Three-Phase Power Calculator
Real, apparent and reactive power from voltage, current and power factor. With the formula, a worked example and typical values.
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Estimate only. Not engineering or safety advice. Check the result against the applicable standard and the equipment data, and have a competent engineer review it before it is relied on. Terms of use.
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About this calculator
This page calculates real power, apparent power and reactive power from line voltage, line current and power factor. Change any value or its unit and the result updates. The steps below show the working for the default values, so you can check each line against your own method.
Limits of this calculator
Q is a magnitude; lagging or leading is not distinguished.
Cross-check: 6 reference cases, calculated from textbook formulas coded separately from the engine by the same author, agree with this calculator. This is not an independent review.
Verification status: Engineering reference
Engineering reference. Formula and method documented and tested against separately coded reference calculations. Not yet Verified: the evidence listed on this page is still needed.
What this calculator checks
- The arithmetic of the published formula for the values you entered, in the units shown.
What remains unverified
- That the inputs suit your application. Take ratings, resistances and constants from the manufacturer data sheet or project specification.
Verification register entry
| Calculation author | Rahul Sharma (author) |
|---|---|
| Technical review | No independent technical review has been carried out |
| Individual professional approval | Not recorded |
| Formula reference | not recorded |
| Standard and edition | Not applicable: Textbook power and energy identity (single-phase, three-phase, power factor, per-unit); no governing standard |
| Standard review state | Not applicable |
| Scope-screening note | not recorded |
| Cross-check test cases | 6 reference vectors (tests/reference_vectors.json) |
| Review date | not recorded |
| Next review date | not recorded |
| Status | Engineering reference |
Needed before this calculator can be marked Verified: reviewer name, qualification and review date; exact formula reference; formula source (textbook or standard); next review date.
Formula
Worked example
| Input | Value |
|---|---|
| Line voltage (L-L) | 400 V |
| Line current | 100 A |
| Power factor | 0.9 |
- S = √3 × 400 × 100 = 69.282 kVA
- P = S × pf = 62.354 kW
- Q = S × sin φ = 30.199 kVAR
Assumptions
- Balanced three-phase load
- V is line-to-line RMS
Q is a magnitude; lagging or leading is not distinguished.
Inputs and results
| Input | Unit | Allowed or shown | Note |
|---|---|---|---|
| Line voltage (L-L) | V | greater than 0 V | |
| Line current | A | greater than 0 A | |
| Power factor | (number) | greater than 0, up to 1 | Rough starting point only. Resistive heating and incandescent loads are 1.0; a fully loaded induction motor is typically 0.8 to 0.88 and falls sharply when lightly loaded; discharge lighting depends on its ballast or driver. For real work use the nameplate or a measured value. |
| Result | Unit | Allowed or shown | Note |
|---|---|---|---|
| Real power | kW | Shown to 3 decimal places | |
| Apparent power | kVA | Shown to 3 decimal places | |
| Reactive power | kVAR | Shown to 3 decimal places |
How it is calculated
Each input is converted to the base unit of its quantity, the formula above is applied in the order shown in the worked example, and each result is shown in the unit you choose. Results are held at full precision and rounded only for display, except where a step selects a standard size, as the worked example shows. A value outside its allowed range is refused with a message instead of giving a result.
How the result changes with line voltage (l-l)
| Line voltage (L-L) (V) | Real power (kW) | Apparent power (kVA) | Reactive power (kVAR) |
|---|---|---|---|
| 40 | 6.235 | 6.928 | 3.02 |
| 100 | 15.588 | 17.321 | 7.55 |
| 200 | 31.177 | 34.641 | 15.1 |
| 400 | 62.354 | 69.282 | 30.199 |
| 800 | 124.708 | 138.564 | 60.399 |
| 1,600 | 249.415 | 277.128 | 120.797 |
| 4,000 | 623.538 | 692.82 | 301.993 |
Other inputs are the same as in the worked example above.
Standards and further reading
These are textbook relationships (Ohm's law, series and parallel networks, AC phasors, three-phase quantities). No standard sets the method; standards apply when the result feeds a design, for example cable or protection selection.
Frequently asked questions
What do I need to enter?
Enter line voltage (L-L), line current and power factor. Change the unit of a value with its selector and the result stays the same.
What does this calculator assume?
Balanced three-phase load. V is line-to-line RMS.
Which calculators should I use next?
Common next steps are Amps to kW and Power Factor Correction. The related links at the bottom of this page open them.
How accurate are the results?
Every figure comes from the same tested engine as the Elecmetric calculators and is meant for estimating. 6 reference cases, calculated from textbook formulas coded separately from the engine by the same author, agree with this calculator. This is not an independent review. Check design values against the standard and the equipment data you work to.
Formula guides and reference
Longer explanations with worked examples and tables, written for the same topic.
- Three-Phase Power Formulas: Three-phase power formulas for kW, kVA, kVAR and line current, star and delta relations
- Power Factor and the Power Triangle: Power factor formulas: kW, kVA and kVAR from the power triangle, capacitor kVAR to raise power factor
- Two-Wattmeter Method Formulas: Two-wattmeter method formulas: the total power of a three-phase load from two readings, the reactive power
More Electrical Fundamentals calculatorsAll engineering calculatorsThree-Phase Power in Elecmetric