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Three-Phase Power Calculator

Computes real, apparent and reactive power of a balanced three-phase load from line voltage, line current and power factor, or the line current needed for a given real power, and reports the phase voltage and phase current for wye (star) or delta connection.

Modepower_from_current needs current_a; current_from_power needs real_power_kw. Line-to-line voltage (V) (optional)RMS line-to-line voltage (400 V Europe, 480 V North America, 415 V UK/Australia, 208 V US commercial). Line current (A) (optional)RMS line current per conductor (power_from_current mode). Real power (kW) (optional)Real (active) power drawn by the load in kilowatts (current_from_power mode); for a motor use input power = shaft kW / efficiency. Power factor (optional)cos φ of the load: 0.85 typical for loaded induction motors, 1.0 for resistive heaters. Connection (optional)Winding connection; it changes only the per-phase values, not the total power.

When to use

You need the power drawn by a three-phase motor, heater or feeder from its current, the full-load current for a given kW, or the per-phase voltage and current for a wye or delta winding.

Do not use when: The load is unbalanced (compute each phase separately), single-phase (use kva-kw-power-factor or electric-power), or you only know kVA and power factor without a voltage (use kva-kw-power-factor).

Formula

apparent_power_kva = √3 × line_voltage_v × current_a / 1000; real_power_kw = apparent_power_kva × power_factor; reactive_power_kvar = √(S² − P²); current_a = real_power_kw × 1000 / (√3 × line_voltage_v × power_factor); wye: phase_voltage_v = line_voltage_v / √3, phase_current_a = current_a; delta: phase_voltage_v = line_voltage_v, phase_current_a = current_a / √3; power_per_phase_kw = real_power_kw / 3

Balanced sinusoidal three-phase system: the √3 relations hold for both wye and delta when line quantities are used, so total power does not depend on the connection. Motor nameplate kW is shaft output; divide by efficiency to obtain the electrical input power before computing current.

Inputs

Parameter	Type	Unit	Required	Description
`mode`	enum: power_from_current \| current_from_power		yes	power_from_current needs current_a; current_from_power needs real_power_kw.
`line_voltage_v`	number	V	default 400	RMS line-to-line voltage (400 V Europe, 480 V North America, 415 V UK/Australia, 208 V US commercial). Range: > 0, ≤ 1000000
`current_a`	number	A	no	RMS line current per conductor (power_from_current mode). Range: ≥ 0, ≤ 1000000
`real_power_kw`	number	kW	no	Real (active) power drawn by the load in kilowatts (current_from_power mode); for a motor use input power = shaft kW / efficiency. Range: > 0, ≤ 10000000
`power_factor`	number		default 0.85	cos φ of the load: 0.85 typical for loaded induction motors, 1.0 for resistive heaters. Range: > 0, ≤ 1
`connection`	enum: wye \| delta		default wye	Winding connection; it changes only the per-phase values, not the total power.

Outputs

Output	Type	Unit	Description
`real_power_kw`	number	kW	P = √3 × V_L × I_L × PF / 1000.
`apparent_power_kva`	number	kVA	S = √3 × V_L × I_L / 1000.
`reactive_power_kvar`	number	kVAR	Q = √(S² − P²).
`current_a`	number	A	I_L = P × 1000 / (√3 × V_L × PF), or the given current.
`phase_voltage_v`	number	V	Voltage across one winding: V_L / √3 for wye, V_L for delta.
`phase_current_a`	number	A	Current through one winding: I_L for wye, I_L / √3 for delta.
`power_per_phase_kw`	number	kW	P / 3 = V_phase × I_phase × PF / 1000.
`phase_angle_degrees`	number	°	arccos(power_factor).

Example

400 V, 10 A, PF 0.85, wye: {"mode":"power_from_current","line_voltage_v":400,"current_a":10,"power_factor":0.85,"connection":"wye"} → {"real_power_kw":5.889,"apparent_power_kva":6.928,"reactive_power_kvar":3.65,"current_a":10,"phase_voltage_v":230.94,"phase_current_a":10,"power_per_phase_kw":1.963}

15 kW at 400 V, PF 0.85, delta: {"mode":"current_from_power","line_voltage_v":400,"real_power_kw":15,"power_factor":0.85,"connection":"delta"} → {"current_a":25.471,"apparent_power_kva":17.647,"reactive_power_kvar":9.296,"phase_voltage_v":400,"phase_current_a":14.706}

GET https://tttkmbb.com/api/v1/calculate/three-phase-power?mode=power_from_current&line_voltage_v=400&current_a=10&power_factor=0.85&connection=wye

Machine access

API: GET https://tttkmbb.com/api/v1/calculate/three-phase-power (query parameters) or POST with a JSON body {"inputs": {...}}
Schema: https://tttkmbb.com/api/v1/calculators/three-phase-power · Markdown: https://tttkmbb.com/engineering/three-phase-power.md · JSON definition: https://tttkmbb.com/engineering/three-phase-power.json
MCP: server https://tttkmbb.com/mcp, tool run_calculator with calculator_id="three-phase-power"
OpenAPI operationId: calculate_three_phase_power
Freshness: static. Authentication: none. Rate limit: fair use (see rate limits).

Sources

Wikipedia – Three-phase electric power (reference)
Wikipedia – AC power (reference)

FAQ

Why does the connection not change the power?

With line-to-line voltage and line current the power is √3 × V_L × I_L × PF in both cases; wye and delta only differ in how that splits into winding voltage and winding current.

Is the voltage line-to-line or line-to-neutral?

Enter the line-to-line (phase-to-phase) voltage, e.g. 400 V in a 230/400 V system; the calculator reports the 230 V line-to-neutral value as the wye phase voltage.

How do I get a motor's current from its nameplate kW?

Nameplate kW is mechanical output; use real_power_kw = kW / efficiency (e.g. 15 / 0.9 = 16.7 kW) with the nameplate power factor for a realistic full-load current.

Related calculators

kVA, kW and Power Factor Calculator — Complete the power triangle from any two power quantities.
Wire Voltage Drop Calculator — Voltage drop of the three-phase feeder at this current.
Electric Power Calculator — Single-phase and DC power P = V × I.