Active Low-Pass Filter (Sallen-Key) Calculator

Find the resistor and gain-setting resistor values for an equal-component Sallen-Key active low-pass filter from your target cutoff frequency and Q factor.

🔌 Active Low-Pass Filter (Sallen-Key) Calculator
Hz
nF
kΩ
Resistor (R1 = R2)
—
Amplifier gain (K)
—
Feedback resistor (Rf2)
—
Step-by-step working

🔌 What is a Sallen-Key Low-Pass Filter?

A Sallen-Key low-pass filter is a widely used active filter topology that implements a second-order (two-pole) low-pass response using an operational amplifier, two resistors, and two capacitors, no inductor required. In the equal-component design, R1 = R2 = R and C1 = C2 = C, which fixes the cutoff frequency through R and C together, while the amplifier's gain K, set by a simple feedback resistor pair, controls the filter's Q factor independently.

Electronics engineers reach for this topology constantly in anti-aliasing filters ahead of an ADC, audio crossover and equalization circuits, and any signal chain needing a compact, inductor-free active filter stage. The equal-component method is popular specifically because it reduces the design down to just two free choices, a capacitor value and a gain-setting resistor ratio, rather than solving four independent component values simultaneously.

A common point of confusion is expecting any Q value to be achievable. Because the equal-component method sets Q purely through amplifier gain K = 3 - 1/Q, and a non-inverting op-amp stage cannot have gain below 1, this design method is limited to Q >= 0.5. Lower Q targets require switching to an unequal-component (unequal R or C) Sallen-Key design instead.

This calculator computes the resistor value needed for your target cutoff frequency and chosen capacitor, then finds the amplifier gain and feedback resistor needed to hit your target Q, covering the common Butterworth case (Q = 0.7071) and any other standard second-order response.

📐 Formula

R = 1/(2πfcC)      K = 3 − 1/Q
R = R1 = R2 (ohms)
C = C1 = C2 (your chosen capacitor value)
fc = target cutoff frequency (Hz)
K = amplifier gain = 1 + Rf2/Rf1
Rf2 = Rf1(K−1)
Example: fc = 1000 Hz, Q = 0.7071 (Butterworth), C = 10 nF, Rf1 = 10 kΩ → R ≈ 15,915.49 Ω, K ≈ 1.5858, Rf2 ≈ 5.858 kΩ.

📖 How to Use This Calculator

Steps

1
Enter the target cutoff frequency. Type fc, the desired -3dB cutoff frequency, in Hertz.
2
Enter the target Q factor. Type Q, the desired quality factor (0.7071 for a Butterworth response).
3
Enter the capacitor value. Type C, your chosen capacitor value (C1 = C2 = C), in nanofarads.
4
Enter the reference feedback resistor. Type Rf1, your chosen reference resistor for the gain-setting network, in kilohms.

💡 Example Calculations

Example 1 — Butterworth Anti-Aliasing Filter

fc = 1000 Hz, Q = 0.7071 (Butterworth), C = 10 nF, Rf1 = 10 kΩ

1
R = 1/(2π × 1000 × 10×10⁻⁹) = 15,915.49 Ω
2
K = 3 − 1/0.7071 = 1.5858
3
Rf2 = 10 × (1.5858−1) = 5.858 kΩ
R = 15,915.49 Ω, Rf2 = 5.858 kΩ
Try this example →

Example 2 — Critically-Damped Filter (Q = 1)

fc = 5000 Hz, Q = 1, C = 4.7 nF, Rf1 = 10 kΩ

1
R = 1/(2π × 5000 × 4.7×10⁻⁹) = 6,772.55 Ω
2
K = 3 − 1/1 = 2.0000
3
Rf2 = 10 × (2.0000−1) = 10.000 kΩ
R = 6,772.55 Ω, Rf2 = 10.000 kΩ
Try this example →

Example 3 — Bessel-Like Low-Q Filter

fc = 500 Hz, Q = 0.577, C = 22 nF, Rf1 = 15 kΩ

1
R = 1/(2π × 500 × 22×10⁻⁹) = 14,468.63 Ω
2
K = 3 − 1/0.577 = 1.2669
3
Rf2 = 15 × (1.2669−1) = 4.003 kΩ
R = 14,468.63 Ω, Rf2 = 4.003 kΩ
Try this example →

❓ Frequently Asked Questions

What is a Sallen-Key filter?+
A Sallen-Key filter is a widely used active filter topology that implements a second-order (two-pole) filter response using an operational amplifier, two resistors, and two capacitors (for a low-pass design), no inductor required, making it practical to build at audio and lower RF frequencies.
What is the formula for the Sallen-Key low-pass filter's resistor value?+
For the equal-component design (R1 = R2 = R, C1 = C2 = C), R = 1 / (2 pi fc C), where fc is the target cutoff frequency and C is your chosen capacitor value. This single resistor value sets the cutoff frequency once C is fixed.
How is the Q factor set in this filter design?+
In the equal-component Sallen-Key design, Q is controlled entirely by the non-inverting amplifier's gain K, following K = 3 - 1/Q. The gain K is itself set by a feedback resistor pair, K = 1 + Rf2/Rf1, so choosing Q determines the required ratio between Rf1 and Rf2.
What Q value gives a Butterworth response?+
A Q of 1/sqrt(2), approximately 0.7071, gives the maximally-flat (Butterworth) second-order low-pass response, the most common target for a general-purpose filter with no passband ripple and no peaking near cutoff.
Why does this calculator require Q to be at least 0.5?+
In the equal-component design, K = 3 - 1/Q, and K must be at least 1 because a non-inverting op-amp stage cannot have a gain below unity. Solving K >= 1 for Q gives Q >= 0.5, so this design method cannot reach a Q below 0.5 without switching to an unequal-component design.
What happens if Q is set higher than about 3?+
As Q approaches 3, the required gain K approaches 3 exactly, and the filter becomes increasingly sensitive to small component tolerance variations near that point, in practice, high-Q Sallen-Key stages (Q above about 5) are usually avoided or built with more tolerance-tolerant topologies instead.
Why choose the capacitor value before calculating the resistor?+
Capacitors come in far fewer standard values than resistors, so fixing a convenient, commonly available capacitor value first and solving for the resistor usually lands closer to a standard resistor value than fixing the resistor first and solving for an oddball capacitor value.
What is the reference resistor Rf1 used for?+
Rf1 and Rf2 form the feedback network that sets the operational amplifier's non-inverting gain K = 1 + Rf2/Rf1. Rf1 is a free design choice (commonly a round number like 10 kohm), and Rf2 is then computed to achieve the exact gain your target Q requires.
Does this calculator design a high-pass or band-pass Sallen-Key filter?+
No, this calculator is scoped to the low-pass Sallen-Key configuration only. High-pass and band-pass Sallen-Key filters use a different component arrangement (resistors and capacitors swapped or combined differently) and different design equations.
What units does this calculator use?+
Cutoff frequency is entered in Hertz, the capacitor value in nanofarads, and the reference feedback resistor in kilohms. Results are shown in ohms for the main resistor and kilohms for the gain-setting feedback resistor.
Tags: Sallen Key Filter Calculator Active Low Pass Filter Calculator Sallen Key Calculator Second Order Filter Design Calculator Op Amp Filter Calculator Calculator Formula Free Online

🔗 Related Calculators

🔌
Resonant Frequency Calculator (LC Circuit)
Engineering - Electrical
🔌
Quality Factor Calculator
Engineering - Electrical
📻
Bessel Filter Group Delay Calculator
Engineering - Electrical
📶
Butterworth Digital Filter Calculator
Engineering - Signal Processing
🔌
RLC Series Circuit Impedance Calculator
Engineering - Electrical

What is a Sallen-Key filter?

A Sallen-Key filter is a widely used active filter topology built from an operational amplifier, two resistors, and two capacitors (for a low-pass design), that implements a second-order (two-pole) filter response without needing an inductor, making it practical to build at audio and lower RF frequencies.

What is the formula for the Sallen-Key low-pass filter's resistor value?

For the equal-component design (R1 = R2 = R, C1 = C2 = C), R = 1 / (2 pi fc C), where fc is the target cutoff frequency and C is your chosen capacitor value. This single resistor value sets the cutoff frequency once C is fixed.

How is the Q factor set in this filter design?

In the equal-component Sallen-Key design, Q is controlled entirely by the non-inverting amplifier's gain K, following K = 3 - 1/Q. The gain K is itself set by a feedback resistor pair, K = 1 + Rf2/Rf1, so choosing Q determines the required ratio between Rf1 and Rf2.

What Q value gives a Butterworth response?

A Q of 1/sqrt(2), approximately 0.7071, gives the maximally-flat (Butterworth) second-order low-pass response, the most common target for a general-purpose filter with no passband ripple and no peaking near cutoff.

Why does this calculator require Q to be at least 0.5?

In the equal-component design, K = 3 - 1/Q, and K must be at least 1 because a non-inverting op-amp stage cannot have a gain below unity. Solving K >= 1 for Q gives Q >= 0.5, so this design method cannot reach a Q below 0.5 without switching to an unequal-component design.

What happens if Q is set higher than about 3?

As Q approaches 3, the required gain K approaches 3 exactly, and the filter becomes increasingly sensitive to small component tolerance variations near that point, in practice, high-Q Sallen-Key stages (Q above about 5) are usually avoided or built with more tolerance-tolerant topologies instead.

Why choose the capacitor value before calculating the resistor?

Capacitors come in far fewer standard values than resistors, so fixing a convenient, commonly available capacitor value first and solving for the resistor usually lands closer to a standard resistor value than fixing the resistor first and solving for an oddball capacitor value.

What is the reference resistor Rf1 used for?

Rf1 and Rf2 form the feedback network that sets the operational amplifier's non-inverting gain K = 1 + Rf2/Rf1. Rf1 is a free design choice (commonly a round number like 10 kohm), and Rf2 is then computed to achieve the exact gain your target Q requires.

Does this calculator design a high-pass or band-pass Sallen-Key filter?

No, this calculator is scoped to the low-pass Sallen-Key configuration only. High-pass and band-pass Sallen-Key filters use a different component arrangement (resistors and capacitors swapped or combined differently) and different design equations.

What units does this calculator use?

Cutoff frequency is entered in Hertz, the capacitor value in nanofarads, and the reference feedback resistor in kilohms. Results are shown in ohms for the main resistor and kilohms for the gain-setting feedback resistor.

📌 Quick Tips

💡This calculator uses the equal-component Sallen-Key design (R1 = R2 = R, C1 = C2 = C), where Q is set entirely by the amplifier gain K, this is the most common design method since it needs only one resistor value and one capacitor value to set the cutoff frequency.
💡A Q of 0.7071 (1/sqrt(2)) gives a Butterworth (maximally flat passband) response, this is the most common target Q for a general-purpose low-pass filter.
💡This topology needs K >= 1 (equivalently Q >= 0.5), since a non-inverting op-amp stage cannot have a gain below 1, if your target Q is below 0.5, a different Sallen-Key design method (unequal R or C values) is required.
💡Pick a convenient standard capacitor value first (like 10 nF, 4.7 nF, or 22 nF), then let the calculator find the matching resistor value, this usually gives a more standard, easier-to-source resistor than fixing the resistor first.
💡Rf1 is your choice of reference resistor for the gain-setting feedback network, any convenient value (commonly 10 kohm) works, the calculator finds the matching Rf2 needed for your target gain K.