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Physics

Three-Phase Power Calculator

P = √3 × V × I × pf. Free online Three-Phase Power Calculator. Calculate three-phase power online — fast, accurate, mobile-friendly, no signup needed.

Power (W)
6,469.209766

Derivation

  1. ├── 01GivenV = 415, I = 10, pf = 0.9
  2. ├── 02Formula√(3) × t × a × n
  3. └── 03Compute Power (W)6,469.209766
Did you know?

Exponent notation aⁿ was coined by Descartes in 1637 — three centuries after Indian and Arab mathematicians worked with the concept in words.

§01What is

Understanding the Three-Phase Power Calculator

The Three-Phase Power Calculator computes Power (W) from 3 inputs: line voltage (v), current (a), power factor. P = √3 × V × I × pf.

Physics is the toolkit for turning a real-world observation into a prediction. Whether it’s a falling object, a moving car, or a stressed beam, the equations here are the same ones every engineer relies on. The Three-Phase Power Calculator sits in that toolkit — it P = √3 × V × I × pf. Enter your numbers above and the result updates instantly; every step of the math is shown in the Derivation panel so you can see exactly how the answer was reached.

§02The Formula

How it’s calculated

√(3) × t × a × n

Where

V
Line voltage (V)
I
Current (A)
pf
Power factor
§03Practical Example

Step-by-step walkthrough

Scenario

Apply the formula to a realistic set of inputs: Line voltage (V) = 415, Current (A) = 10, Power factor = 0.9.

  1. 01Start by noting the input — Line voltage (V): 415.
  2. 02Start by noting the input — Current (A): 10.
  3. 03Start by noting the input — Power factor: 0.9.
  4. 04Substitute these values into the formula: √(3) × t × a × n
  5. 05Compute Power (W): the calculator returns 6469.21.
  6. 06Cross-check the answer by opening the Derivation panel above — every line of math is shown so you can follow the computation end-to-end.
§04Variants

Common Three-Phase Power Problems

The formula gets rearranged depending on which variable you need. Here are the patterns you’ll run into in the real world — find the one that matches your problem and follow the worked steps.

01 · PATTERN

Line voltage (V) halved

V = 207.5 (from 415)

Keep every other input at its default and halve the line voltage (v). See how power (w) responds.

  1. 01New Line voltage (V): 207.5
  2. 02Baseline Power (W): 6469.21
  3. 03New Power (W): 3234.6
  4. 04Power (W) decreases by 50% → use this sensitivity to plan for real-world variation.
02 · PATTERN

Line voltage (V) doubled

V = 830 (from 415)

Keep every other input at its default and double the line voltage (v). See how power (w) responds.

  1. 01New Line voltage (V): 830
  2. 02Baseline Power (W): 6469.21
  3. 03New Power (W): 12938.4
  4. 04Power (W) increases by 100% → use this sensitivity to plan for real-world variation.
03 · PATTERN

Current (A) halved

I = 5 (from 10)

Keep every other input at its default and halve the current (a). See how power (w) responds.

  1. 01New Current (A): 5
  2. 02Baseline Power (W): 6469.21
  3. 03New Power (W): 3234.6
  4. 04Power (W) decreases by 50% → use this sensitivity to plan for real-world variation.
04 · PATTERN

Current (A) doubled

I = 20 (from 10)

Keep every other input at its default and double the current (a). See how power (w) responds.

  1. 01New Current (A): 20
  2. 02Baseline Power (W): 6469.21
  3. 03New Power (W): 12938.4
  4. 04Power (W) increases by 100% → use this sensitivity to plan for real-world variation.
§05FAQ

Frequently asked questions

Yes. The calculator implements the standard formula as documented and returns exact floating-point results. No approximations are used unless noted in the formula.
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