RC filter calculator: cutoff frequency, R or C • The Science 360

By Shounak Das · Updated November 2026 · 5 min read

How do you calculate an RC filter?

The cutoff of an RC filter is fc = 1 ÷ (2πRC). 10 kΩ and 10 nF give 1.59 kHz. For a 1 kHz low-pass with a 10 nF capacitor, R = 15.9 kΩ; the nearest E24 resistor, 16 kΩ, puts the cutoff at 995 Hz.

What the −3 dB point means and how loading moves it is covered in RC low-pass filter cutoff; the step response is in the RC time constant. For picking parts, with worked examples, see how to choose R and C for a low-pass filter.

Key results from the calculator

10 kΩ and 10 nF: 1.59 kHz, time constant 100 µs.
1 kHz with 10 nF: 16 kΩ (E24, −0.5%), 15.8 kΩ (E96, +0.7%) or 15 kΩ (E12, +6.1%).
10 Hz with 10 kΩ: 1.5 µF gives 10.6 Hz and cuts 50 Hz hum to 21%.
Tolerances: with a 5% resistor and a 10% capacitor, a 1.59 kHz filter can land anywhere from 1.38 kHz to 1.86 kHz.

Six filters

Each example loads the filter type, the part being solved, the value series and the test signal.

10 kΩ and 10 nF

Textbook values

1 ÷ (2π × 10,000 × 10 × 10⁻⁹) = 1.59 kHz. A 1 kHz signal passes at 85% and lags by 32°.

Cutoff 1.59 kHz Time constant 100 µs At 1 kHz -1.4 dB Spread 1.38 kHz to 1.86 kHz

A 1 kHz low-pass with a 10 nF capacitor

Solve for R

The exact resistor is 15.9 kΩ. The nearest E24 value, 16 kΩ, gives 995 Hz, −0.5% from target and well inside a 5% resistor's own tolerance.

Exact R 15.9 kΩ E24 R 16 kΩ Cutoff 995 Hz Error −0.5%

The same filter with 1% resistors

E96 series

E96 offers 15.8 kΩ, +0.7% off. The tighter resistor narrows the spread to 950 Hz to 1.07 kHz with a 5% capacitor; the capacitor now dominates.

E96 R 15.8 kΩ Cutoff 1.01 kHz Error +0.7% Spread 950 Hz to 1.07 kHz

A 10 Hz filter in front of an ADC

Solve for C

With R fixed at 10 kΩ, the source impedance the ATmega328P datasheet asks for, C = 1.59 µF. E12 gives 1.5 µF, so 10.6 Hz; 50 Hz mains hum is cut by 13.7 dB.

Exact C 1.59 µF E12 C 1.5 µF Cutoff 10.6 Hz At 50 Hz -13.7 dB

A coupling capacitor into a 10 kΩ input

High-pass

A series capacitor and the next stage's 10 kΩ input form a high-pass filter. For a 20 Hz corner, C = 796 nF; the E12 820 nF gives 19.4 Hz.

Exact C 796 nF E12 C 820 nF Cutoff 19.4 Hz At 20 Hz -2.9 dB

A 100 Hz square wave through 10 kΩ and 100 nF

Time domain

The time constant is 1 ms and each half cycle lasts 5 ms, five time constants, so the output just about reaches each level before the input flips.

Cutoff 159 Hz Time constant 1 ms Half period 5 ms At 100 Hz -1.4 dB

Resistor for a 10 nF capacitor, by cutoff

Cutoff	Exact R	E24	Cutoff with E24	E96	Cutoff with E96
100 Hz	159 kΩ	160 kΩ	99.5 Hz	158 kΩ	101 Hz
300 Hz	53.1 kΩ	51 kΩ	312 Hz	53.6 kΩ	297 Hz
1 kHz	15.9 kΩ	16 kΩ	995 Hz	15.8 kΩ	1.01 kHz
3 kHz	5.31 kΩ	5.1 kΩ	3.12 kHz	5.36 kΩ	2.97 kHz
10 kHz	1.59 kΩ	1.6 kΩ	9.95 kHz	1.58 kΩ	10.1 kHz
30 kHz	531 Ω	510 Ω	31.2 kHz	536 Ω	29.7 kHz

Same for low-pass and high-pass. For another capacitor, scale R inversely: 100 nF needs a tenth of these resistances.

How the calculator works

Cutoff: fc = 1 ÷ (2πRC), where the capacitor’s reactance equals R.

Solving: R = 1 ÷ (2π fc C), or C = 1 ÷ (2π fc R), then rounded to the nearest value in the chosen series (E12, E24 or E96, from Vishay’s decade table).

Response: gain 1 ÷ √(1 + (f/fc)²) for low-pass and (f/fc) ÷ √(1 + (f/fc)²) for high-pass; phase −arctan(f/fc), plus 90° for high-pass.

Spread: the cutoff with both parts at the ends of their tolerances: the series tolerance for R (E12 10%, E24 5%, E96 1%) and the one you pick for C.

What the model leaves out

Source and load: the source resistance adds to R, and a load across the output lowers the gain and raises the cutoff of a low-pass.
Capacitor voltage and temperature: X7R ceramics lose capacitance with DC voltage and change up to ±15% over temperature; C0G does neither.
Parasitics: at very high frequencies the capacitor’s own inductance and the board’s capacitance take over.
Higher orders: one RC stage rolls off at 20 dB per decade; steeper filters need more stages or active designs.

Common misconceptions

"Above the cutoff, nothing gets through." At twice the cutoff a first-order filter still passes 45%; at ten times, 10%.

"Any R and C with the right product will do." The product sets the cutoff, but R decides how hard the source works and how much the load matters.

"The calculated value is what you get." A 10% capacitor moves the cutoff by about 10% before the resistor is even counted.

Frequently asked questions

What is the formula for an RC filter cutoff?

fc = 1 ÷ (2πRC), with R in ohms and C in farads. 10 kΩ and 10 nF give 1.59 kHz.

How do I pick R and C for a cutoff?

Choose the capacitor first, since it comes in fewer values, then R = 1 ÷ (2π fc C) and round to a standard resistor. For 1 kHz with 10 nF: 16 kΩ in E24.

Is the formula the same for a high-pass filter?

Yes. Swapping R and C changes which side of the cutoff passes, not where the cutoff is.

What is the time constant of an RC filter?

τ = RC, which equals 1 ÷ (2π fc). For 10 kΩ and 10 nF it is 100 µs; a step reaches 63% in one τ and 99% in five.

Why does my filter cut off at the wrong frequency?

Usually part tolerance, a capacitor losing value under DC voltage, or the source and load resistances adding to the circuit. Measure the parts, or buffer the filter.