Capacitive Reactance Calculator: X = 1 / (2 pi f C)

The opposition of a capacitor to alternating current.

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

Choose which quantity you want to find.

Enter the other values in the units shown.

The calculator gives the answer with the formula, the substituted numbers, and the answer in other units.

Formulas used

  • X_C = \frac{1}{2\pi fC}
  • C = \frac{1}{2\pi fX_C}

Worked example

With the default numbers in the calculator above:

  1. The formula, arranged to find the capacitive reactance: capacitive reactance = (1/(2 pi)) / (frequency x capacitance)
  2. Put the values in (every value in its SI unit): capacitive reactance = (1/(2 pi)) / (50 x 0.0001)
  3. The answer: capacitive reactance: 31.831 ohm
  4. The same answer in other units: 0.031831 kohm

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

A second worked example

A different case, with these numbers: What do you want to find? Capacitance; Capacitive reactance (leave it as it is if this is what you are finding) 31.831 ohm; Frequency (leave it as it is if this is what you are finding) 50 Hz.

  1. The formula, arranged to find the capacitance: capacitance = (1/(2 pi)) / (capacitive reactance x frequency)
  2. Put the values in (every value in its SI unit): capacitance = (1/(2 pi)) / (31.831 x 50)
  3. The answer: capacitance: 0.0001 F
  4. The same answer in other units: 100 uF; 100000 nF

Common questions

What is the formula for capacitive reactance?

One over two pi times the frequency times the capacitance. 100 uF at 50 Hz has a reactance of 31.8 ohm.

Does a capacitor block DC?

Yes. At zero frequency the reactance is very large, so no steady current flows.

How is it different from an inductor?

The reactance of a capacitor falls with frequency, while that of an inductor rises.

Related calculators

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Further reading: Any electrical text (reactance).

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