# Capacitive Reactance Calculator

By Wojciech Sas, PhD candidate
Last updated: Oct 21, 2020

This is the capacitive reactance calculator - a great tool that helps you estimate the so-called resistance of a capacitor in an electric circuit. You can find the capacitive reactance formula in the text below, and we explain why the reactance occurs for alternating current but not direct current. If you want to know how to calculate the capacitive reactance, you're at the right place - let's go!

## What is a capacitive reactance?

Reactance is a property of an electric circuit element to oppose the flow of current. Using this definition, we can say that the capacitive reactance is like capacitor resistance. Even the unit of reactance is the same as resistance - the Ohm (`Ω`). Typically, we denote a reactance as `X`.

Although both the reactance (`X`) and the resistance (`R`) tend to be the same thing in a circuit, there is a certain distinction between them. The reactance influences the alternating current (AC), while the resistance affects the direct current (DC). In general, they are the components of an impedance `Z`, a complex quantity which determines the total opposition of a circuit to the current flow:

`Z = R ± j * X`,

where `j = √-1` is an imaginary number (square root of a negative number).

The capacitive reactance is a property of a capacitor. Similarly, the inductive reactance is a property of an inductor. An ideal resistor has zero reactance while it's a purely resistive element. On the contrary, perfect capacitors and inductors have zero resistance.

So, strictly speaking, there is no such thing as capacitor resistance. We usually treat this phrase as a mental shortcut for the capacitive reactance.

## How to calculate capacitive reactance? Capacitive reactance formula

As we've mentioned in the previous section, the capacitive reactance is a capacitor's property that opposes alternating current. The same is true for any set of capacitors that we can arrange in series or parallel.

One of the crucial properties of AC is its frequency `f`. We can calculate the capacitive reactance `X` of a capacitor `C` using the following equation:

`X = 1 / (2 * π * f * C)`.

Alternatively, we can write the capacitive reactance formula as:

`X = 1 / (ω * C)`,

where `ω = 2 * π * f` is the angular frequency of the current.

As you can see, the higher the frequency of the capacitance, the lower the reactance. Does it make sense?

Absolutely! Remember that a capacitor stores electric energy. While it's charging, it looks like the capacitor passes the current almost freely. The more it can absorb (the higher the capacity), the less it resists to let the current flow. Additionally, when the AC frequency gets higher, the less time there is for the capacitor to charge fully. In the case of DC (`f = 0`), the capacitor initially charges, but then (in the equilibrium state), it acts as an open circuit.

## How to use the capacitive reactance calculator?

There is nothing challenging about estimating the capacitive reactance of any capacitor. Let's practice the computations with an example.

Let's say we have a circuit with a spherical capacitor of a capacitance `C = 30 nF`. We apply a voltage source, which alternates with the frequency `f = 60 Hz`. What is the capacitive reactance in this circuit?

1. Convert the unit of the capacitance to Farads. We can use scientific notation to write the values compactly: `C = 30 nF = 3·10⁻⁸ F`.

2. Work out the product of all the values in the denominator from the capacitive reactance formula: `2 * π * f * C = 2 * π * 60 * 3·10⁻⁸ = 1.131·10⁻⁵`.

3. Find its multiplicative inverse, which is the ratio of `1` and our product: `1 / 1.131·10⁻⁵ = 88,419.41 Ω`. Don't forget about the unit of reactance!

4. Write the result using an appropriate prefix: `X = 88.41941 kΩ`.

5. Let's round the outcome to four significant figures:

`X = 88.42 kΩ`.

6. Check the result with our capacitive reactance calculator! Wow, relatively painless, wasn't it?

Wojciech Sas, PhD candidate
Capacitance (C)
pF
Frequency (f)
Hz
Reactance (X)
Ω
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