Capacitance to Reactance Calculator
Evaluate capacitive reactance (Xc) in Ohms from capacitance and AC frequency, or convert reactance back to required farad storage limits. Settle AC components dynamically.
Capacitance & Reactance Converter
How to Use the Capacitance to Reactance Calculator
Converting physical storage size of a capacitor to active capacitive reactance (opposition in Ohms) is direct. Follow these steps:
- 1Enter Frequency: Input the AC frequency of the system and select the frequency 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 Reactance" button to run the conversion.
How to Convert Capacitance to Reactance
In alternating current (AC) networks, capacitive reactance (Xc) represents the opposition a capacitor presents to sinusoidal AC current flow. Unlike resistance, which dissipates energy as heat, reactance stores and returns energy to the electric field. Capacitive reactance is inversely proportional to both the frequency of the AC signal and the physical capacitance rating in Farads. Designing passive high-pass/low-pass filters, sizing motor start capacitors, and matching RF lines requires converting capacitance to reactance. To calculate capacitive reactance in Ohms, divide one by the product of two, Pi, frequency, and capacitance.
Real-Life Sizing Scenarios
Scenario 1: Sizing Reactance for AC Power Supply Filters
An electrical technician evaluates the reactance of a large 200 µF filter capacitor operating on a standard 60 Hz power system line. Sizing the equivalent capacitive reactance:
Reactance (Xc) = 1 ÷ (2 × π × 60 Hz × 200 × 10⁻⁶ F) = 13.26 Ω
Scenario 2: Sizing Reactance for Motor Run Capacitors
A motor designer checks a 5 µF starting capacitor operating at 60 Hz. Sizing the signal path reactance:
Reactance (Xc) = 1 ÷ (2 × π × 60 Hz × 5 × 10⁻⁶ F) = 530.52 Ω
Step-by-Step Manual Sizing Guide
- 1Identify system values: Settle the AC operating frequency (Hz) and target capacitance (F).
- 2Apply Reactance Formula: Write:
Xc = 1 ÷ (2 × π × f × C). - 3Solve the calculation: Multiply 2, Pi, frequency, and capacitance, and divide 1 by the product.
Capacitance to Reactance Conversion Chart
The table below displays standard capacitance sizes and their corresponding capacitive reactance (Xc) values at a standard frequency of 60 Hz:
| Capacitance | Reactance (Xc at 60 Hz) |
|---|---|
| 1.0 µF | 2652.58 Ω |
| 5.0 µF | 530.52 Ω |
| 10.0 µF | 265.26 Ω |
| 20.0 µF | 132.63 Ω |
| 50.0 µF | 53.05 Ω |
| 100.0 µF | 26.53 Ω |
| 200.0 µF | 13.26 Ω |
Convert Capacitance to Reactance
To convert a capacitor's physical size in farads to capacitive reactance in ohms, divide one by the product of 2, Pi, frequency, and capacitance:
Xc = 1 ÷ (2 × π × f × C)
Capacitance to Reactance
The mathematical relationship where capacitor opposition decreases as frequency or capacitance increases. This is key for designing high-pass and low-pass audio filters.
How to Find Capacitance with Capacitive Reactance
To calculate the required capacitance size when the target reactance and frequency are known, rearrange the equation:
C = 1 ÷ (2 × π × f × Xc)
How to Find Capacitive Reactance without Capacitor
If the physical capacitor is unavailable, you can measure AC voltage across the capacitive component (Vc) and current passing through it (Ic) to calculate reactance using Ohm's Law:
Xc = Vc ÷ Ic
Capacitive Reactance to Capacitance Formula
The standard thermodynamic reactance conversion formula rearranged to solve for physical capacitance:
C = 1 ÷ (2 × π × f × Xc)
How to Calculate Capacitive Reactance
Step-by-step math converts Farads to Ohms. Multiply 2, Pi, frequency, and capacitance, and divide 1 by the result:
Xc = 1 ÷ (2 × π × f × C)
How to Find Capacitive Reactance
Settle the capacitive reactance by inputting the system parameters (operating AC frequency and capacitor farad rating) into the calculator tool or formula.
Capacitive Reactance to Capacitance Calculation
The calculation converting impedance in Ohms to capacitance in Farads. Sizing filter networks requires this conversion to select matching commercial components.
Frequently Asked Questions (FAQs)
To convert capacitance to reactance, multiply 2, Pi (3.14159), the AC operating frequency in Hertz, and the capacitance in Farads. Take the reciprocal of this product: Xc = 1 ÷ (2 × π × f × C). This calculation converts the capacitor's storage capacity into its equivalent opposition to AC in Ohms.
At 60 Hz, a 200 µF capacitor has a capacitive reactance of exactly 13.26 Ohms. Settle this by applying the formula: Xc = 1 ÷ (2 × π × 60 × 0.0002 F) = 13.26 Ω. This represents the total opposition to alternating current flow for the capacitor under these specific frequency limits.
A capacitive reactance calculator is an interactive tool that performs bidirectional conversions between capacitance (Farads) and capacitive reactance (Ohms) at specific operating AC frequencies. It helps electrical engineers and students size components accurately without manual calculation errors.
Capacitive reactance is the opposition a capacitor presents to alternating current (AC) flow. Unlike static DC circuits where capacitors block all current, AC systems allow capacitors to charge and discharge continuously, which creates a frequency-dependent impedance measured in Ohms.
No. Capacitance is a physical property of a capacitor that measures its ability to store an electrostatic charge (in Farads). Reactance is the electrical opposition (in Ohms) that capacitance creates when connected to an active AC system, and it changes dynamically with the operating frequency.
Frequency and capacitive reactance share an inverse relationship. If you increase the operating AC frequency, the capacitive reactance decreases. Conversely, at low frequencies, the capacitive reactance increases, becoming theoretically infinite in static DC circuits (zero frequency).