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RC Time Constant & Cutoff Frequency

Calculate an ideal RC time constant and cutoff frequency, with reverse solutions for resistance and capacitance.

  • Formula & worked example
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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

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Formula and method

A 1,000 Ω resistor with 1,000 µF capacitance has a one-second time constant and about 0.159155 Hz cutoff frequency.

τ = RC; f_c = 1/(2πRC)

Worked example

Enter these known values and leave the other values blank.

Resistance (R)
1000 Ω
Capacitance (C)
1000 μF
First-order RC cutoff frequency
0.15915 Hz
Time constant τ
1 sec

Assumptions and limitations

  • The time output is one time constant, not the time to complete charging. An ideal charging capacitor reaches approximately 63.2% of its final change after one τ.
  • The cutoff relation applies to the ideal first-order RC network. Loading, leakage, tolerances and parasitic components are omitted.
  • All values must be positive. Calendar-length unit options use fixed average durations rather than actual calendar dates.

Common questions

When is the capacitor fully charged?

The ideal exponential approaches its final value asymptotically. Choose a required tolerance; five time constants corresponds to about 99.3% of the final change.

References

The calculation equations, inverse formulas, units, and input rules were imported from this source. Bookify provides the interface and equation solver.

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