Power & phase
Power Factor Calculator
Power factor equals real power divided by apparent power. Reactive power and phase angle follow from the same right-triangle relationship.
Calculate power factor, reactive power, and phase angle from real and apparent power.
Calculated result
Power factor result
Calculating…
Calculated locally in your browser
Planning math only. Verify equipment specifications and installation requirements separately.
What this calculator returns
Real power cannot exceed apparent power in this model. Use measured values from the same operating condition.
Formula and variables
The calculation runs entirely in your browser. Static formulas, definitions, examples, and tables remain readable without JavaScript.
PF = P/S; Q = √(S² - P²); φ = cos⁻¹(PF).
- P
- Real power, in watts or kilowatts.
- S
- Apparent power, in volt-amperes or kilovolt-amperes.
- V
- RMS voltage; line-to-line voltage in three-phase modes.
- I
- Line or circuit current, in amperes.
- PF
- Power factor, expressed as a ratio from greater than zero through one.
- Q
- Reactive power, in volt-amperes reactive.
P is real power, S is apparent power, Q is reactive power, and φ is phase angle.
Worked example
| Input | Value |
|---|---|
| Real power | 8 kW |
| Apparent power | 10 kVA |
8 kW divided by 10 kVA gives PF 0.8, 6 kVAR, and a phase angle of about 36.87°.
Reference table
| System | Apparent power | Real power | Voltage entry |
|---|---|---|---|
| DC | S = V × I | P = V × I | Circuit voltage |
| Single-phase AC | S = V × I | P = V × I × PF | RMS circuit voltage |
| Balanced three-phase AC | S = √3 × VLL × I | P = √3 × VLL × I × PF | Line-to-line RMS voltage |
Frequently asked questions
Can real power be greater than apparent power?
No in this magnitude model. The entered kW must not exceed kVA because power factor cannot exceed 1.
What does the phase angle result mean?
It is the arccosine of power factor in the displayed power triangle, not a time-domain waveform analysis.
Assumptions and limitations
- Magnitude-only power triangle.
- No capacitor-bank recommendation.
Method and sources
Review the electrical formulas, calculation methodology, and reference tables for the references most relevant to this calculation. The broader technical sources index records source scope and verification. Last reviewed .