Impedance Calculator
Enter resistance R and reactance X — impedance Z, phase angle θ, and power factor are calculated instantly. Formula: Z = √(R² + X²). Positive X = inductive, negative X = capacitive.
Last updated: May 2026
Enter resistance R and/or reactance X above.
Z = √(R² + X²) — positive X = inductive, negative X = capacitive
Impedance — formula and use
Impedance Z is the total opposition to AC current in a circuit containing both resistance and reactance. It combines the energy-dissipating effect of resistance (R) with the energy-storing effect of reactance (X) — from inductors (positive X) or capacitors (negative X). The phase angle θ shows how much the current leads or lags the voltage, and the power factor gives the ratio of real to apparent power.
Formula reference
| Quantity | Formula | Example (R=100 Ω, X=100 Ω) |
|---|---|---|
| Impedance Z (Ω) | Z = √(R² + X²) | Z = √(100² + 100²) = 141.4 Ω |
| Phase angle θ (°) | θ = arctan(X / R) | θ = arctan(100/100) = +45.00° |
| Power factor PF | PF = cos(θ) = R / Z | PF = 100 / 141.4 = 0.7071 |
Sign convention
- Positive X (inductive) — current lags voltage; θ > 0°. Use XL from the Inductor Reactance Calculator.
- Negative X (capacitive) — current leads voltage; θ < 0°. Use XC from the Capacitor Reactance Calculator and enter it as a negative value.
- X = 0 (pure resistive) — voltage and current in phase; θ = 0°; PF = 1.
Frequently Asked Questions
What is the difference between impedance and resistance?
Resistance R dissipates energy as heat and applies equally to DC and AC. Impedance Z is the AC equivalent: it includes resistance and the frequency-dependent opposition from inductors or capacitors (reactance X). At DC (f = 0 Hz), inductors are short circuits (XL = 0) and capacitors are open circuits (XC → ∞), so only resistance remains. At AC, all three must be combined: Z = √(R² + X²).
How do I combine inductive and capacitive reactance in one circuit?
When a circuit has both inductance and capacitance in series, their reactances partially cancel: Xnet = XL − XC. Calculate XL using the Inductor Reactance Calculator and XC using the Capacitor Reactance Calculator, subtract (XL − XC), then enter the result as X here. At resonance XL = XC, so Xnet = 0 and Z = R.
What does the phase angle tell me about a circuit?
The phase angle θ is how many degrees the current waveform is shifted relative to the voltage. A positive angle (0° to +90°) means the current lags voltage — the circuit is inductive. A negative angle (0° to −90°) means current leads voltage — capacitive. At θ = 0° the circuit is purely resistive and power transfer is maximised. At θ = ±90° no real power is consumed — all power is reactive and returns to the source each cycle.
What is a good power factor and why does it matter?
Power factor (PF) ranges from 0 to 1. PF = 1 means all supplied power does useful work. PF < 1 means some power oscillates between source and load without being consumed. In mains power systems, low power factor increases current draw for the same real power, raising conductor losses. In audio and RF circuits, matching source and load impedances (which implies maximising real power transfer) is the key design goal. A PF of 0.707 corresponds to θ = ±45°, the −3 dB point of an RC or RL filter.
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