Reactance to Impedance Calculator
Evaluate total electrical impedance magnitude (Z) from resistance (R) and reactance (X), or convert measured circuit impedance back to reactive limits. Settle phase loads dynamically.
Reactance to Impedance Converter
How to Use the Reactance to Impedance Calculator
Converting conductor resistance (R) and circuit reactance (X) to total impedance (Z) is direct. Follow these steps:
- 1Enter Resistance: Input the circuit resistance (R) in Ohms.
- 2Enter Reactance: Input the net inductive or capacitive reactance (X) in Ohms.
- 3Select Unit: Choose Ohms (Ω), kilohms (kΩ), or megohms (MΩ).
- 4Calculate: Click the "Calculate to Impedance" button to run the vector sum.
How to Convert Reactance to Impedance
In alternating current (AC) circuits, impedance (Z) represents the total opposition to the flow of current. Unlike DC circuits where resistance (R) is the only opposing factor, AC systems must also account for reactance (X), which is the opposition caused by capacitors and inductors. Because resistance and reactance operate 90 degrees out of phase, they cannot be added algebraically. Instead, they must be combined vectorially using the Pythagorean theorem. The total impedance is represented as the hypotenuse of the impedance triangle, with resistance as the adjacent side and reactance as the opposite side.
Real-Life Sizing Scenarios
Scenario 1: Sizing Winding Impedance for an Induction Motor
An electrical engineer calculates the winding impedance of a motor stator possessing a resistance of 8 Ohms and an inductive reactance of 6 Ohms:
Z = √(8² + 6²) = √(64 + 36) = √100 = 10.00 Ohms
Scenario 2: Sizing an AC Filter Node
A technician calculates total impedance for an AC filter featuring a resistance of 120 Ohms in series with a capacitive reactance of 50 Ohms:
Z = √(120² + 50²) = √(14400 + 2500) = √16900 = 130.00 Ohms
Step-by-Step Manual Sizing Guide
- 1Identify circuit metrics: Settle the resistance (R) and reactance (X) in Ohms.
- 2Apply the Sizing Formula: Write:
Z = √(R² + X²). - 3Solve the calculation: Square both resistance and reactance, sum the results, and calculate the square root to find Z.
Reactance to Impedance Conversion Chart
The table below displays typical resistance and reactance values along with their calculated total impedance magnitudes in Ohms (Ω):
| Resistance (R) | Reactance (X) | Calculated Impedance (Z) |
|---|---|---|
| 3.00 Ω | 4.00 Ω | 5.00 Ω |
| 8.00 Ω | 6.00 Ω | 10.00 Ω |
| 12.00 Ω | 5.00 Ω | 13.00 Ω |
| 20.00 Ω | 15.00 Ω | 25.00 Ω |
| 30.00 Ω | 40.00 Ω | 50.00 Ω |
| 50.00 Ω | 50.00 Ω | 70.71 Ω |
| 80.00 Ω | 60.00 Ω | 100.00 Ω |
| 120.00 Ω | 50.00 Ω | 130.00 Ω |
Reactance to Impedance Formula
The total electrical impedance magnitude is calculated as the vector sum of resistance and reactance:
Z = √(R² + X²)
How to Convert Reactance to Impedance
Because resistance and reactance are perpendicular phasor quantities, convert them to impedance by squaring both values, adding them, and taking the square root: Z = √(R² + X²).
Capacitive Reactance to Impedance
Capacitive reactance opposes AC current and lags the voltage by 90 degrees. Combine it with resistance vectorially:
Z = √(R² + X_C²)
Inductive Reactance to Impedance
Inductive reactance opposes current changes and leads voltage by 90 degrees. Combine it with series resistance:
Z = √(R² + X_L²)
How to Calculate Impedance from Resistance and Reactance
Impedance calculation involves taking the square root of the sum of the squared resistance and reactance values. This magnitude represents the total impedance vector length.
Ratio of Impedance to Capacitive Reactance Has
The ratio of total impedance (Z) to capacitive reactance (X_C) in an RC series circuit represents the cosecant of the phase angle. It determines the relative sizing of voltage drop components.
Convert Impedance to Resistance and Reactance
To convert impedance back to resistance and reactance, use: R = √(Z² − X²) and X = √(Z² − R²). This requires knowing at least one of the other parameters.
How to Find Impedance with Resistance and Inductive Reactance
Substitute resistance (R) and inductive reactance (X_L) into the Pythagorean magnitude formula: Z = √(R² + X_L²) to compute total AC impedance.
Frequently Asked Questions (FAQs)
To convert reactance (X) to impedance (Z), you must combine it with series resistance (R) using the magnitude formula: Z = √(R² + X²).
Reactance is the imaginary (reactive) component of impedance. Impedance represents the total complex value combining both real resistance and imaginary reactance: Z = R + jX.
First, convert inductance (L) to inductive reactance using the frequency (f): X_L = 2πfL. Then, combine X_L with resistance (R) to calculate total impedance: Z = √(R² + X_L²).
To find inductive reactance (X_L) from total impedance (Z) and resistance (R), rearrange the magnitude formula: X_L = √(Z² − R²).
Yes. Like resistance and impedance, reactance is measured in Ohms (Ω) because it represents a physical opposition to alternating current flow.
The formula for the magnitude of impedance is: Z = √(R² + X²). In complex phasor notation, it is written as: Z = R + jX.
