Science
Single-phase AC power
Estimate real, apparent, and reactive power for a single-phase AC load.
Calculators / Science / AC power triangle
AC power triangle calculator
Calculate apparent power and power-factor magnitude from real and reactive power.
On this page
Apparent power500VA
Power factor magnitude0.6
Phase angle magnitude53.13degrees
Calculator controls
How to calculate
Calculate apparent power and power-factor magnitude from real and reactive power.
Apparent power =
sqrt(P^2+Q^2) VAPower factor magnitude =
P/sqrt(P^2+Q^2)Phase angle magnitude =
acos(P/sqrt(P^2+Q^2))*180/pi degreesWorked example
- Real power (W): 300
- Reactive power (var): 400
- Apparent power: 500 VA
- Power factor magnitude: 0.6
- Phase angle magnitude: 53.13 degrees
Assumptions and limits
This is an ideal educational model. Enter quantities in the stated SI units; it does not certify equipment safety or real operating limits. Assumes sinusoidal AC. Positive Q is inductive and negative Q capacitive; harmonics require true-power-factor analysis.
Results are rounded for display; calculations use unrounded values. Read our calculation methodology.
Understanding the result
Calculate apparent power and power-factor magnitude from real and reactive power. The angle output is a magnitude. Use the sign of reactive power separately to identify leading or lagging operation.
When this tool is useful
The angle output is a magnitude. Use the sign of reactive power separately to identify leading or lagging operation.
Understanding your inputs
| Input | Example |
|---|---|
Real power (W) P | 300 |
Reactive power (var) Q | 400 |
Frequently asked questions
Which assumptions matter for this result?
This is an ideal educational model. Enter quantities in the stated SI units; it does not certify equipment safety or real operating limits. Assumes sinusoidal AC. Positive Q is inductive and negative Q capacitive; harmonics require true-power-factor analysis.
How can I check the worked example?
Use the displayed example inputs in the stated formula. Keep each quantity in its labelled unit and compare the unrounded result before applying display rounding.