Second year AC theory Free · works offline once loaded

Capacitive and inductive reactance calculator

Enter a frequency and an inductance, a capacitance, or both. You get X_L, X_C, the net reactance and — when both are there — the frequency where they cancel. Add a series resistance for the impedance and its angle.

Frequency, then an inductance, a capacitance, or both.

Frequency (Hz) Inductance Inductance unit Capacitance Capacitance unit Series resistance (Ω) optional

X_L inductive—

X_C capacitive—

Net X—

Resonant freq.—

Impedance Z—

Phase angle—

Ideal parts: a real coil also has its winding resistance — enter it as the series resistance.

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How it works

Reactance is the opposition a coil or a capacitor puts up to alternating current. It is measured in ohms like resistance, but it takes no power — it stores energy and hands it back each half-cycle. Two formulas do all of it:

X_L = 2πfLrises with frequency
X_C = 1 ÷ (2πfC)falls with frequency
Z = √(R² + X²)X = X_L − X_C in series

f is in hertz, L in henries, C in farads — the calculator converts mH, µF and the rest for you. Where X_L and X_C are equal they cancel; that frequency is f₀ = 1 ÷ (2π√(LC)), the resonant frequency.

Worked example

100 mH and 100 µF in series with 10 Ω, at 60 Hz

X_L = 2π × 60 × 0.1 = 37.70 Ω.
X_C = 1 ÷ (2π × 60 × 0.0001) = 1 ÷ 0.037699 = 26.53 Ω.
Net X = 37.70 − 26.53 = 11.17 Ω, inductive (the coil wins).
Z = √(10² + 11.17²) = √(100 + 124.8) = 14.99 Ω, at atan(11.17 ÷ 10) = 48.2° lagging.
Resonance: 1 ÷ (2π√(0.1 × 0.0001)) = 1 ÷ (2π × 0.003162) = 50.33 Hz. On a 50 Hz supply this pair would nearly cancel.

Questions people ask

Why does inductive reactance go up with frequency but capacitive reactance goes down?

A coil fights change in its current, and a higher frequency means faster change, so it fights harder: X_L rises in step with f. A capacitor has to charge and discharge every half-cycle; the faster that happens, the less charge builds up to oppose the supply, so X_C falls as f rises. At zero frequency (DC) a coil is just its wire resistance and a capacitor is an open circuit.

What is the net reactance?

Inductive and capacitive reactance push the current in opposite directions in time — one makes it lag, the other lead — so in a series circuit they subtract. X = X_L − X_C. A positive answer means the circuit acts inductive; negative, capacitive; zero is resonance.

Why can’t I just add the resistance to the reactance?

Because they are 90° apart. Resistance takes power in step with the voltage; reactance stores it and gives it back a quarter-cycle later. They combine like the two short sides of a right triangle: Z = √(R² + X²).

Reactance and impedance — the lesson behind this tool.
Inductance — the lesson behind this tool.
Capacitance — the lesson behind this tool.
RC / RL time constant calculator — the same parts, switched on instead of fed AC.
Power triangle & power factor — what reactance does to the watts.
Power factor — in the glossary.
Single & three phase formula sheet

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