Capacitive and inductive reactance calculator
Enter a frequency and an inductance, a capacitance, or both. You get XL, XC, the net reactance and — when both are there — the frequency where they cancel. Add a series resistance for the impedance and its angle.
Composants idéaux : une vraie bobine a aussi la résistance de son enroulement — entrez-la comme résistance série.
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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:
- XL = 2πfLrises with frequency
- XC = 1 ÷ (2πfC)falls with frequency
- Z = √(R² + X²)X = XL − XC in series
f is in hertz, L in henries, C in farads — the calculator converts mH, µF and the rest for you. Where XL and XC 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
- XL = 2π × 60 × 0,1 = 37,70 Ω.
- XC = 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 fréquentes
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: XL 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 XC 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 = XL − XC. 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).
Voir aussi
- 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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