LC resonance and RC/RL filter calculator

Resonant frequency of a coil and capacitor, or the L or C you need for a frequency, with the reactances. Below it, the −3 dB cutoff and time constant of simple RC and RL filters. Results update as you type.

Indicative calculation; verify before use.

LC resonance

Solve for

Inductance L

Capacitance C

Frequency f

Use a prefix: p, n, u or µ, m, k, M, G (10u = 10 µH, 100p = 100 pF, 7.1M = 7.1 MHz). 4u7 and 2n2 work too. m is milli, M is mega.

Result

Resonant frequency

–

Inductive reactance X_L at f: –
Capacitive reactance X_C at f: –
Characteristic impedance √(L/C): –
Angular frequency ω = 2πf: –
Period 1/f: –
Wavelength in free space: –

RC and RL filters (first order)

RC: resistor and capacitor

Resistance R

Capacitance C

Cutoff (−3 dB) frequency f_c

–

Time constant τ = RC: –
ω_c = 1/τ: –
Step 63.2 % / 99.3 % at τ / 5τ: –

RL: resistor and inductor

Resistance R

Inductance L

Cutoff (−3 dB) frequency f_c

–

Time constant τ = L/R: –
ω_c = 1/τ: –
Step 63.2 % / 99.3 % at τ / 5τ: –

Response at a frequency

Signal frequency

Gain is the output/input voltage ratio with no load on the output and a source with zero internal resistance.

Filter	f / f_c	Gain	Gain (dB)	Phase
RC low-pass	–	–	–	–
RC high-pass	–	–	–	–
RL low-pass	–	–	–	–
RL high-pass	–	–	–	–

Low-pass: output across the capacitor (RC) or the resistor (RL). High-pass: output across the resistor (RC) or the inductor (RL).

How it works

f = 1 / (2π √(L C)) L = 1 / ((2π f)² C), C = 1 / ((2π f)² L) X_L = 2π f L, X_C = 1 / (2π f C) RC: τ = R C, f_c = 1 / (2π R C) RL: τ = L / R, f_c = R / (2π L) Low-pass |H| = 1 / √(1 + (f/f_c)²), phase = −atan(f/f_c) High-pass |H| = (f/f_c) / √(1 + (f/f_c)²), phase = 90° − atan(f/f_c) Gain in dB = 20 log10 |H|; step response 1 − e^(−t/τ)

A coil and a capacitor resonate where their reactances are equal: X_L rises with frequency and X_C falls, and they cross at f = 1/(2π√LC). In a series LC circuit the impedance is lowest there, in a parallel (tank) circuit it is highest. The calculator assumes ideal parts: real coils have resistance and self-capacitance, and stray capacitance from wiring and the circuit around it adds to C, so a real circuit usually resonates a little lower. That matters most with small capacitors at HF and VHF.

An RC or RL filter of first order rolls off by 6 dB per octave (20 dB per decade) beyond the cutoff. At f_c the output is 1/√2 = 0.707 of the input (−3.01 dB) with 45° phase shift. The same R and C give the same f_c for low-pass and high-pass; only where you take the output changes. A load on the output or resistance in the source changes the cutoff.

Worked example (LC): L = 10 µH and C = 100 pF. √(LC) = √(10⁻⁵ × 10⁻¹⁰) = 3.1623 × 10⁻⁸ s, so f = 1 / (2π × 3.1623 × 10⁻⁸) = 5.033 MHz. At that frequency X_L = 2π × 5.033 MHz × 10 µH = 316.2 Ω and X_C = 1 / (2π × 5.033 MHz × 100 pF) = 316.2 Ω, equal as they must be. To resonate at 7.1 MHz with L = 2 µH: C = 1 / ((2π × 7.1 MHz)² × 2 µH) = 251.2 pF.

Worked example (RC and RL): R = 10 kΩ and C = 100 nF give τ = 10⁴ × 10⁻⁷ = 1 ms and f_c = 1 / (2π × 1 ms) = 159.2 Hz. At 1 kHz, f/f_c = 6.283, so the RC low-pass passes 1 / √(1 + 6.283²) = 0.1572 of the input (−16.07 dB, phase −80.96°) and the high-pass 0.9876 (−0.11 dB). R = 100 Ω and L = 10 mH give τ = 10 mH / 100 Ω = 0.1 ms and f_c = 1.592 kHz.

Sources (checked 2026-11-03):

Resonant frequency of an LC circuit, series and parallel resonance: https://en.wikipedia.org/wiki/LC_circuit
X_L = 2πfL and X_C = 1/(2πfC): https://en.wikipedia.org/wiki/Electrical_reactance
RC low-pass/high-pass, τ = RC, cutoff and phase: https://en.wikipedia.org/wiki/RC_circuit
RL filters, τ = L/R: https://en.wikipedia.org/wiki/RL_circuit
−3 dB cutoff frequency: https://en.wikipedia.org/wiki/Cutoff_frequency
Time constant and step response 1 − e^(−t/τ): https://en.wikipedia.org/wiki/Time_constant