Capacitive Reactance
Xc = 1 / (2πfC)
Quick answer
This calculator solves Xc = 1 / (2πfC) for Reactance. With Frequency 1 kHz, Capacitance 100 µF, the result is 1.592 Ω. It solves in 3 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
Capacitive reactance is the frequency-dependent opposition that a capacitor presents to alternating current. Unlike resistance, reactance does not dissipate energy as heat but instead stores and releases it in the electric field between the capacitor plates. At low frequencies the capacitor has time to fully charge and block current flow, resulting in high reactance. At high frequencies the capacitor barely charges before the polarity reverses, presenting very low opposition. At DC (0 Hz), a capacitor is an open circuit with infinite reactance.
Variables
- Xc — Capacitive reactance in ohms (Ω)
- f — Frequency in hertz (Hz)
- C — Capacitance in farads (F)
Practical Notes
Capacitive reactance causes current to lead voltage by 90 degrees. This phase relationship is essential in filter design, power factor correction, and coupling/decoupling applications. In bypass capacitor selection, choose a capacitor whose reactance is less than one-tenth of the circuit impedance at the frequency of interest.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| Xc | Reactance | Ω | mΩ, Ω, kΩ, MΩ |
| f | Frequency | Hz | Hz, kHz, MHz, GHz |
| C | Capacitance | µF | pF, nF, µF, mF, F |
Step by step
- 1. What you know: Frequency 1 kHz, Capacitance 100 µF
- 2. The relation: Xc = 1 / (2πfC)
- 3. Substitute: f = 1 kHz, C = 100 µF
- 4. Result: Reactance = 1.592 Ω
Nearest standard component values
| Series | Nearest value | Error |
|---|---|---|
| E12 | 1.5 Ω | 5.8% |
| E24 | 1.6 Ω | 0.53% |
Worked examples
Minimum range
Given: Frequency 5 Hz, Capacitance 100 nF
Result: Reactance = 0.3183 MΩ
Low range
Given: Frequency 50 Hz, Capacitance 1 µF
Result: Reactance = 3.183 kΩ
Typical
Given: Frequency 1 kHz, Capacitance 100 µF
Result: Reactance = 1.592 Ω
High range
Given: Frequency 20 kHz, Capacitance 1 mF
Result: Reactance = 7.958 mΩ
Maximum range
Given: Frequency 0.2 MHz, Capacitance 10 mF
Result: Reactance = 0.07958 mΩ
Solving for each variable
Solve for Reactance
Frequency 5 Hz, Capacitance 100 nF → 0.3183 MΩ
Solve for Frequency
Reactance 1 Ω, Capacitance 100 nF → 1.592 MHz
Solve for Capacitance
Reactance 1 Ω, Frequency 5 Hz → 31.83 mF
How Reactance changes with Frequency
| Frequency (input) | Reactance (result) |
|---|---|
| 100 Hz | 15.92 Ω |
| 0.25 kHz | 6.366 Ω |
| 0.5 kHz | 3.183 Ω |
| 0.75 kHz | 2.122 Ω |
| 1 kHz | 1.592 Ω |
| 1.5 kHz | 1.061 Ω |
| 2 kHz | 0.7958 Ω |
| 4 kHz | 0.3979 Ω |
| 7 kHz | 0.2274 Ω |
| 10 kHz | 0.1592 Ω |
The same result in other units
| Unit | Value |
|---|---|
| mΩ | 1592 |
| Ω | 1.592 |
| kΩ | 0.001592 |
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<p><a href="https://vbatpower.com/formulas/capacitive-reactance/">Capacitive Reactance</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Capacitive Reactance?
Use Xc = 1 / (2πfC). With Frequency 1 kHz, Capacitance 100 µF, Reactance works out to 1.592 Ω.
What is the formula for Capacitive Reactance?
The formula is Xc = 1 / (2πfC). Capacitive reactance is the frequency-dependent opposition that a capacitor presents to alternating current.
How do you find Frequency when you know the other values?
Rearrange for Frequency: with Reactance 1 Ω, Capacitance 100 nF, Frequency is 1.592 MHz.
How do you find Capacitance when you know the other values?
Rearrange for Capacitance: with Reactance 1 Ω, Frequency 5 Hz, Capacitance is 31.83 mF.
What units does Capacitive Reactance use?
Reactance is shown in mΩ, Ω, kΩ. Values are held in SI base units internally, so you can mix prefixes without converting by hand.
Related Concepts
All Capacitors formulas →Need more features?
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