Capacitance to Impedance Calculator
Evaluate capacitive reactance in Ohms from capacitance and AC frequency, or convert impedance back to farad storage limits. Settle AC filter networks dynamically.
Capacitance & Impedance Converter
How to Use the Capacitance to Impedance Calculator
Converting capacitor physical storage size into active capacitive reactance impedance is direct. Follow these steps:
- 1Enter Frequency: Input the AC system frequency and select your operating unit (Hz, kHz, or MHz).
- 2Enter Capacitance: Input the target capacitance value and select the appropriate farad unit (Farad, mF, µF, nF, or pF).
- 3Calculate: Click the "Calculate to Impedance" button to run the conversion.
How to Convert Capacitance to Impedance
In alternating current (AC) networks, capacitors present an opposition to current flow known as capacitive reactance (or capacitive impedance). Unlike static DC circuits where capacitors act as open circuit blocks, AC systems experience dynamic charge and discharge cycles that permit sinusoidal current flow. Capacitor impedance is inversely proportional to both the system frequency and the physical capacitance size in Farads. Designing passive filter circuits, sizing motor start capacitors, and matching RF antennas requires converting capacitance to impedance. To calculate the impedance in Ohms, divide one by the product of two, Pi, frequency, and capacitance.
Real-Life Sizing Scenarios
Scenario 1: Sizing Input Impedance for Power Supply Ripple Filters
An engineer checks the input impedance presented by a 10 µF AC filtering capacitor connected to a standard 60 Hz utility line. Sizing the equivalent capacitive impedance:
Impedance = 1 ÷ (2 × π × 60 Hz × 10 × 10⁻⁶ F) = 265.26 Ω
Scenario 2: Sizing High-Frequency RF Coupling Capacitors
An RF technician measures a small 100 nF capacitor in a signal path operating at 1 MHz. Sizing the signal opposition impedance:
Impedance = 1 ÷ (2 × π × 10⁶ Hz × 100 × 10⁻⁹ F) = 1.59 Ω
Step-by-Step Manual Sizing Guide
- 1Identify circuit parameters: Settle the AC operating frequency (Hz) and target capacitance (F).
- 2Apply Reactance Formula: Write:
Z = 1 ÷ (2 × π × f × C). - 3Solve the calculation: Multiply 2, Pi, frequency, and capacitance, then take the reciprocal to find Ohms.
Capacitance to Impedance Conversion Chart
The table below displays standard capacitance sizes and their corresponding capacitive impedance values at a utility frequency of 50 Hz:
| Capacitance | Impedance (Ω at 50 Hz) |
|---|---|
| 1.0 µF | 3183.10 Ω |
| 2.2 µF | 1446.86 Ω |
| 4.7 µF | 677.26 Ω |
| 10.0 µF | 318.31 Ω |
| 22.0 µF | 144.69 Ω |
| 47.0 µF | 67.73 Ω |
| 100.0 µF | 31.83 Ω |
Capacitor Impedance Formula
The standard thermodynamic reactance conversion formula dividing one by the product of 2, Pi, frequency, and capacitance to find Ohms:
Xc = 1 ÷ (2 × π × f × C)
Impedance Formula for Capacitor and Resistor
When a capacitor is paired with a resistor in series, the total complex circuit impedance (Z) is found using vector addition:
Z = √(R² + Xc²)
Where R is resistance in Ohms and Xc is capacitive reactance.
Capacitor Impedance Graph
An ideal capacitive impedance graph plots impedance (Y-axis) against frequency (X-axis). The curve shows a hyperbolic decrease, demonstrating that capacitor opposition drops as frequency rises.
Impedance of Capacitor and Inductor in Parallel
In a parallel LC resonant tank, the net impedance is determined by combining their reactances:
Zp = (Xl × Xc) ÷ (Xl - Xc)
At the resonant frequency, the parallel impedance theoretically approaches infinity.
Capacitor Impedance vs Frequency
Because capacitive reactance is inversely proportional to frequency, raising the frequency drops the impedance. For example, a 10 µF capacitor presents 318.3 Ω at 50 Hz, but only 0.318 Ω at 50 kHz.
Frequently Asked Questions (FAQs)
To convert capacitance to impedance, you must know the AC operating frequency. Apply the capacitive reactance formula: Z = 1 ÷ (2 × π × f × C). This calculation converts the capacitor's storage capacity in Farads into its equivalent opposition to alternating current in Ohms.
To calculate impedance from capacitance, multiply 2, Pi (3.14159), the AC frequency in Hertz, and the capacitance in Farads. Take the reciprocal of this product: Z = 1 ÷ (2 × π × f × C). For example, a 10 µF capacitor operating at 50 Hz has an impedance of approximately 318.31 Ohms.
Impedance and capacitance share an inverse relationship. If you increase the capacitance (or frequency), the capacitor's impedance decreases. Conversely, smaller capacitors or lower frequencies result in higher impedance because the capacitor restricts AC current flow more severely.
The formula for the capacitive reactance impedance is: Xc = 1 ÷ (2 × π × f × C). In complex notation, it is represented as Zc = -j ÷ (2 × π × f × C), where the negative imaginary 'j' operator shows a 90-degree phase shift between voltage and current.
No, increasing capacitance decreases impedance. A larger capacitor has a greater electrostatic surface area, which allows it to charge and discharge more current per cycle. This reduces its opposition to AC flow at any given frequency.
The 'Z' represents the total electrical impedance of the capacitor. In an ideal capacitor, Z is equal to its capacitive reactance (Xc). In real-world capacitors, Z also includes the equivalent series resistance (ESR) and equivalent series inductance (ESL): Z = R_esr + j(Xl - Xc).
Yes. Smaller capacitors have less physical storage capacity, which limits the amount of AC current that can pass through them. Consequently, they present a higher capacitive impedance to the circuit compared to larger capacitors operating at the same frequency.