RC filter cutoff frequency calculator
This RC filter cutoff frequency calculator uses f = 1/(2π·R·C) from resistance and capacitance, shows the time constant and frequency response, and also handles RL filters and LC resonant circuits.
Example: Which circuit: RC filter (resistor and capacitor) · Resistance R 1 · Resistance R (unit): kΩ · Capacitance C 100 · Capacitance C (unit): nF → Result: Cutoff frequency = 1.5915 kHz · τ = 100 µs. Source: Wikipedia – Tiefpass (cutoff frequency, time constant of RC and RL circuits). Updated: .
How it is calculated
The cutoff frequency of an RC filter is f = 1 / (2π·R·C). With 1 kΩ and 100 nF that is 1,591.5 Hz, and the time constant is 100 µs.
What the cutoff frequency means
At the cutoff frequency the output voltage has fallen to 1/√2 (about 71 %), which is −3 dB. A low-pass passes everything below and attenuates above, a high-pass does the opposite. In an RC filter the low-pass output is taken across the capacitor and the high-pass output across the resistor. The time constant τ = R·C says how fast the capacitor charges: after 5·τ it has reached more than 99 %.
RL filters and resonant circuits
- RL filter: f = R / (2π·L), τ = L/R
- LC resonant circuit: resonant frequency f₀ = 1/(2π·√(L·C)), characteristic impedance Z₀ = √(L/C)
- With a series loss resistance R: Q factor Q = Z₀/R, bandwidth B = f₀/Q
Example: a 10 mH coil and a 100 nF capacitor resonate at 5.03 kHz with a characteristic impedance of 316 Ω.
Frequently asked questions
How do you calculate the cutoff frequency of an RC filter?
With f = 1/(2π·R·C). For R = 1 kΩ and C = 100 nF that gives about 1.59 kHz.
How do you calculate the resonant frequency of an LC circuit?
With Thomson’s formula f₀ = 1/(2π·√(L·C)). For L = 10 mH and C = 100 nF that is about 5.03 kHz.
What is the time constant?
τ = R·C for an RC filter and τ = L/R for an RL filter. After one time constant the capacitor has reached 63 % of the final voltage, after five more than 99 %.
Sources and legal basis
- Wikipedia – Tiefpass (cutoff frequency, time constant of RC and RL circuits)
- Wikipedia – Hochpass (Grenzfrequenz, Übertragungsfunktion)
- Wikipedia – Schwingkreis (Resonanzfrequenz, Güte, Bandbreite)
- Wikipedia – RC circuit
- Wikipedia – LC circuit (resonant frequency)
As of: · Editorial policy
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