Impedance Calculator
Calculate total AC impedance from resistance and inductive and capacitive reactance, along with the phase angle between voltage and current.
Impedance Calculator
Calculator
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Formula: Z = √(R² + (X_L - X_C)²) | φ = arctan((X_L-X_C)/R)
Worked example — 141.4 Ω at 45°
Formula
Z = √(R² + (X_L - X_C)²) | φ = arctan((X_L-X_C)/R)
Total opposition to AC current flow. Combines resistance and reactance.
Worked Examples
Example 1: RLC circuit
Problem:R=100Ω, XL=150Ω, XC=50Ω
Solution:Z=√(10000+10000)=141.4Ω, φ=45°
Result:141.4 Ω at 45°
Frequently Asked Questions
What is AC impedance?
Impedance (Z) is the total opposition to alternating current in a circuit, combining resistance (R) and reactance (X). It is calculated as Z = √(R² + (X_L − X_C)²), where X_L = ωL is inductive reactance and X_C = 1/(ωC) is capacitive reactance. The SI unit of impedance is ohms (Ω).
How do you calculate impedance in an RLC circuit?
Use Z = √(R² + (X_L − X_C)²) and phase angle φ = arctan((X_L − X_C)/R). For R = 100 Ω, X_L = 150 Ω, X_C = 50 Ω: net reactance X = 100 Ω, Z = √(10000 + 10000) = 141.4 Ω, and φ = arctan(1) = 45°, indicating an inductive circuit.
What units does the impedance calculator use?
Resistance R, inductive reactance X_L, and capacitive reactance X_C are all entered in ohms (Ω). Reactance can also be computed as X_L = 2πfL and X_C = 1/(2πfC) before entering. Output impedance Z is in ohms, phase angle φ in degrees, and power factor PF is dimensionless (0 to 1).
How do I turn inductance and capacitance into the reactance values Impedance Calculator wants?
Inductive reactance is X_L = 2 x pi x f x L and capacitive reactance is X_C = 1 / (2 x pi x f x C), both in ohms. At 60 Hz a 10 mH inductor gives about 3.77 ohms, while a 100 microfarad capacitor gives about 26.5 ohms. Reactance is frequency dependent, so recompute both whenever the operating frequency changes.
What happens at resonance in a series RLC circuit?
Resonance occurs when X_L equals X_C, so the net reactance cancels. Impedance falls to its minimum value of R alone, the phase angle is zero and the power factor is unity, giving the largest current for a given supply voltage. The resonant frequency is f0 = 1 / (2 x pi x sqrt(LC)). Below f0 the circuit looks capacitive; above it the circuit looks inductive.
What is the difference between impedance and plain resistance?
Resistance dissipates energy as heat and is frequency independent. Reactance stores energy in a magnetic or electric field and returns it each cycle, dissipating nothing. Impedance is the complex sum, written R + jX, whose magnitude Impedance Calculator returns. An ohmmeter reads only the resistive part, so a coil measuring a fraction of an ohm at DC can present hundreds of ohms at mains frequency.
What does the sign of the phase angle tell me about the circuit?
A positive phase angle means net inductive reactance, and the current lags the applied voltage. A negative angle means net capacitive reactance, and the current leads. Zero means the circuit behaves resistively at that frequency. The old mnemonic ELI the ICE man captures it: voltage leads current in an inductor, current leads voltage in a capacitor.
How do I combine two impedances in series or in parallel?
Impedances add as complex numbers. In series, add the resistances and add the reactances separately, then take the magnitude; you cannot simply add the two magnitudes. In parallel, add the reciprocals, or equivalently add the admittances, and invert the result. Ignoring the phase relationship is the most common source of error in hand calculations of AC networks.
How do I get current, real power and reactive power once I know the impedance?
Ohm's law in AC form gives the rms current as I = V / Z. Apparent power is S = V x I in volt-amperes, real power is P = V x I x cos(phi), equal to I squared times R in watts, and reactive power is Q = V x I x sin(phi) in volt-amperes reactive. For 120 V rms across an impedance of 141.4 ohms the current is about 0.85 A.
Why is power factor corrected with capacitors?
Motors, transformers and ballasts are inductive, so their current lags and the power factor is below unity. Connecting capacitance in parallel supplies the lagging reactive current locally, cancelling part of X_L and pulling the phase angle back toward zero. Line current and the resistive losses in cables and transformers drop as a result, which is why correction capacitors sit close to the load.
Reviewed for accuracy by Manoj Kumar, Mathematics Educator · Editorial policy
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