Low-Pass Filter

How to use this calculator

A first-order low-pass filter passes frequencies below its cutoff and attenuates those above it. For an RC filter the cutoff is fc = 1/(2πRC); for an RL filter it's fc = R/(2πL). In **Cutoff** mode, enter R and C (or R and L) to get the cutoff frequency. In **Sensitivity** mode, enter the nominal values plus the component tolerances, and the calculator shows how much the cutoff shifts when the components vary within tolerance.

What it means in a real circuit

For R = 10 kΩ and C = 10 nF, fc = 1/(2π×10 kΩ×10 nF) ≈ 1.59 kHz. If R has ±5% tolerance and C has ±10%, the cutoff can shift by roughly ∓15% (since fc ∝ 1/RC) — the calculator shows the exact perturbed value and deviation. This matters when a filter's cutoff must land within a narrow band, e.g. an anti-alias filter before an ADC or a speaker crossover. Use this to pick standard-value R and C that land near your target, and to check that component tolerances won't push the cutoff out of spec.

Definitions

Cutoff frequency (fc): the frequency at which the output falls to 1/√2 (≈ 70.7%, −3 dB) of its low-frequency value. Roll-off: a 1st-order filter attenuates at 20 dB per decade (6 dB per octave) above fc. Time constant (τ): τ = RC (or L/R); fc = 1/(2πτ). Tolerance: the ±% a real component can deviate from its marked value.

Design tips

Pick R so it doesn't over-load the driving stage or the following stage; R is usually 1 kΩ–100 kΩ. Choose C from the resulting product (C = 1/(2πfc·R)). If fc is too high, increase R or C; if too low, decrease them. For a sharper transition, cascade two identical 1st-order sections (a 2nd-order Butterworth) — each section's component values are set by the same fc formula. Add a small series resistor after the capacitor if the following stage is very high-impedance, to avoid peaking.

Common mistakes

Forgetting that fc depends on the product RC (doubling R and halving C leaves fc unchanged). Using the source/load resistance as part of R without accounting for it (the effective R is often R in parallel with the next stage's input impedance). Choosing a capacitor with a poor temperature coefficient when the cutoff must be stable. Ignoring that electrolytic capacitors lose value as they age.

Component-selection advice

Use 1% metal-film resistors and C0G/NP0 ceramic (or film) capacitors for stable cutoffs; avoid X7R/X5R ceramics whose value drifts with voltage and temperature. Keep C in the 1 nF–100 µF range for easy sourcing. For audio, film caps are preferred for linearity. When in doubt, choose a standard E24/E96 value nearest the calculated R and C, then re-check fc with the calculator.

Limitations of this calculation

The formula assumes ideal components, infinite source and load impedance, and a single pole. It does not include the op-amp or active stage's own bandwidth, parasitic capacitance, or ESR. The sensitivity mode uses a first-order (linear) estimate of the cutoff shift — fine for small tolerances, approximate for very large ones. Real cutoffs can differ by a few percent from the ideal value.

Example use cases

Anti-alias filtering before an ADC; smoothing a PWM signal into an analog voltage; a bass (low-frequency) path in a 2-way speaker crossover; removing high-frequency noise from a sensor; the input stage of an audio amplifier.