Phase Angle from Power Factor

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

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

Enter your known values, leave one input blank, and solves for the missing one. Tap a variable’s symbol to see what it means, with a typical value. Try different units for next level excitement!

Here the solver did the work — could you?

Impedance →

UniversityCircuits & Electrical Power

Test your skills in the Exam Room: new numbers every attempt — free lessons for students, no sign-up, just pure learning. Find 1 more lesson on this formula.

See your Report Card
Compete with your friends
share your results
Learning zone

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

Missing one of these? Work it out first, then come back