Impedance Calculator
Calculate total electrical impedance, magnitude, and phase angle for RL, RC, and RLC AC circuits instantly. Supports multiple units for resistance, reactance, inductance, capacitance, and frequency.
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Impedance Calculator
Calculations are standard engineering estimates based on balanced loads. Real values depend on component tolerances and supply grid conditions.
💡 Impedance combines resistance and reactance in AC circuits and is measured in ohms (Ω). It determines the opposition offered to alternating current flow.
How to Use Impedance Calculator
Determining total impedance in alternating current (AC) circuits is essential for analyzing power distribution networks and industrial electrical designs. Follow this step-by-step workflow to configure your parameters and compute circuit impedance values:
- Step 1: Select Calculation Mode. Select from three available modes: Resistance and Reactance, Resistance and Inductance with Frequency (RL series circuit), or Resistance and Capacitance with Frequency (RC series circuit).
- Step 2: Enter Resistance (R). Input the nominal resistance value of the circuit, choosing between ohms (Ω) and kilohms (kΩ).
- Step 3: Enter Reactance or Circuit Components. Depending on the selected mode, input the Reactance (X) in ohms, the Inductance (L) in henries or millihenries, or the Capacitance (C) in farads or microfarads.
- Step 4: Enter AC System Frequency (f). If you chose the inductive or capacitive mode, enter the frequency of the AC signal in hertz (Hz) or kilohertz (kHz).
- Step 5: Click Calculate. Press the Calculate Impedance button to compute the magnitude, complex representation, and phase angle.
- Step 6: Review Outputs. Evaluate the total impedance magnitude, the complex impedance form (R ± jX), and the phase angle in degrees. Click Reset to perform a new calculation.
How to Calculate Impedance
Electrical impedance is a complex quantity that generalizes Ohm's law to AC circuit analysis. While resistance opposes current directly, reactance accounts for the phase shifts introduced by inductors and capacitors. Follow these mathematical engineering procedures to evaluate total impedance:
Step 1: Calculate Reactance if Inductor or Capacitor is Present
If you have inductance (L) or capacitance (C) in your AC circuit, calculate their respective reactances at the system frequency (f) using these equations. You can verify these values using our reactance calculator.
Step 2: Calculate Net Reactance (X)
In a standard series circuit, the net reactance is the difference between inductive and capacitive reactance. In pure RL circuits, net reactance is positive (X = XL), whereas in pure RC circuits, reactance is negative (X = -XC).
Step 3: Calculate Total Impedance Magnitude (Z)
Compute the magnitude of total impedance by combining resistance and reactance quadratically, using the Pythagorean theorem.
Step 4: Calculate Phase Angle (θ)
Determine the angular displacement between the voltage and current waveforms. This represents how much the current lags or leads the voltage waveform.
Verified Engineering Calculation Example
Consider a practical RL series circuit with the following balanced parameters:
- Resistance (R): 10 Ω
- Inductive Reactance (XL): 15 Ω
Step 1: Calculate Impedance Magnitude (Z)
Z = √(102 + 152)
Z = √(100 + 225)
Z = √(325) = 18.03 Ω
Step 2: Calculate Phase Angle (θ)
θ = tan-1(15 / 10)
θ = tan-1(1.5)
θ = 56.3°
Walkthrough Final Verified Results
- Impedance Magnitude (|Z|): 18.03 Ω
- Complex Impedance Form (Z): 10.00 + j15.00 Ω
- Phase Angle (θ): 56.3° (Current lags voltage by 56.3 degrees)
Impedance calculations are vital in electrical design to size protective devices like circuit breakers, calculate expected voltage drops using a voltage drop calculator, select transformers, design industrial AC motors, and model overall electrical power system loads.
Impedance Chart
This reference chart displays total impedance magnitude and phase angle values calculated across common combinations of resistance (R) and reactance (X) in AC circuits. All calculations assume a standard series connection.
| Resistance (Ω) | Reactance (Ω) | Impedance (Ω) | Phase Angle (°) |
|---|---|---|---|
| 5 Ω | 5 Ω | 7.07 Ω | 45.0° |
| 10 Ω | 5 Ω | 11.18 Ω | 26.6° |
| 10 Ω | 10 Ω | 14.14 Ω | 45.0° |
| 10 Ω | 15 Ω | 18.03 Ω | 56.3° |
| 20 Ω | 10 Ω | 22.36 Ω | 26.6° |
| 25 Ω | 25 Ω | 35.36 Ω | 45.0° |
| 50 Ω | 20 Ω | 53.85 Ω | 21.8° |
| 100 Ω | 50 Ω | 111.80 Ω | 26.6° |
Note: Values are based on the impedance equation Z = √(R² + X²).
Impedance Calculator Frequently Asked Questions
Impedance is the total opposition that a circuit offers to the flow of alternating current (AC) at a given frequency. It combines both resistance, which opposes current in both AC and DC circuits, and reactance, which only opposes AC due to inductance and capacitance. Impedance is represented as a complex number and is measured in ohms (Ω).
To calculate impedance (Z), use the formula Z = √(R² + X²), where R is the resistance and X is the net reactance. Reactance consists of inductive reactance (XL = 2πfL) and capacitive reactance (XC = 1 / (2πfC)). By calculating R and X from the circuit components, you can find the impedance magnitude and its phase angle using θ = tan⁻¹(X / R).
Resistance is the opposition to electrical current flow in both AC and DC circuits, dissipating energy as heat. Impedance is a broader term used only in AC circuits that combines resistance and reactance. Unlike resistance, impedance depends on the frequency of the AC signal and accounts for phase shifts between the voltage and current waveforms.
Impedance is crucial in power systems for sizing conductors, analyzing short-circuit currents, and designing protection systems. High impedance can lead to significant voltage drops and power losses across transmission lines, while matching impedance between sources and loads ensures maximum active power transfer and prevents damaging signal reflections.
The magnitude of impedance is always a positive value representing total opposition. However, the reactive part of impedance (reactance) can be negative for capacitive loads or positive for inductive loads. In polar form, a negative phase angle indicates a capacitive circuit where current leads voltage, but the overall impedance magnitude itself is never negative.
Impedance is measured in ohms, represented by the Greek letter omega (Ω). Because impedance combines resistance and reactance, all three quantities share the ohm as their standard unit of measurement. For large-scale industrial electrical systems or power grids, impedance is often expressed in kilohms (kΩ) or as a percentage of base impedance.
Frequency directly affects the reactance component of impedance. Inductive reactance increases linearly as frequency rises (XL = 2πfL), making inductors oppose high frequencies. Conversely, capacitive reactance decreases as frequency rises (XC = 1 / (2πfC)), meaning capacitors oppose low frequencies and allow high-frequency AC signals to pass easily.
The phase angle (θ) represents the time-shift or angular difference between the voltage applied to an AC circuit and the resulting current flowing through it. Measured in degrees or radians, it is calculated as θ = tan⁻¹(X / R). A positive angle means current lags voltage (inductive), while a negative angle means current leads voltage (capacitive).