Inductors and capacitors resist alternating current in a way that depends on frequency. That opposition is called reactance, and it is what lets these parts filter, tune and couple signals. This calculator gives the inductive and capacitive reactance at any frequency, the resonant frequency where the two cancel, the impedance and Q of a series RLC circuit, and the capacitor or inductor value needed to resonate at a chosen frequency.
How to use the reactance and resonance calculator
- Choose what you want to find. The default shows both reactances plus resonance; you can also compute XL or XC alone, or solve for the capacitor or inductor that tunes a circuit.
- Enter the frequency in Hz, kHz, MHz or GHz. For the tuning options this is the resonant frequency you want.
- Enter the inductance (nH to H) and/or capacitance (pF to mF) that the option needs.
- Optionally add the series resistance of the coil and wiring to see the circuit’s impedance, phase angle and Q.
- The table shows how the reactances change over four decades of frequency.
Reactance and resonance formulas
Inductive reactance grows with frequency and capacitive reactance shrinks, so on a log scale they are two straight lines that cross at f0. Below resonance a series LC circuit behaves like a capacitor; above it, like an inductor.
Worked examples
10 mH and 2.2 µF at 1 kHz with 10 Ω (the default)
XL = 2π × 1,000 × 0.01 = 62.83 Ω; XC = 1 ÷ (2π × 1,000 × 2.2 × 10⁻⁶) = 72.34 Ω.
Resonance: f0 = 1 ÷ (2π√(0.01 × 2.2 × 10⁻⁶)) = 1.073 kHz, just above the test frequency, so the circuit is slightly capacitive (net −9.511 Ω).
With 10 Ω: |Z| = √(10² + 9.511²) = 13.8 Ω at −43.6°, Q = 6.742 and the bandwidth is 159.2 Hz.
Tuning an AM-band circuit. To resonate a 100 µH coil at 1 MHz, choose the capacitor option: C = 1 ÷ ((2π × 10⁶)² × 10⁻⁴) = 253.3 pF. At resonance both reactances equal 628.3 Ω.
A capacitor on a 60 Hz line. A 10 µF capacitor has XC = 265.3 Ω at 60 Hz but only 2.653 Ω at 6 kHz, which is why capacitors are used to shunt high-frequency noise away while leaving the power frequency alone.
Reactance across the spectrum
| Part | 60 Hz | 1 kHz | 100 kHz | 10 MHz |
|---|---|---|---|---|
| 1 mH inductor | 0.377 Ω | 6.283 Ω | 628.3 Ω | 62.83 kΩ |
| 100 nF capacitor | 26.53 kΩ | 1.592 kΩ | 15.92 Ω | 0.159 Ω |
The two columns run in opposite directions, which is the whole basis of passive filters: an inductor in series and a capacitor to ground form a low-pass filter, and swapping them gives a high-pass filter.
Practical notes
Real inductors have winding resistance and stray capacitance, and real capacitors have equivalent series inductance, so every part has its own self-resonant frequency above which it behaves like the opposite component. Part tolerances of 5–20% also move the resonant frequency, so radio circuits use a trimmer to adjust it. For the energy stored in a capacitor or combining several, use the capacitor calculator; for how reactance affects AC power, the power factor calculator. The wavelength calculator converts a resonant frequency into a wavelength for antenna work.
Resonant circuits can develop voltages across L and C many times the supply voltage. These calculations are for estimation; follow your local electrical code and use a licensed electrician for installations.
Frequently asked questions
What is the formula for inductive reactance?
XL = 2πfL. It rises in proportion to frequency, so an inductor passes DC freely and opposes high frequencies. A 10 mH inductor at 1 kHz has XL = 2π × 1000 × 0.01 ≈ 62.83 Ω.
What is the formula for capacitive reactance?
XC = 1 ÷ (2πfC). It falls as frequency rises, so a capacitor blocks DC and passes high frequencies. A 10 µF capacitor at 60 Hz has XC = 1 ÷ (2π × 60 × 0.00001) ≈ 265.3 Ω.
How do I calculate resonant frequency?
f0 = 1 ÷ (2π√(LC)), the frequency where XL equals XC. A 10 mH inductor with a 2.2 µF capacitor resonates at about 1.073 kHz. At resonance a series LC circuit has its lowest impedance and a parallel LC circuit its highest.
What is the Q factor of a series RLC circuit?
Q = (1/R)√(L/C), the ratio of the reactance at resonance to the resistance. It describes how sharp the resonance is: the −3 dB bandwidth is f0 ÷ Q. With 10 mH, 2.2 µF and 10 Ω, Q ≈ 6.7 and the bandwidth is about 159 Hz.
Is reactance the same as resistance?
Both are measured in ohms, but resistance turns energy into heat while reactance stores it and returns it each cycle. Reactance also shifts the phase between voltage and current by 90°, so it combines with resistance as Z = √(R² + X²), not by simple addition.