Sallen-Key Low-Pass Filter Calculator (Cutoff Frequency & Q)
By Santaji GadepatilinUpdated November 6, 2026
The Sallen-Key topology builds a second-order active filter from one op-amp, two resistors and two capacitors, giving a 40 dB-per-decade roll-off. This Sallen-Key low-pass filter calculator finds the cutoff frequency, the Q factor and the attenuation at any frequency for the unity-gain version — see the Sallen and Key active filter explained and compare it with a simple RC low-pass filter.
How to use the Sallen-Key low-pass filter calculator
Enter the two resistors and two capacitors of a unity-gain Sallen-Key low-pass stage: R₁ from the input, R₂ to the op-amp’s non-inverting input, C₁ from the R₁–R₂ junction back to the output, and C₂ from the non-inverting input to ground. Add a frequency to see the gain there.
Sallen-Key low-pass formulas
f₀ = 1 / (2π √(R₁R₂C₁C₂)) · Q = √(R₁R₂C₁C₂) / [C₂(R₁ + R₂)]
|H(f)| = 1 / √[(1 − (f/f₀)²)² + (f / (f₀Q))²]
Worked example
R₁ = R₂ = 10 kΩ, C₁ = 22 nF, C₂ = 10 nF:
- f₀ = 1 ÷ (2π √(10k × 10k × 22n × 10n)) = 1,073.0 Hz
- Q = ½ √(22/10) = 0.7416 — close to Butterworth
- At 5 kHz the gain is 0.0462 (-26.7 dB)
Response types for an equal-resistor design (R₁ = R₂)
| Response | Q | C₁ / C₂ = 4Q² | Gain at f₀ |
|---|---|---|---|
| Critically damped | 0.5000 | 1.000 | -6.02 dB |
| Bessel | 0.5774 | 1.333 | -4.77 dB |
| Butterworth | 0.7071 | 2.000 | -3.01 dB |
| Q = 1 | 1.0000 | 4.000 | +0.00 dB |
| Chebyshev 1 dB ripple | 0.9565 | 3.660 | -0.39 dB |
For the Chebyshev case f₀ is the natural frequency, not the −3 dB point.
Design notes
- Use C0G/NP0 or film capacitors; X7R ceramics change value with voltage and add distortion.
- The op-amp’s gain-bandwidth product should be at least 100 × f₀ × Q for an accurate response.
- High-frequency feedthrough limits the stop-band depth of Sallen-Key low-pass filters; a multiple-feedback (MFB) topology is better when deep attenuation is needed.
Frequently asked questions
What is the cutoff frequency of a Sallen-Key low-pass filter?
f₀ = 1 ÷ (2π√(R₁R₂C₁C₂)). For a Butterworth response (Q = 0.707) f₀ is also the −3 dB frequency.
How is Q calculated for a unity-gain Sallen-Key filter?
Q = √(R₁R₂C₁C₂) ÷ [C₂(R₁ + R₂)], where C₁ is the feedback capacitor and C₂ goes to ground. With R₁ = R₂, Q = ½√(C₁/C₂).
How do I design a Butterworth Sallen-Key filter?
Choose R₁ = R₂ = R and C₁ = 2C₂ (so Q = 0.707), then set f₀ = 1/(2πR C₂√2). For example R = 10 kΩ, C₂ = 10 nF and C₁ = 20 nF give about 1.13 kHz.
What is the roll-off of a Sallen-Key filter?
40 dB per decade (12 dB per octave) above the cutoff. Cascade two stages with the right Q values for a fourth-order, 80 dB/decade filter.