Enter the cutoff frequency fc (Hz) into the Time Constant From Frequency Calculator. The calculator will evaluate the time constant τ for a first-order system.

Frequency to Time Constant Calculator

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Enter either cutoff frequency fc (−3 dB) or time constant τ. The calculator uses τ = 1 / (2π fc).

Results will appear here.

Time Constant From Frequency Formula

The following two example problems outline the steps and information needed to calculate the time constant from cutoff frequency for a first-order system.

\tau = \frac{1}{2\pi f_c}

Variables:

  • τ is the time constant (seconds)
  • fc is the cutoff frequency (−3 dB) (Hz) 

To calculate the time constant from cutoff frequency, divide 1 by (2π times the cutoff frequency). Note: 1/f is the period, not the first-order time constant unless you are using angular frequency (rad/s).

Frequency to Time Constant Conversion Table (τ = 1/(2πfc))
Frequency (Hz) Time Constant (s)
10.159155
100.0159155
500.00318310
600.00265258
1000.00159155
2000.000795775
5000.000318310
1,0000.000159155
2,0000.0000795775
5,0000.0000318310
10,0000.0000159155
20,0000.00000795775
50,0000.00000318310
100,0000.00000159155
200,0000.000000795775
500,0000.000000318310
1,000,0000.000000159155
2,000,0000.0000000795775
5,000,0000.0000000318310
10,000,0000.0000000159155
For a first-order system, time constant τ relates to cutoff frequency fc by τ = 1/(2πfc). Units: Hz for frequency, seconds for time.

How to Calculate Time Constant From Frequency?

The following steps outline how to calculate the time constant from cutoff frequency.

  1. First, determine the cutoff frequency fc (Hz). 
  2. Next, gather the formula from above: τ = 1 / (2π fc).
  3. Finally, calculate the time constant τ.
  4. After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

cutoff frequency fc (Hz) = 35

τ = 1 / (2π fc) = 1 / (2π · 35) ≈ 0.00455 s (4.55 ms)