How would I go about finding the phase angle at different times?

For example at 50 Hz with a full cycle time of 20 ms I know at 10 ms the phase angle would be 180°.

What calculation could I use to find the phase angle based on how many milliseconds I am into the cycle?

  • 2
    \$\begingroup\$ Phase angle increases linearly with time: $$\phi (t) = \omega t + \phi_0$$ \$\endgroup\$
    – Ben Voigt
    Commented Jan 13, 2022 at 17:19

1 Answer 1


Assuming at t=0 you have a phase angle of zero, you just need to use proportions. You're correct that with 50 Hz, the cycle time is \$1/f\$ = 20 ms, and 10 ms in (half a cycle) means you're at 180 degrees, and we can generalize that example and use it to check the formula below.

Since a full cycle of time 1/f means a phase angle of 360 degrees, your formula generalizes as:

$$ \phi = 360\deg \cdot \frac{t}{1/f} = 360\deg \cdot f \cdot t$$

(phi in degrees, t in seconds, f in hertz). This matches up with your example: 360 degrees * 10 ms * 50 Hz = 360 degrees * 0.5 (dimensionless) = 180 degrees.

If you wanted radians, remember that a full cycle is 2 pi radians, so you'd simply replace 360 degrees with that in the above formula.


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