Reactance & LC Resonance Calculator

Capacitive reactance Xc and inductive reactance XL at a frequency, C or L for a target reactance, LC resonant frequency, and capacitor current and kvar.

Frequency f (Hz)Capacitor C Inductor L

Capacitor voltage U (V rms) — current and reactive powerTarget reactance X (Ω) — solve C or L

Results
Capacitive reactance Xc = 1 ÷ (2π f C)
Inductive reactance XL = 2π f L
LC resonant frequency f0
Characteristic impedance √(L/C)
Capacitor current / reactive power at U
C for X at this f
L for X at this f

The defaults (50 Hz, 100 µF, 10 mH) are an example. Real parts change with tolerance, temperature, voltage and frequency, and inductors also have resistance.

Results update as you type. Everything runs in your browser; nothing you type is sent anywhere.

Formulas

Xc = 1 ÷ (2π × f × C) — falls as frequency rises
XL = 2π × f × L — rises with frequency
f0 = 1 ÷ (2π × √(L × C)) — where Xc = XL
Z0 = √(L ÷ C)
Capacitor current I = U ÷ Xc, reactive power Q = U² ÷ Xc = 2π f C U²

Xc by capacitance

C	50 Hz	60 Hz	1 kHz
100 nF	31.83 kΩ	26.53 kΩ	1.592 kΩ
1 µF	3.183 kΩ	2.653 kΩ	159.2 Ω
10 µF	318.3 Ω	265.3 Ω	15.92 Ω
100 µF	31.83 Ω	26.53 Ω	1.592 Ω
1000 µF	3.183 Ω	2.653 Ω	0.1592 Ω

How to read it

A capacitor passes current more easily as frequency rises (Xc falls); an inductor blocks it more (XL rises). At DC (0 Hz) a capacitor is an open circuit and an ideal inductor a short.
The same capacitor at 60 Hz has 5/6 of its 50 Hz reactance, so 1.2 times the current and reactive power.
At resonance Xc equals XL and they cancel. A series LC has its lowest impedance there and a parallel LC its highest (ideal parts).

Where it is used

Power factor capacitors: check one capacitor's current and kvar from its µF and voltage. About 367 µF at 400 V, 50 Hz is about 18.4 kvar (the same example as the Power Factor Correction Capacitor Calculator).
Estimate the corner of an LC low-pass filter (e.g. a supply noise filter) from f0. Real filters change shape with the load and the parts' resistance.
For reactors on drives or motors quoted in ohms, look at XL at the operating frequency — the reactance changes with frequency.

FAQ

What is the capacitive reactance formula?

Xc = 1 ÷ (2π f C). 100 µF at 50 Hz is 1 ÷ (2π × 50 × 0.0001) ≈ 31.8 Ω, and about 26.5 Ω at 60 Hz.

What is the inductive reactance formula?

XL = 2π f L. 10 mH is about 3.14 Ω at 50 Hz and about 62.8 Ω at 1 kHz.

How do I find the LC resonant frequency?

f0 = 1 ÷ (2π √(LC)). 10 µH with 100 nF gives about 159 kHz, where Xc and XL are both 10 Ω.

How do reactance and resistance add?

For R and X in series the magnitude is √(R² + X²) — they are 90° apart, so they do not simply add. This calculator shows reactance only.

For the RC time constant and first-order low-pass cut-off, use the RC Time Constant & Cut-off Calculator. For power factor capacitor sizing (kvar → µF), use the Power Factor Correction Capacitor Calculator.

Basis

Xc, XL, resonant frequency, characteristic impedance, capacitor current and reactive power are all computed from AC circuit definitions. Check part tolerances and equivalent series resistance in their datasheets.