power in three-phase AC systems
Enter any three of the four values — line voltage (V), line current (A), active power (W), and power factor — to compute all remaining electrical quantities for a balanced three-phase system.
Three Phase Power Calculator
Calculate apparent, active, and reactive power in three-phase AC systems
Enter any 3 of the 4 fields to calculate all remaining quantities.
About the Three Phase Power Calculator
Three-phase alternating current (AC) power is the standard method of electricity generation, transmission, and distribution worldwide. Unlike single-phase power, which delivers energy in a single pulsating wave, three-phase power delivers energy in three overlapping sine waves separated by 120 degrees. This produces a smooth, constant power flow, allows motors to start and run more efficiently, and enables more economical use of conductors over long transmission distances.
The three fundamental quantities that characterise a three-phase system are apparent power S (measured in volt-amperes, VA), active power P (measured in watts, W), and reactive power Q (measured in volt-amperes reactive, VAR). Apparent power is the total rate at which energy is delivered to the load; active power is the portion that performs useful work such as heating, lighting, or driving a motor shaft; and reactive power is the energy that oscillates between the source and inductive or capacitive elements without doing net work over a full cycle.
The key formulas for a balanced three-phase system are S = √3 × V_L × I_L, P = S × cos(φ), and Q = S × sin(φ), where V_L is the line-to-line voltage, I_L is the line current, and φ is the phase angle between voltage and current. The power factor PF = cos(φ) = P/S quantifies how efficiently the supplied current is converted to useful work.
This calculator accepts any three of the four main inputs — line voltage, line current, active power, and power factor — and computes all remaining quantities. The results include apparent, active, and reactive power in both base units and kilounits, the power factor, and the phase angle in degrees. This makes the tool suitable for sizing electrical cables and switchgear, checking motor loads, calculating power factor correction requirements, and verifying utility billing data.
Three-phase systems are characterised by two connection types: wye (star) and delta. In a wye connection the phase voltage is V_L/√3 and the phase current equals the line current; in a delta connection the phase voltage equals the line voltage and the phase current is I_L/√3. For balanced loads, the three-phase power formulas using line quantities apply to either topology, which is why this calculator uses V_L and I_L directly. Unbalanced loads require per-phase analysis and are outside the scope of this tool.
Three Phase Power Examples
These examples show typical three-phase calculations for industrial and utility applications.
| System Parameters | Power Values | Notes |
|---|---|---|
| V = 400 V, I = 50 A, PF = 0.85 | S = 34 641 VA, P = 29 445 W, Q = 18 248 VAR | Standard European 400 V three-phase supply with a typical industrial load power factor of 0.85. |
| V = 11 000 V, I = 100 A, PF = 0.90 | S = 1 905 255 VA (1.9 MVA), P = 1 714 730 W, Q = 827 567 VAR | Medium-voltage feeder at 11 kV. Apparent power exceeds 1.9 MVA; active power is 1.71 MW. |
| V = 480 V, P = 75 000 W, PF = 0.95 | I = 94.9 A, S = 78 948 VA, Q = 24 641 VAR | A 75 kW motor on a 480 V US industrial supply. Current draw and reactive power are calculated from voltage and active power. |
| V = 230 V, I = 10 A, P = 3 450 W | S = 3 984 VA, PF = 0.866, Q = 1 992 VAR | Low-voltage three-phase load where the power factor is derived from the measured active power and apparent power. |
How to use the three phase power calculator
- Enter the line voltage (V_L) in volts — this is the voltage measured between any two line conductors in a three-phase system.
- Enter the line current (I_L) in amperes, the active power (P) in watts, and/or the power factor (cos φ, between 0 and 1).
- Provide at least three of the four inputs; the calculator will determine the missing quantity and compute apparent power S = √3 × V × I, reactive power Q = √(S² − P²), and the phase angle φ.
- Click Calculate to display all results. Use the preset buttons to load common industrial scenarios.
- Click Reset to clear all inputs and start a new calculation.
Three Phase Power FAQ
What is the formula for three-phase apparent power?
For a balanced three-phase system, apparent power S = √3 × V_L × I_L, where V_L is the line-to-line voltage and I_L is the line current. This formula applies to both star (wye) and delta connections because the factor √3 accounts for the phase relationship. Apparent power is measured in volt-amperes (VA) and represents the total power drawn from the supply regardless of power factor.
What is the difference between apparent, active, and reactive power?
Apparent power S (VA) is the total power supplied by the source. Active power P (W) is the real power that does useful work — heating, mechanical output, light. Reactive power Q (VAR) is the power stored and released by inductors and capacitors every cycle without doing net work. They are related by S² = P² + Q². The power factor PF = P/S indicates how efficiently the apparent power is converted to active work.
What is power factor and why does it matter?
Power factor (cos φ) is the ratio of active power to apparent power, ranging from 0 to 1. A power factor of 1 means all the supplied current does useful work; a lower power factor means more current is drawn from the supply for the same useful output, increasing cable and transformer losses. Industrial customers often pay a power factor penalty if their PF falls below 0.9 or 0.95, so power factor correction capacitors are added to improve it.
What is the difference between wye and delta connections?
In a wye (star) connection, each phase is connected between a line and a neutral point. The phase voltage equals V_L / √3 and the phase current equals the line current. In a delta connection, each phase is connected between two lines. The phase voltage equals V_L and the phase current equals I_L / √3. For balanced loads, both connections produce the same three-phase power, so this calculator uses line quantities (V_L, I_L) and applies correctly to either topology.
How do I calculate three-phase current from power and voltage?
Rearranging S = √3 × V × I gives I = S / (√3 × V) = P / (√3 × V × PF). For example, a 30 kW load on a 400 V supply at PF = 0.85 draws I = 30 000 / (1.732 × 400 × 0.85) ≈ 51 A. This calculator automates that rearrangement when you provide voltage, active power, and power factor.