RC Filter Calculator

How to use this RC filter calculator

What this calculator does

This calculator solves the standard first-order passive RC relationship among Resistance (R), Capacitance (C), and Cutoff frequency (f_c). It can be used for either a low-pass circuit, where the output is taken across the capacitor, or a high-pass circuit, where the output is taken across the resistor. The numerical corner frequency is the same for both topologies. The model assumes ideal components and an unloaded filter, so it is a design estimate rather than a substitute for checking source resistance, load impedance, capacitor parasitics, component tolerances, or bandwidth limits in a real circuit. Analog Devices' passive filter laboratory notes describe the same first-order RC cutoff relation and the approximately 70.7% amplitude at the corner frequency.

When to use it

Use the calculator when you want to choose an RC pair for removing high-frequency noise with a low-pass filter, block DC or low-frequency content with a high-pass filter, check the cutoff produced by parts already on hand, or work backward from a required cutoff to one missing component value. It is also useful for quickly estimating the ideal Bode magnitude and phase trend around the corner before you run a SPICE simulation or bench measurement.

How to calculate

1. The calculator opens with a ready-to-use demonstration: 10 kΩ, 25 nF, and a matching cutoff of about 636.62 Hz. The live results, response table, chart, and Excel workbook are already valid on first open.
2. Choose Select filter type as Low-pass or High-pass. This changes the response curve and phase convention, not the RC cutoff equation.
3. Enter any two of the three electrical quantities. To solve for a missing value, clear the field you want calculated. If all three are filled, Resistance (R) and Capacitance (C) are treated as the defining pair and the entered cutoff is checked for consistency.
4. Use the adjacent unit selectors to work in Ω, kΩ, or MΩ; pF through F; and Hz, kHz, or MHz. Changing a unit converts the current number instead of merely relabeling it.
5. Read the primary cutoff result, the solved component values, the time constant, angular cutoff, and gain at cutoff. Then use the response table and line chart to inspect how gain and phase behave from 0.01× to 100× the corner frequency.
6. Select Download Excel to export the current validated inputs, results, and complete response table as a real XLSX workbook. Reset clears the demonstration data, results, table, chart, validation residue, and workbook state; after Reset, Excel export stays disabled until at least two complete valid electrical values are entered again.

Input guide

Select filter type is a required choice between Low-pass and High-pass. Low-pass means the ideal output magnitude starts near unity at frequencies well below cutoff and falls above cutoff; High-pass does the opposite. The startup example is Low-pass. A common mistake is to expect the filter type to change the formula for f_c; it does not for a simple first-order RC network.

Resistance (R) is a positive decimal value with a separate R unit selector for Ω, kΩ, or MΩ. The startup example uses 10 kΩ. Larger resistance increases the RC time constant and therefore lowers cutoff when capacitance is held fixed. Enter ordinary decimal notation such as 4.7 or properly grouped values such as 10,000; decimal-comma notation and scientific notation are rejected to avoid ambiguous interpretation. Clear R if you want it solved from C and f_c.

Capacitance (C) is a positive decimal value with a C unit selector for pF, nF, µF, mF, or F. The demonstration uses 25 nF. Increasing capacitance lowers cutoff for a fixed resistance. Check prefixes carefully: 1 µF is 1,000 nF and 1,000,000 pF. Clear C if you want the calculator to solve it from R and f_c.

Cutoff frequency (f_c) is a positive decimal value with a f_c unit selector for Hz, kHz, or MHz. The startup value is 636.6197723676 Hz so that it agrees closely with 10 kΩ and 25 nF. A higher requested cutoff requires a smaller R, a smaller C, or both. Clear f_c when you simply want the corner created by the resistor-capacitor pair. If all three fields are filled, R and C define the model and the frequency field becomes a consistency check rather than an overriding third independent parameter.

Output guide

Cutoff frequency is the primary result in Hz and is an exact identity of the ideal model once R and C are known. Resistance and Capacitance repeat the canonical solved values so you can see the missing component result even when its input field is blank. Time constant (RC) is R×C in seconds; a larger time constant means a lower corner frequency. Angular cutoff (ω_c) equals 2πf_c in radians per second. Gain at cutoff is always about – 3.01 dB for this first-order ideal amplitude response, corresponding to a magnitude of 1/√2. Texas Instruments' first-order RC filter application report shows the same transfer-function behavior and cutoff definition.

The three header pills summarize Mode, Cutoff, and Time constant. In the Response table, Frequency ratio states each test point relative to f_c; Frequency gives the actual Hz value; Magnitude is |Vout/Vin|; Gain is 20·log10(magnitude) in dB; and Phase is the ideal phase shift in degrees. The chart plots that same Gain series against logarithmic frequency ratio. A value near 0 dB means little amplitude attenuation, while increasingly negative dB means a smaller output-to-input amplitude ratio.

Worked example

With the startup values R = 10 kΩ = 10,000 Ω and C = 25 nF = 25×10 ^{– 9} F, the time constant is RC = 0.00025 s, or 250 µs. The cutoff is f_c = 1/(2πRC) = 1/(2π×0.00025) = 636.619772... Hz, displayed as 636.62 Hz. The angular cutoff is 1/RC = 4,000 rad/s. At the corner, the ideal magnitude is 1/√2 = 0.707107, giving 20 log10(0.707107) = – 3.01 dB. For the startup low-pass response, one decade above cutoff – about 6.37 kHz – the magnitude is approximately 0.0995 and the gain is about – 20.04 dB. These exact values are also written to the initial Excel workbook.

Learn more

For hands-on measurement context, Analog Devices' low-pass and high-pass filter training activity explains how to observe the corner on an oscilloscope. For a focused explanation of passband, stopband, and the – 3 dB concept, see the passive RC low-pass filter tutorial. In a physical design, treat the calculator as the ideal starting point, then evaluate resistor and capacitor tolerance, source impedance, load impedance, and parasitic effects against the bandwidth and attenuation your application actually requires.