Phase Angle from Power Factor
Worked example: PF 0.8 → 36.87° lag — press Try an example to run it live, then adjust anything.
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Phase Angle from Power Factor explained
Power factor and phase angle are the same fact in two languages. A PF of 0.8 means the current waveform is 36.87° out of step with the voltage — the 3-4-5 triangle again, since cos 36.87° = 0.8 and sin 36.87° = 0.6. Once you have φ you can get the reactive burden directly as Q = P tan φ, which is how correction tables are built.
The number alone does not say which way: motors and transformers pull lagging current (current behind voltage), while capacitor banks and lightly loaded long cables push leading current. Both give the same cos φ, so meters mark them separately, and it matters — leading power factor on a weak system raises voltage rather than lowering it. Note this calculator works in radians internally and displays degrees.
Phase Angle from Power Factor formula
- = Phase angle (°)
- = Power factor
Missing one of these? Work it out first, then come back
- Phase angle — Phasor Sum of Two Series Impedances, Magnetic Flux (Φ = BA cos θ)
- Power factor — Three-Phase Real Power, Single-Phase Real Power with Power Factor