# 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.

- Calculator id: `three-phase-power` · Category: Engineering & Automotive (`engineering`) · Tool name: `calculate_three_phase_power`
- Canonical page: https://tttkmbb.com/engineering/three-phase-power · This document: https://tttkmbb.com/engineering/three-phase-power.md · JSON definition: https://tttkmbb.com/engineering/three-phase-power.json

## Purpose

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.

**Use when:** 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).

## Input

| Parameter | Type | Unit | Required | Description |
| --- | --- | --- | --- | --- |
| `mode` | enum: power_from_current \| current_from_power |  | required | power_from_current needs current_a; current_from_power needs real_power_kw. |
| `line_voltage_v` | number | V | optional, default 400 | RMS line-to-line voltage (400 V Europe, 480 V North America, 415 V UK/Australia, 208 V US commercial). (> 0, max 1000000) |
| `current_a` | number | A | optional | RMS line current per conductor (power_from_current mode). (min 0, max 1000000) |
| `real_power_kw` | number | kW | optional | Real (active) power drawn by the load in kilowatts (current_from_power mode); for a motor use input power = shaft kW / efficiency. (> 0, max 10000000) |
| `power_factor` | number |  | optional, default 0.85 | cos φ of the load: 0.85 typical for loaded induction motors, 1.0 for resistive heaters. (> 0, max 1) |
| `connection` | enum: wye \| delta |  | optional, default "wye" | Winding connection; it changes only the per-phase values, not the total power. |

## Output

| Field | 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). |

## 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.

## Data Sources

- Wikipedia – Three-phase electric power — https://en.wikipedia.org/wiki/Three-phase_electric_power (reference, retrieved 2026-09-24)
- Wikipedia – AC power — https://en.wikipedia.org/wiki/AC_power (reference, retrieved 2026-09-24)

Data freshness: `static`. Deterministic formula with fixed constants; results never go stale. Inputs supplied by the caller determine the output.

## API

- `GET https://tttkmbb.com/api/v1/calculate/three-phase-power?mode=…`
- `POST https://tttkmbb.com/api/v1/calculate/three-phase-power` with JSON body `{"inputs": {…}}`
- Response: unified envelope (`success`, `request`, `result.values`, `result.units`, `sources`, `freshness`, `timestamp`, `next_actions`, `links`); see https://tttkmbb.com/docs/response-format.md
- Schema: https://tttkmbb.com/api/v1/calculators/three-phase-power · OpenAPI operationId `calculate_three_phase_power` in https://tttkmbb.com/openapi.json
- Authentication: none. Rate limit: fair use, see https://tttkmbb.com/docs/rate-limits.md.

## MCP

- Server: `https://tttkmbb.com/mcp` (Streamable HTTP, JSON-RPC 2.0, no auth)
- Tool:  `run_calculator` with `{"calculator_id": "three-phase-power", "inputs": {…}}`

## Example

- 400 V, 10 A, PF 0.85, wye: inputs `{"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: inputs `{"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
```

## Limitations

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). 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. All values are computed from the formula above; no measurement or live data is involved.

## 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

- [kVA, kW and Power Factor Calculator](https://tttkmbb.com/engineering/kva-kw-power-factor.md) — Complete the power triangle from any two power quantities.
- [Wire Voltage Drop Calculator](https://tttkmbb.com/engineering/wire-voltage-drop.md) — Voltage drop of the three-phase feeder at this current.
- [Electric Power Calculator](https://tttkmbb.com/physics/electric-power.md) — Single-phase and DC power P = V × I.