Cutoff Frequency Calculator - RC and RL -3 dB Corner Frequency

A cutoff frequency calculator solves for the corner frequency of an RC or RL filter directly from resistance and capacitance, or resistance and inductance, without converting units by hand. The result fc in hertz is the frequency at which the filter output power has fallen to one-half of its passband value, also known as the -3 dB point. The form also reports omega c, the cutoff period, and tau.

• • RC Low-Pass and High-Pass Filters: Find the -3 dB cutoff of a first-order RC filter from a resistor and capacitor.
• • RL High-Pass Networks: Find the cutoff of an RL high-pass network used in audio crossovers and DC bias removal.
• • Audio Crossover and Tone-Control Design: Choose R and C (or R and L) so the cutoff lands on the desired speaker crossover or de-emphasis frequency.
• • Time-Constant to Frequency Conversion: Convert a measured tau equals R C or L over R into the matching fc for oscilloscope cross-checks.

The form is most useful when filter design starts with the passive components on hand rather than a target frequency, since fc is what connects component selection to frequency response. The same form covers classroom problems, lab measurements, and audio product design because the RC and RL formulas drive every first-order passive filter.

Because the RC cutoff depends on capacitive reactance at the same frequency, the Capacitive Reactance Calculator is the right next step when the question is the per-frequency Xc value of the capacitor.

The form reads the filter topology selector to decide whether to use the RC formula or the RL formula. It then converts the resistance, capacitance, and inductance values into base SI units and applies fc = 1 divided by 2 pi R C or fc = R divided by 2 pi L. The result is the cutoff frequency in hertz for the chosen topology.

• fc: Cutoff frequency in hertz at which the filter output is attenuated by 3 dB.
• R: Series resistance in ohms.
• C: Capacitance in farads. Used only for the RC topology.
• L: Inductance in henries. Used only for the RL topology.
• tau: Time constant tau equals R C for RC filters and L divided by R for RL filters. The cutoff period equals 2 pi tau.

For RC, the form multiplies the entered resistance by 1000 or 1,000,000 for kohm or Mohm so the internal value is always in ohms. The capacitance is scaled into farads using the chosen unit, the product R C is formed, and fc follows as 1 divided by 2 pi tau.

For RL, the form scales the inductance into henries, divides it by the ohms value of the resistor, and applies fc = R divided by 2 pi L. Switching topologies re-runs the same logic with a different component pair, so the result panel always reflects one internally consistent filter.

According to the Wikipedia RC circuit article, the cutoff frequency equals one divided by two pi R C, the point at which the filter attenuates the signal to half its unfiltered power and the voltage gain drops to one over root two

According to BIPM SI Brochure, the hertz is the SI unit of frequency and one full cycle equals 2 pi radians, which is why a cutoff frequency in Hz corresponds to an angular cutoff omega c in rad/s

When the goal is to pick C for a target fc, the Capacitance Calculator converts between capacitance units so the right component value can be ordered.

Four ideas make every cutoff frequency calculator result easier to interpret: the topology, tau, the -3 dB corner, and the difference between cutoff and resonant frequency.

Keeping these four concepts separate prevents the most common reporting mistake: quoting a cutoff value where a resonant value is expected, or treating tau as a period instead of the time needed for the step response to reach 63.2 percent of its final value. The factor of two pi between fc and omega c is the same relationship used throughout oscillation, wave, and AC circuit analysis.

Because omega c is just 2 pi fc, the Angular Frequency Calculator is the natural extension when the result needs to be reported in rad/s for transfer-function analysis.

Pick the topology, enter the resistance and matching reactive component, and read fc in hertz alongside the period and omega c rows in the result panel.

1. 1 Select the filter topology: Use the Filter Topology dropdown to choose RC (R and C) or RL (R and L).
2. 2 Enter the resistance: Type the resistor value. The unit selector lets you enter ohm, kohm, or Mohm without pre-converting.
3. 3 Enter the reactive component: For RC, type the capacitance and pick F, mF, uF, nF, or pF. For RL, type the inductance and pick H, mH, or uH.
4. 4 Read fc and the supporting rows: The primary result is fc in hertz. Other rows show the same filter in rad/s, period in seconds, and tau.

For a 1 kohm resistor and 100 nF capacitor in a low-pass filter, switch to RC mode and read fc = 1591.55 Hz before plugging it into a Bode plot.

When only the cycles-per-second side of the answer matters, the Frequency Calculator handles the period, wavelength, and Hz conversions without the RC step.

The form speeds up the unit math and makes the -3 dB corner easier to verify against other electrical-engineering tools.

• • Covers both RC and RL filters: A single form handles both topologies, fitting passive low-pass, high-pass, and coupling-network design.
• • Internally consistent outputs: Changing R, C, L, or any unit selector recomputes tau, fc, omega c, and the period.
• • Direct fit for transfer functions: omega c in rad/s is the argument that transfer-function, Bode plot, and Laplace-domain analysis expect.
• • Cross-checking against lab measurements: The tau row compares to an oscilloscope trace of the step response.
• • Quick classroom reference: Worked examples next to the formula give students a known answer to compare against by-hand work.

The form is most useful when the next step in the design already uses omega c, because omega c is the value that fits a transfer function, Bode plot, or Laplace analysis without an extra conversion layer. If only the frequency or only the time constant is needed, the math-conversion and capacitance peers below cover those simpler conversions directly.

Once fc is known, the Wave Speed Calculator extends the result to wavelength and speed for the same wave, which is useful in transmission-line and audio-bandwidth problems.

The cutoff formulas themselves are exact, so most result differences come from the input source, unit choice, or precision kept during calculation.

• • The form assumes an ideal first-order RC or RL filter. It does not model second-order RLC responses, op-amp active filters, or parasitic capacitance.
• • Output units are limited to hertz, radians per second, and seconds. Conversions to RPM, degrees per second, or cycles per minute are not produced.

When a measured value disagrees with the calculator, the first check is whether the unit selector matches the entered number, and the second is whether the topology selector matches the actual circuit. Both are common sources of factor-of-thousand mismatches, since two pi is exact and once the internal R, C, or L value is correct, fc is mathematically fixed.

According to NIST Guide for the Use of the SI, capacitance is measured in farads, inductance in henries, resistance in ohms, and frequency in hertz, which are the units used in the RC and RL cutoff formulas

When the cutoff value is needed in cycles per minute or per hour for documentation, the CPS Converter translates the Hz value without losing precision.