# [Capacitor Impedance Calculator](https://blog.hirnschall.net/tools/capacitor-impedance/)

author: [Sebastian Hirnschall](https://blog.hirnschall.net/about/)

meta description: Calculate capacitive reactance, impedance magnitude, and phase angle. Solve for X_C, capacitance, or frequency given the other two. Optional series resistance.

meta title: Capacitor Impedance Calculator — Reactance, |Z|, and Phase Angle

date published: 01.04.2025 (DD.MM.YYYY format)
date last modified: 22.04.2025 (DD.MM.YYYY format)

---

Calculator
----------

Fill in any two of \( f \), \( C \), \( X\_C \) — the third is solved. \( R \) is optional: if provided, \( |Z| \) and \( \phi \) are computed as additional outputs. \( \phi \) can also be used as an input together with \( R \) to replace one of the three main variables.

* Frequency (f):
* Hz
  kHz
  MHz

* Capacitance (C):
* F
  mF
  µF
  nF
  pF

* Capacitive reactance (XC):
* Ω
  kΩ
  MΩ

---

* Resistance (R) — optional:
* Ω
  kΩ
  MΩ

* Phase angle (φ) — optional:
* deg
  rad

Fill in any two of f, C, X\_C to calculate.

Calculate



Capacitive Reactance — Explanation
----------------------------------

A capacitor resists changes in voltage. At AC, this opposition is called capacitive reactance \( X\_C \) and depends on both the capacitance and the signal frequency:
\[
X\_C = \frac{1}{2\pi f C}
\]
Where:

* \( X\_C \) is the capacitive reactance (in Ohms, \( \Omega \)),
* \( f \) is the frequency (in Hertz, \( \text{Hz} \)),
* \( C \) is the capacitance (in Farads, \( \text{F} \)).

Unlike resistance, reactance is frequency-dependent: \( X\_C \) decreases as frequency increases. At DC (\( f = 0 \)) a capacitor blocks current entirely — \( X\_C \to \infty \). At very high frequencies it approaches a short circuit — \( X\_C \to 0 \). This is the basis for using capacitors as high-pass or low-pass filter elements.

Purpose of the Calculator
-------------------------

Given any two of \( f \), \( C \), \( X\_C \), the calculator solves for the third. The rearranged formulas are:

* To solve for \( X\_C \):
  \[
  X\_C = \frac{1}{2\pi f C}
  \]
* To solve for \( C \):
  \[
  C = \frac{1}{2\pi f X\_C}
  \]
* To solve for \( f \):
  \[
  f = \frac{1}{2\pi X\_C C}
  \]

Full Impedance with Series Resistance
-------------------------------------

A real capacitor or RC circuit also has a series resistance \( R \). The total impedance magnitude and phase angle are:
\[
|Z| = \sqrt{R^2 + X\_C^2}
\]
\[
\phi = -\arctan\!\left(\frac{X\_C}{R}\right)
\]
The phase angle \( \phi \) is always negative for a capacitor, meaning the current leads the voltage. It ranges from \( 0° \) (purely resistive, \( X\_C \ll R \)) to \( -90° \) (purely capacitive, \( X\_C \gg R \)).

If \( \phi \) and \( R \) are known instead of \( X\_C \), the reactance can be recovered:
\[
X\_C = -R \cdot \tan(\phi)
\]

More info
---------

Looking for more helpful tools and calculators? Explore a wide range of resources to simplify your engineering projects and calculations. Head over to our [tools section](https://blog.hirnschall.net/tools/) to find our free online calculators.  
For actual projects and informational articles head over to [blog.hirnschall.net](https://blog.hirnschall.net/).