How to Use the Cutoff Frequency Calculator
The cutoff frequency (also called the corner frequency or -3 dB frequency) is the point where a first-order filter's output power falls to half its passband value — equivalently, the output voltage amplitude drops to 1/√2 ≈ 70.7% of the input amplitude. It marks the boundary between the passband, where a signal passes through with little attenuation, and the stopband, where attenuation increases with frequency. This calculator finds that frequency for the two most common first-order networks: a resistor-capacitor (RC) circuit and a resistor-inductor (RL) circuit.
Deriving the RC and RL cutoff frequency formulas
The cutoff frequency occurs where the reactance of the reactive component equals the resistance, so the two elements divide the signal equally. For a capacitor, reactance is X_C = 1/(2πfC); setting X_C = R and solving for f gives f_c = 1 / (2πRC). For an inductor, reactance is X_L = 2πfL; setting X_L = R and solving for f gives f_c = R / (2πL). In both cases, R is in ohms, C is in farads, L is in henries, and f_c comes out in hertz. The same formulas apply whether the components are arranged as a low-pass filter (output taken across the capacitor, or across the resistor for RL) or a high-pass filter (the connections reversed) — only the direction of attenuation changes, not the corner frequency itself. The calculator also reports the angular cutoff frequency ω_c = 2πf_c = 1/(RC) (or R/L), the time constant τ = RC (or L/R), which is the reciprocal of ω_c, and the period T = 1/f_c.
Practical design notes
- Component tolerance matters: standard resistors (±5%) and especially electrolytic capacitors (±20% or worse) shift the actual cutoff frequency away from the calculated value — use tighter-tolerance parts when the corner frequency needs to be precise.
- Common uses: RC low-pass filters remove high-frequency noise from sensor signals and set anti-aliasing limits before an ADC; RC high-pass filters block DC offset in audio coupling stages; RL filters appear in power-supply and RF circuits where inductors are more practical than large capacitors.
- Roll-off rate: a first-order RC or RL filter attenuates at about 6 dB per octave (20 dB per decade) beyond the cutoff frequency — cascading stages increases the roll-off but also shifts the effective corner frequency.
- Loading effects: the formulas assume an ideal source and an unloaded output; a downstream load resistance in parallel with C, or in series with L, changes the effective cutoff frequency in a real circuit.