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Phase Angle from Power Factor

φ=arccos⁡(PF)\varphi = \arccos(\text{PF})
sig figs

Worked example: PF 0.8 → 36.87° lag. Press Try an example to run it live, then adjust anything.

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Phasor Sum of Two Series Impedances
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See also

Phasor Sum of Two Series Impedances: Both use phase angle.Power Factor from Real and Apparent Power: Both use power factor.Power-Factor Correction kvar: Both use power factor.Single-Phase Real Power with Power Factor: Both use power factor.Three-Phase Motor Full-Load Current: Both use power factor.Three-Phase Real Power: Both use power factor.
1 more relatedTransformer Efficiency from Core and Copper Losses: Both use power factor.
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Phase Angle from Power Factor explained

φPF

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

φ=arccos⁡(PF)\varphi = \arccos(\text{PF})
Where
  • φ\varphi= Phase angle (°)
  • PF\text{PF}= Power factor
In this toolkit

Three-phase power and power factor

8 formulasReal, reactive and apparent power, power factor, phase angle and correction kvar — the power triangle as an electrician uses it.

Revised 16 October 2026
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formula.expert. (2026, October 16). Phase Angle from Power Factor Formula & Calculator. https://formula.expert/solvers/phase-angle-power-factor

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