A capacitor resists alternating current, and that resistance is called capacitive reactance. It depends on two things only: the frequency of the signal and the size of the capacitor. This guide shows the formula and the unit traps to avoid.
How it works
Capacitive reactance Xc = 1 / (2 x pi x f x C), where f is frequency in hertz and C is capacitance in farads. Larger capacitance gives smaller reactance, and higher frequency gives smaller reactance too. The result is in ohms. The common trap is units: capacitors are usually labelled in microfarads, so convert to farads first by multiplying by 10^-6.
Step by step
- Write down the frequency in hertz and the capacitance, converting microfarads to farads.
- Multiply 2 x pi x frequency x capacitance.
- Take the reciprocal: 1 divided by that product.
- Read the result in ohms.
- Check the direction: doubling frequency should halve the reactance.
- For a circuit check, combine reactance with resistance using impedance, not by simple addition.
Worked example
Frequency 1,000 Hz, capacitance 10 microfarads = 10 x 10^-6 = 0.00001 farads. Denominator = 2 x 3.1416 x 1000 x 0.00001 = 0.0628. Xc = 1 / 0.0628 = 15.9 ohms. At 10,000 Hz with the same capacitor, Xc falls to about 1.59 ohms, ten times smaller, which matches the rule that reactance falls as frequency rises.
Common mistakes
- Using microfarads directly as farads, which makes the answer a million times too small.
- Saying larger capacitance raises reactance. It lowers it.
- Forgetting the 2 x pi factor, which makes the answer about six times too large.
- Adding reactance to resistance directly instead of using the impedance formula for AC circuits.
Try it with the free tool
You can follow every step above by hand, but the free tool below does the same calculation instantly. Try your own numbers in it, then check one result by hand so you trust the method as well as the answer. Open the full tool here: open the tool.
Checklist before you finish
- Write down every input number first, with its unit, before you calculate anything.
- Work through the steps in order, and do not skip the unit conversions.
- Check the answer against the worked example above: is it the right size, and does the direction make sense?
- Round only at the end, and keep the unrounded figure for any follow-up calculation.
Practice with your own numbers
Pick three cases of your own and work each one by hand. First, try a simple round-number case you can check mentally. Second, try a realistic case with awkward numbers, the kind you will actually meet. Third, try an edge case, such as a very small or very large input, and confirm the answer still behaves sensibly. If any case gives a surprising result, re-check the units and the formula step by step before you trust it.
If your answer looks wrong
Most errors come from a small set of causes. Check that you used the same units throughout, that you divided where the formula divides and multiplied where it multiplies, and that you applied any percentage as a decimal. Check the order of operations: powers and brackets come before multiplication and division, which come before addition and subtraction. Finally, test the method on the worked example in this guide. If your method reproduces the example answer, the method is right and the inputs deserve a second look.
Quick tips
At mains frequency, 50 or 60 Hz, even a large capacitor has noticeable reactance, which is why capacitors are used for motor starting and power-factor correction. Always state frequency with a reactance value; without it, the number is meaningless.