Calculate the −3 dB cutoff frequency of low-pass and high-pass filters, or find the R, C or L value needed for a target cutoff frequency.
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Filter Type
Solve For
Filter Formulas
RC & RL Filter — All Forms
RC Cutoff Frequency
f_c = 1 / (2π × R × C)
RL Cutoff Frequency
f_c = R / (2π × L)
Find C from f & R
C = 1 / (2π × f_c × R)
Find R from f & C
R = 1 / (2π × f_c × C)
Find L from f & R
L = R / (2π × f_c)
Time Constant τ
τ = RC = L/R = 1/(2πf_c)
Roll-off (1st order)
−20 dB / decade
Phase at f_c
LP: −45° HP: +45°
Worked Examples
1Audio low-pass 3.4 kHz
R = 10 kΩ, C = ?
C = 1/(2π×3400×10k)≈ 4.7 nF
Cutoff3.39 kHz
2RC high-pass 100 Hz
C = 100 nF, R = ?
R = 1/(2π×100×100n)≈ 15.9 kΩ
Cutoff100 Hz
3RL low-pass 1 kHz
R = 100 Ω, L = ?
L = 100/(2π×1000)≈ 15.9 mH
Cutoff1 kHz
4EMI RC filter 100 kHz
R = 50 Ω, C = ?
C = 1/(2π×100k×50)≈ 31.8 nF
Cutoff100 kHz
Frequently Asked Questions
How do I calculate RC filter cutoff frequency? ▾
f_c = 1 / (2π × R × C). For R=10kΩ and C=10nF: f_c = 1/(2π×10000×0.00000001) ≈ 1592 Hz. This is the −3 dB point where output voltage is 70.7% of input.
What is the −3 dB frequency? ▾
The −3 dB frequency is the cutoff point where output power drops to half (−3 dB) and voltage drops to 70.7% (1/√2) of input. For a first-order filter this is f_c = 1/(2πRC) and is the standard definition of the filter's bandwidth.
What is the difference between low-pass and high-pass? ▾
Low-pass: passes frequencies below f_c, attenuates above (capacitor to ground, or inductor in series). High-pass: passes frequencies above f_c, attenuates below (capacitor in series, or inductor to ground). Same cutoff formula: f_c = 1/(2πRC).
What is the time constant of a filter? ▾
τ = RC = 1/(2πf_c). The time constant is directly related to the cutoff frequency. A larger τ means a lower cutoff frequency. At t=τ, the capacitor charges to 63.2% of the supply voltage in an RC circuit.
How steep is the roll-off of an RC filter? ▾
A first-order RC filter has a roll-off of −20 dB per decade (−6 dB per octave). At 10× the cutoff frequency, the output is −20 dB (10% of input). To get steeper roll-off, cascade multiple stages (2nd order: −40 dB/decade).