Filter Cutoff Frequency
Cutoff and resonant frequency for RC, RL, and LC filters.
The half-power point, where output amplitude falls to 1/√2 of the input — about 70.7%.
The filter reaches 63% of a step change in one τ, and about 99% in five. fc and τ are the same fact: fc = 1 ÷ (2πτ).
The same RC network is a low-pass or a high-pass filter depending only on where the output is taken — across the capacitor gives low-pass, across the resistor gives high-pass. The cutoff frequency is identical either way, so one number covers both.
An RC filter turns over at fc = 1 ÷ (2πRC), so 1 kΩ with 100 nF gives 1.59 kHz. An LC circuit resonates at f₀ = 1 ÷ (2π√(LC)) — 10 mH with 100 nF resonates at about 5.03 kHz.
The corner is where power halves
The cutoff frequency is not where a filter stops working — filters have no such point. It is the −3 dB frequency, where the output amplitude has fallen to 1/√2 of the input, about 70.7%. Since power goes as amplitude squared, that is exactly half the power, which is why it is also called the half-power point.
Beyond the corner a simple one-stage filter rolls off at 6 dB per octave, or 20 dB per decade: ten times the frequency gives a tenth of the amplitude. Getting a sharper transition means cascading stages, and each additional order adds another 6 dB per octave.
Low-pass and high-pass are the same circuit
This surprises people learning filters: an RC low-pass and an RC high-pass use identical components in the same arrangement. The only difference is where the output is taken. Across the capacitor gives low-pass, because the capacitor's reactance falls as frequency rises and shorts the high frequencies away. Across the resistor gives high-pass for the same reason inverted.
Because the components are the same, so is the cutoff frequency — one calculation covers both, which is why this tool does not ask which one you are building.
The RC and RL time constants are τ = RC and τ = L/R, and fc = 1 ÷ (2πτ) in both cases — the corner frequency and the time constant are the same fact in different units.
Worked example: 1 kΩ and 100 nF
Time constant first, then the corner:
- 1 Multiply R by C. 1000 Ω × 100 × 10⁻⁹ F = 100 µs. This is the time constant τ.
- 2 Apply the 2π factor. 2π × 100 µs = 628 µs.
- 3 Invert. 1 ÷ 628 µs ≈ 1592 Hz — the −3 dB corner.
- 4 Sanity-check the direction. Bigger R or bigger C means a longer time constant and therefore a lower cutoff. Both slow the circuit down.
- 5 Read the roll-off. At 15.9 kHz — ten times the corner — a low-pass output is down about 20 dB, to a tenth of the amplitude.
RC cutoff frequencies
fc = 1 ÷ (2πRC). Note that scaling R and C in opposite directions leaves the corner unchanged.
| Resistor | Capacitor | Cutoff |
|---|---|---|
| 1 kΩ | 100 nF | 1.59 kHz |
| 10 kΩ | 100 nF | 159 Hz |
| 1 kΩ | 1 µF | 159 Hz |
| 10 kΩ | 10 nF | 1.59 kHz |
| 4.7 kΩ | 22 nF | 1.54 kHz |
| 100 kΩ | 1 µF | 1.59 Hz |
Choosing the component values
Any R and C giving the right product will produce the right corner, but the absolute values still matter. A very low resistance loads whatever drives the filter and wastes current; a very high one makes the circuit sensitive to stray capacitance and to the input impedance of whatever comes next. Resistors in the 1 kΩ to 100 kΩ range are the usual compromise, with the capacitor chosen to suit.
The one thing a passive RC filter cannot do is present a constant impedance to both sides. Connecting a second RC stage directly to the first changes the first stage's behaviour, because the second one loads it. That is why cascaded passive filters do not simply multiply, and why active filters — which buffer each stage with an op-amp — exist.
For the LC case, the characteristic impedance √(L/C) matters as much as the frequency: together with the circuit resistance it determines how sharp the resonance is. A high-Q circuit rings and is selective; a heavily damped one is broad and settles quickly. Which you want depends entirely on whether you are building a radio tuner or suppressing a transient.