Low-Pass Filter Calculator — RC Cutoff Frequency
Enter the resistance and capacitance of an RC low-pass filter to find the −3 dB cutoff frequency, the time constant τ, and the Bode gain plot. Optionally enter a signal frequency to see its exact attenuation and phase shift.
Resistance unit
Capacitance unit
Hz
Signals above this frequency are attenuated; at this point gain = 70.7%
- 1
Resistance R (in Ω)
10,000 - 2
Capacitance C (in F)
0.0000001 - 3
Time constant τ = R × C
10,000 × 0.0000001 = 0.001 - 4
Cutoff frequency fc = 1 ÷ (2π × τ)
1 ÷ (2π × 0.001) = 159.155
How does this calculator work?
For an RC low-pass filter, cutoff frequency f_c = 1/(2πRC) and time constant τ = RC. At f_c, the output is 70.7% of input (−3 dB). Above f_c, gain falls at −20 dB/decade. Gain at any frequency: |H| = 1/√(1+(f/f_c)²); phase shift: φ = −arctan(f/f_c).
Formula
How this is calculated
A first-order RC low-pass filter passes low-frequency signals and progressively attenuates higher frequencies. The key design parameter is the cutoff (−3 dB) frequency f_c = 1/(2πRC). At this frequency the output amplitude is 1/√2 ≈ 70.7% of the input, which corresponds to −3 dB — exactly half the input power. Frequencies well below f_c pass nearly unchanged; frequencies well above f_c are increasingly suppressed at a rate of −20 dB per decade (−6 dB per octave).
The time constant τ = RC describes how quickly the capacitor charges: in one time constant the capacitor reaches ≈63% of the applied voltage. τ and f_c are simply related: f_c = 1/(2πτ). The capacitive reactance X_C = 1/(2πfC) equals R at the cutoff frequency — that is how the −3 dB point emerges mathematically from the voltage-divider structure of the RC network.
The Bode plot in the output shows gain in dB versus log₁₀(f/f_c). The flat pass-band, the −3 dB knee, and the −20 dB/decade roll-off are visible. When you enter an optional signal frequency, the calculator also reports the phase shift φ = −arctan(f/f_c): the output lags the input, reaching −45° exactly at f_c and approaching −90° at very high frequencies.
Frequently asked questions
The −3 dB cutoff is the frequency at which a filter attenuates the input signal to 1/√2 ≈ 70.7% of its original amplitude. At this point the signal power is halved. Frequencies below the cutoff pass through; frequencies above are progressively reduced.
Rearrange the formula: for a target f_c and a chosen R, pick C = 1/(2π·f_c·R). For example, a 1 kHz cutoff with R = 10 kΩ gives C = 1/(2π × 1000 × 10000) ≈ 15.9 nF — use the nearest standard value (15 nF or 16 nF).
No — this calculator models the passive first-order RC filter only. Active filters (Sallen-Key, multiple-feedback, etc.) have sharper roll-offs and can have gain, but require op-amp circuit equations. The RC formula and −20 dB/decade slope here apply to the simple two-component passive circuit.
Also known as
TG we-Calculate Editorial Team. (2026). Low-Pass Filter Calculator — RC Cutoff Frequency [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/low-pass-filter-calculator
TG we-Calculate Editorial Team. "Low-Pass Filter Calculator — RC Cutoff Frequency." TG we-Calculate. 2026. https://we-calculate.com/calculator/low-pass-filter-calculator.
TG we-Calculate Editorial Team, "Low-Pass Filter Calculator — RC Cutoff Frequency," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/low-pass-filter-calculator
@misc{wecalculate_low_pass_filter_calculator, title = {Low-Pass Filter Calculator — RC Cutoff Frequency}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/low-pass-filter-calculator}}, year = {2026}, note = {TG we-Calculate} }
Did this calculator help you?