Cutoff Frequency Calculator: RC, RL, and LC Filters
Enter your component values to find the -3 dB cutoff frequency of an RC, RL, or LC passive filter. Switch the "Solve for" selector to reverse the calculation and find the resistor, capacitor, or inductor you need to hit a target frequency. All results include the time constant, angular frequency, and a worked step-by-step solution.
Formula
Worked example
RC example: R = 10 kohm, C = 25 nF. fc = 1 / (2 * 3.14159 * 10000 * 25e-9) = 1 / (1.5708e-3) = 636.6 Hz. The time constant is tau = RC = 10000 * 25e-9 = 250 us. RL example: R = 1 kohm, L = 10 mH. fc = 1000 / (2 * 3.14159 * 0.01) = 15.915 kHz. LC example: L = 10 mH, C = 25 nF. fc = 1 / (2 * 3.14159 * sqrt(0.01 * 25e-9)) = 1 / (2 * 3.14159 * 15.81e-6) = 10.07 kHz.
What is cutoff frequency?
The cutoff frequency (fc) of a passive filter is the frequency at which the output signal power drops to half of the passband value, which corresponds to a gain of -3 dB. At this frequency the output voltage is 1/sqrt(2), roughly 70.7%, of the input voltage. Below fc, a low-pass filter passes signals with little attenuation; above it, attenuation increases steadily. A high-pass filter does the reverse: it blocks low frequencies and passes high ones. The cutoff point is the boundary between these two zones.
RC filter: formula and worked example
An RC filter consists of a resistor R and a capacitor C. The -3 dB cutoff frequency is fc = 1 / (2 * pi * R * C), where R is in ohms and C is in farads. The time constant tau = RC determines how quickly the circuit responds to a step input: after one tau the output reaches 63.2% of its final value, and after 5 tau it is within 1%. Example: R = 10 kohm and C = 25 nF gives fc = 1 / (2 * 3.14159 * 10,000 * 25e-9) = 636.6 Hz. This is one of the most common filter circuits in electronics, used for audio tone shaping, noise rejection, and anti-aliasing.
RL filter: formula and how it differs from RC
An RL filter pairs a resistor R with an inductor L. The cutoff frequency is fc = R / (2 * pi * L). The time constant is tau = L/R, the dual of the RC case. RL filters behave identically to RC filters in terms of frequency response shape, with the same -20 dB/decade rolloff, but inductors are bulkier and more expensive than capacitors for audio frequencies. RL filters are preferred in power applications and RF chokes, where inductors handle high currents better than capacitors can.
LC filter: resonant frequency and characteristic impedance
An LC filter uses an inductor L and a capacitor C with no resistor in the signal path. The resonant (cutoff) frequency is fc = 1 / (2 * pi * sqrt(L * C)). This is a second-order circuit: the Bode magnitude falls at -40 dB per decade beyond fc, giving sharper roll-off than first-order RC or RL filters. The characteristic impedance Z0 = sqrt(L/C) is the impedance both components present at the resonant frequency. LC filters are used in radio-frequency circuits, power supply EMI filters, and anywhere a steep rolloff is needed without insertion loss.
Reverse-solving: finding R, C, or L for a target frequency
In circuit design you often know the target cutoff and need the component values. Rearranging the RC formula: R = 1 / (2 * pi * fc * C) or C = 1 / (2 * pi * fc * R). For RL: R = 2 * pi * fc * L or L = R / (2 * pi * fc). For LC: L = 1 / ((2 * pi * fc)^2 * C) or C = 1 / ((2 * pi * fc)^2 * L). After computing the exact value, select the nearest standard resistor (E12 or E24 series) or capacitor (E6 or E12 series) and re-enter the real component value to see the resulting frequency shift.
Bode plot and the -20 dB/decade rolloff
The Bode magnitude plot shows gain in decibels versus frequency on a log scale. For a first-order RC or RL filter, gain is flat at 0 dB in the passband, drops to -3 dB at fc, and then falls at exactly 20 dB for every ten-fold increase in frequency (one decade). At 10 * fc the attenuation is about -20 dB, at 100 * fc it is about -40 dB. A second-order LC filter has a rolloff of -40 dB per decade. The phase shift is -45 degrees at fc for a first-order filter. This calculator generates the Bode gain curve for your values so you can see exactly how gain varies from 0.01 fc to 100 fc.
Common passive filter applications and typical cutoff frequencies
| Application | Circuit | Typical fc | Purpose |
|---|---|---|---|
| Audio tone control | RC | 100 Hz - 10 kHz | Treble and bass shelving |
| Audio anti-aliasing | RC or LC | 20 kHz | Limit bandwidth before ADC sampling |
| AM radio IF filter | LC | 455 kHz | Select intermediate frequency |
| FM radio IF filter | LC | 10.7 MHz | Select FM intermediate frequency |
| Power supply decoupling | RC or LC | 1 Hz - 10 kHz | Reject switching noise from DC rail |
| Debounce filter | RC | 10 - 100 Hz | Smooth mechanical switch bounce |
| EMI suppression | LC | 1 - 30 MHz | Attenuate high-frequency conducted emissions |
| Sensor signal conditioning | RC | 10 - 500 Hz | Remove HF noise from slow sensors |
Approximate -3 dB frequencies for common signal-conditioning circuits.
Frequently asked questions
What does the -3 dB cutoff frequency mean?
-3 dB means the output power is exactly half the input power. In voltage terms the output is 1/sqrt(2), about 70.7%, of the input. This is the standard definition of the filter bandwidth boundary, and it is the point where the RC or RL time constant equals the reciprocal of the angular frequency.
What is the difference between a low-pass and a high-pass filter with the same RC values?
The components are identical; only the output tap changes. In a low-pass RC filter the output is taken across the capacitor. In a high-pass filter it is taken across the resistor. Both have the same cutoff frequency fc = 1/(2*pi*RC), but the low-pass attenuates signals above fc and the high-pass attenuates signals below fc.
Why is the LC formula different from the RC formula?
An LC circuit has two reactive components and no resistor loss. Energy oscillates between the magnetic field of the inductor and the electric field of the capacitor. The resonant frequency where this exchange is in balance is fc = 1/(2*pi*sqrt(LC)). Because there are two energy-storing components, the slope of attenuation beyond resonance is -40 dB/decade rather than the -20 dB/decade of a first-order RC or RL filter.
How do I choose between RC, RL, and LC for my circuit?
Use RC for most audio and signal-conditioning applications: resistors and capacitors are cheap, small, and easy to source. Use RL when you need to handle large currents without significant voltage drop (inductors have low DC resistance). Use LC when you need steep roll-off, low insertion loss in the passband, or you are working at radio frequencies where inductor Q is high and resistive loss matters.
What is the time constant and why does it matter?
The time constant tau is RC for an RC circuit or L/R for an RL circuit. It sets how quickly the circuit responds in the time domain: a step input reaches 63.2% of its final value after one tau, 86.5% after two tau, and 99.3% after five tau. The cutoff frequency is related by fc = 1/(2*pi*tau). A shorter time constant means a higher cutoff frequency and a faster transient response.
How do I pick the nearest standard component value?
After computing the exact R or C needed, round to the nearest value in the E12 resistor series (10, 12, 15, 18, 22, 27, 33, 39, 47, 56, 68, 82 and their decade multiples) or the E6 capacitor series (10, 15, 22, 33, 47, 68). Then re-enter the standard value into this calculator to see how much the actual fc shifts from your target. Typical shift is under 10%.
Can I cascade two RC filters to get a steeper rolloff?
Yes, but with a caveat. Two cascaded identical RC filters give a -6 dB point (not -3 dB) at the frequency where each stage alone would be at -3 dB. The overall -3 dB frequency shifts lower. For a true second-order response with -40 dB/decade rolloff and a defined passband, use an LC filter or an active filter (op-amp Sallen-Key or multiple-feedback topology) instead.
What is the angular frequency and how is it different from cutoff frequency?
Angular frequency omega is measured in radians per second: omega = 2 * pi * fc. It appears directly in the circuit equations (reactance of a capacitor is 1/(omega*C), reactance of an inductor is omega*L). The cutoff frequency fc in hertz is what you measure with a frequency counter or spectrum analyzer. Both express the same physical boundary; omega is more convenient in equations and fc is more convenient in specifications.