What Is Cutoff Frequency?
Cutoff frequency (also called the corner frequency or -3dB frequency) is the point at which a filter's output amplitude has dropped to approximately 70.7% (1/root 2) of its input amplitude. In power terms this is a drop of 3 decibels. It marks the boundary between the passband, where the filter passes signals through largely unaffected, and the stopband, where signals are increasingly attenuated. Cutoff frequency is one of the most fundamental figures in filter design, used constantly in audio electronics, power supply design, sensor interfacing and radio frequency work.
RC Filter Cutoff Formula
For a simple RC filter, built from one resistor and one capacitor, the cutoff frequency is:
fc = 1 / (2 π R C)
Where R is resistance in ohms and C is capacitance in farads. This formula is identical whether the filter is arranged as a low-pass (output taken across the capacitor) or a high-pass (output taken across the resistor), because the cutoff point depends only on the RC time constant, not on the physical arrangement.
RL Filter Cutoff Formula
For an RL filter, built from a resistor and an inductor, the cutoff frequency is:
fc = R / (2 π L)
Where R is resistance in ohms and L is inductance in henries. As with RC filters, this applies to both low-pass and high-pass RL arrangements.
Series RLC Filter Cutoff and Bandwidth
A series RLC circuit behaves differently. It has a resonant frequency where the inductive and capacitive reactances cancel out:
f0 = 1 / (2 π √(L C))
Rather than a single cutoff, an RLC band filter has two -3dB points, one above and one below resonance, separated by the bandwidth. The bandwidth depends on the quality factor Q:
Q = (1 / R) √(L / C) and Bandwidth = f0 / Q
A higher Q gives a narrower bandwidth and a sharper filter response around the resonant frequency, while a lower Q gives a broader, more gently sloped response.
| Filter Type | Formula | Common Use |
|---|
| RC low-pass / high-pass | fc = 1 / (2πRC) | Audio tone control, noise filtering, power supply smoothing |
| RL low-pass / high-pass | fc = R / (2πL) | Power electronics, RF chokes, motor drive filtering |
| Series RLC band-pass | f0 = 1 / (2π√(LC)) | Radio tuning, resonant sensors, band-pass filtering |
Time Constant and Angular Frequency
The time constant tells you how quickly a filter responds to a change in input. For an RC filter, the time constant is τ = R × C. For an RL filter, it is τ = L / R. In both cases the cutoff frequency is related to the time constant by fc = 1 / (2πτ). Angular frequency (ω) is simply the cutoff frequency expressed in radians per second rather than hertz, calculated as ω = 2πfc.
Worked Example
For a default RC filter with R = 1,000 ohms and C = 1 microfarad (0.000001 F): the time constant τ = RC = 1,000 × 0.000001 = 0.001 seconds. The cutoff frequency is fc = 1 / (2π × 0.001) = 159.15 Hz. The angular frequency is ω = 2π × 159.15 = 1,000 rad/s, and the period at cutoff is T = 1/fc = 0.00628 seconds.
Frequently Asked Questions
What is cutoff frequency? It is the point where a filter's output has dropped to about 70.7% of input amplitude (a 3dB drop in power), marking the boundary between the passband and stopband.
How do you calculate the cutoff frequency of an RC filter? Use fc = 1 / (2πRC), where R is in ohms and C is in farads. This applies to both RC low-pass and high-pass filters.
Is cutoff frequency the same for RL and RLC filters? No. RL cutoff is fc = R / (2πL). A series RLC filter instead has a resonant frequency f0 = 1 / (2π√(LC)), with cutoff points either side of resonance set by the circuit's quality factor Q.
Related Calculators
Sources: Standard RC, RL and RLC filter formulas from circuit theory (Horowitz and Hill, The Art of Electronics; Sedra and Smith, Microelectronic Circuits).
This calculator covers idealised single-pole RC and RL filters and series RLC filters. Real-world filters may include additional stages, component tolerances, and parasitic effects that shift the actual cutoff point slightly from the calculated value.
