RC Filter Calculator - Cutoff Frequency and Time Constant

Agarapu Ramesh — Editor and content reviewer
Editorially reviewed Reviewed by Agarapu Ramesh, science educator (chemistry). LinkedIn
Last reviewed: May 2026 | Standard electrical engineering formulas

An RC filter uses a resistor and capacitor to pass some frequencies and roll off others. The cutoff frequency is 1 / (2 x pi x R x C). This is bench math, not guesswork with random capacitor drawers.

Formula at a glance

  • cutoff frequency: fc = 1 / (2 x pi x R x C)
  • time constant: tau = R x C
  • at fc, output is about -3 dB

Field note: If the next circuit stage loads the filter, the calculated cutoff can move. Buffer it or include the load in the design.

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RC Filter Calculator

Low-pass & high-pass filter calculator

Ω
Result
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Formulas

ττ = R × C
fcfc = 1 / (2πRC)
XCXC = 1 / (2πfC)

Time Constant Response

Time Charge Discharge
1τ 63.2% 36.8%
2τ 86.5% 13.5%
3τ 95.0% 5.0%
5τ 99.3% 0.7%

Related

RL FilterOhm's LawVoltage Divider

How to use the RC Filter Calculator

Use this as a bench check, then compare it with the part marking, tolerance and a meter reading when the circuit matters. Small components are cheap. Bad assumptions are not.

Worked example

Example: 10 k ohm and 100 nF gives fc = 159 Hz. That is useful for smoothing slow sensor signals, not for audio treble work.

Practical checks before you trust the number

  • Use ohms and farads in the formula.
  • Capacitor tolerance can be wide, often 10% to 20%.
  • Load impedance changes the filter behavior if it is too low.

Common mistake

If the next circuit stage loads the filter, the calculated cutoff can move. Buffer it or include the load in the design.

Sources and references

Related calculators

Frequently Asked Questions

f_c = 1 ÷ (2π × R × C). The cutoff is where the output amplitude drops to 70.7% of input (-3 dB). Example: R = 1 kΩ, C = 100 nF → f_c = 1 ÷ (2π × 1000 × 100e-9) = 1592 Hz. Below f_c the low-pass passes signals; above f_c it attenuates them.

For a low-pass RC filter (R in series, C to ground): V_out = V_in × 1 ÷ √(1 + (2πfRC)²). At f = f_c, V_out drops to 70.7% of V_in. Beyond that, attenuation rolls off at 20 dB/decade (a 6 dB drop per octave).

For high-pass: C in series, R to ground. f_c = 1 ÷ (2π × R × C). Pick R and C to set the cutoff at the desired frequency. Example: cut below 100 Hz → at R = 10 kΩ, C = 1 ÷ (2π × 100 × 10000) = 159 nF, so use 150 nF standard.

τ = R × C, in seconds. The time constant is how long it takes the capacitor to charge to 63.2% of the supply voltage through R. Example: 10 kΩ × 1 µF = 10 ms. After 5τ (50 ms), the capacitor is essentially fully charged (99.3%).

Capacitance and cutoff are inversely related: f_c = 1 ÷ (2π RC). Doubling C halves f_c. Smaller C raises f_c. So pick C based on the desired cutoff and the practical R range (1 kΩ to 100 kΩ usually). Tiny C (pF) gives high f_c (RF range); larger C (µF) gives audio f_c.

Low-pass passes frequencies below f_c and attenuates above. High-pass does the opposite. Topologically: LP has R-C with output across C; HP has C-R with output across R. Both share the same f_c formula but opposite frequency response.

Yes. Enter R and C, get f_c. Or enter desired f_c and one component, get the other. Useful for audio crossovers, anti-aliasing filters, and DC blocking. For sharper cuts, cascade multiple stages or use active filters with op-amps.