About

Miscalculating a filter's cutoff frequency shifts the −3 dB point, causing signal attenuation in the passband or inadequate rejection in the stopband. In power supply design, a wrong f_c allows ripple through; in audio crossovers, it distorts frequency separation between drivers. This calculator computes the cutoff (corner) frequency for first-order RC and RL filters, and the resonant frequency for second-order RLC and LC circuits using the standard relation f_c = 12π√LC. It also derives quality factor Q and −3 dB bandwidth where applicable.

Component tolerances (typically ±5% for resistors, ±10 - 20% for ceramic capacitors) propagate directly into f_c error. This tool assumes ideal components with zero parasitic inductance and capacitance. For frequencies above 100 MHz, PCB trace inductance and stray capacitance dominate, and these results become approximate. Pro tip: always verify with a network analyzer at RF frequencies.

Formulas

For a first-order RC filter (both low-pass and high-pass configurations), the cutoff frequency is defined as the point where output power drops to half (−3 dB) of the passband value:

f_c = 12πRC

For a first-order RL filter:

f_c = R2πL

For second-order RLC and LC circuits, the resonant (center) frequency is:

f₀ = 12π√LC

The quality factor for an RLC series circuit:

Q = 1R √LC

For an RLC parallel circuit:

Q = R √CL

Bandwidth is derived from:

BW = f₀Q

Where R = resistance in Ω, C = capacitance in F, L = inductance in H, f_c = cutoff frequency in Hz, Q = quality factor (dimensionless), BW = bandwidth in Hz.

Reference Data

Filter Type	Order	Cutoff Formula	Roll-off	Phase Shift at f_c	Typical Application
RC Low-Pass	1st	f_c = 12πRC	−20 dB/dec	−45°	Audio noise filtering, ADC anti-aliasing
RC High-Pass	1st	f_c = 12πRC	−20 dB/dec	+45°	DC blocking, audio coupling
RL Low-Pass	1st	f_c = R2πL	−20 dB/dec	−45°	EMI suppression, power filtering
RL High-Pass	1st	f_c = R2πL	−20 dB/dec	+45°	Signal differentiation
RLC Series Band-Pass	2nd	f₀ = 12π√LC	−40 dB/dec	0°	Radio tuning, IF stages
RLC Parallel Band-Pass	2nd	f₀ = 12π√LC	−40 dB/dec	0°	Tank circuits, oscillators
LC Low-Pass	2nd	f_c = 12π√LC	−40 dB/dec	−90°	Power supply output filtering
LC High-Pass	2nd	f_c = 12π√LC	−40 dB/dec	+90°	Tweeter crossover networks
Butterworth (2nd)	2nd	f_c = 12π√LC	−40 dB/dec	−90°	Maximally flat passband
Chebyshev Type I	2nd	Depends on ripple ε	−40 dB/dec	Variable	Steeper roll-off, passband ripple
Bessel (2nd)	2nd	f_c ≈ 1.272π√LC	−40 dB/dec	Linear phase	Pulse preservation, data comms
Sallen-Key LP	2nd	f_c = 12π√R₁R₂C₁C₂	−40 dB/dec	−90°	Active audio filters
Wien-Bridge Band-Pass	2nd	f₀ = 12πRC	Narrow band	0°	Oscillators, tone generation
Notch (Twin-T)	2nd	f_notch = 12πRC	Band-reject	±90°	50/60 Hz hum rejection
All-Pass (1st order)	1st	f_c = 12πRC	0 dB	−90°	Phase compensation, delay lines

Frequently Asked Questions

A resistor with ±5% tolerance and a capacitor with ±20% tolerance can shift f_c by up to ±25% in worst-case combination. For an RC filter designed at 1 kHz, the actual cutoff could land anywhere between 750 Hz and 1.25 kHz. Use 1% metal-film resistors and C0G/NP0 capacitors for precision filter applications.

RL filters are preferred in power electronics and high-current paths where inductors handle current without the energy storage limitations of capacitors. At low frequencies (100 Hz), inductors become physically large and expensive, making RC filters more practical. Above 1 MHz, inductor parasitic capacitance degrades performance. The crossover point depends on impedance level: RL filters suit low-impedance circuits (<50 Ω), while RC filters suit high-impedance circuits.

Quality factor Q is the ratio of energy stored to energy dissipated per cycle. A Q of 10 means the circuit rings for roughly 10 cycles before the amplitude decays to 37% (1/e). Higher Q produces narrower bandwidth: BW = f₀ ÷ Q. For radio receivers, Q > 50 provides good selectivity. For wideband amplifiers, Q ≈ 0.707 (Butterworth) gives maximally flat response.

The cutoff frequency depends only on the RC time constant τ = RC, which is identical for both configurations. The difference is topological: in a low-pass, the capacitor is the output element (shorts high frequencies to ground); in a high-pass, the capacitor is the series element (blocks DC). The −3 dB point occurs at the same frequency where capacitive reactance X_C = R.

Above roughly 10 MHz, resistor lead inductance (typically 5 - 20 nH) creates a self-resonance. Ceramic capacitors exhibit equivalent series resistance (ESR) and equivalent series inductance (ESL) that cause impedance to rise above their self-resonant frequency. A 100 nF ceramic capacitor may self-resonate near 15 MHz, beyond which it behaves as an inductor. PCB traces add roughly 1 nH/mm of parasitic inductance. These effects make calculated f_c values unreliable above 100 MHz without full electromagnetic simulation.

Yes, but each cascaded stage shifts the overall −3 dB point. Two identical RC stages in series give −40 dB/dec roll-off, but the combined −3 dB frequency drops to roughly 0.644 × f_c of a single stage. For n identical stages, multiply by the correction factor √2^1/n − 1. Impedance loading between stages also attenuates the signal unless buffer amplifiers are used.