Capacitor and Inductor Reactance and Resonance Calculator

Find the capacitor and inductor reactance at a frequency, the impedance and current of a series R-L-C circuit, the phase angle and the resonant frequency.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

A capacitor opposes a change in voltage. Its reactance is one over two pi times the frequency times the capacitance, so it falls as the frequency rises. An inductor opposes a change in current. Its reactance is two pi times the frequency times the inductance, so it rises with frequency.

In a series circuit the two reactances act in opposite directions. The net reactance and the resistance combine at right angles to give the impedance. When the reactances are equal the circuit is at resonance.

Formulas used

  • X_C = \dfrac{1}{2\pi f C}
  • X_L = 2\pi f L
  • Z = \sqrt{R^2 + (X_L - X_C)^2}
  • f_0 = \dfrac{1}{2\pi\sqrt{LC}}

Worked example

With the default numbers in the calculator above:

  1. Capacitor reactance: 67.73 Ω
  2. Inductor reactance: 31.42 Ω
  3. Net reactance: -36.31 Ω
  4. Impedance of the series circuit: 37.66 Ω
  5. Phase angle (positive: current lags the voltage): -74.60 °
  6. Power factor: 0.27
  7. Resonant frequency (where X_L = X_C): 73.41 Hz
  8. Current drawn: 6.11 A
  9. Voltage across the capacitor and across the inductor: 413.60 V and 191.86 V

Change the numbers in the calculator to see the full working, every step, for your own case.

Common questions

Why can the voltage across a part be higher than the supply?

Near resonance the voltages across the capacitor and the inductor are large and nearly cancel, so each can be far above the supply voltage.

What is reactance measured in?

Ohms, like resistance, but it stores and returns energy instead of turning it into heat.

Related calculators

Further reading: Standard electrical engineering texts (alternating current circuits).

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