Impedance Calculator
Calculate impedance for AC circuits including RL, RC, RLC, and parallel RLC circuits. See impedance magnitude, rectangular form, polar form, phase angle, power factor, resonance, current, and supporting visuals.
Background
Impedance is the AC version of resistance. In an alternating-current circuit, resistors oppose current the same way they do in DC circuits, while capacitors and inductors add frequency-dependent opposition called reactance. Because resistance and reactance act in perpendicular directions mathematically, impedance is usually written as a complex number.
How to use this calculator
- Choose the circuit type: series RLC, parallel RLC, reactance only, or resonance helper.
- Enter resistance, inductance, capacitance, and frequency.
- Use 0 for any component that is not part of the circuit.
- Optionally enter RMS voltage to estimate current and apparent power.
- Click Calculate Impedance to view magnitude, phase angle, rectangular form, polar form, and visual interpretation.
How this calculator works
- The calculator converts all selected units into base SI units.
- It calculates inductive reactance using frequency and inductance.
- It calculates capacitive reactance using frequency and capacitance.
- For a series circuit, it subtracts capacitive reactance from inductive reactance to get net reactance.
- For a parallel circuit, it adds admittances first and then inverts total admittance to find impedance.
- It converts the complex impedance into magnitude, phase angle, rectangular form, and polar form.
Formula & Equations Used
Inductive reactance: XL = 2πfL
Capacitive reactance: XC = 1/(2πfC)
Series impedance: Z = R + j(XL − XC)
Impedance magnitude: |Z| = √(R² + X²)
Phase angle: φ = atan2(X, R)
Polar form: Z = |Z| ∠ φ
Current from RMS voltage: Irms = Vrms / |Z|
Resonant frequency: f0 = 1/(2π√(LC))
Parallel admittance: Y = 1/R + 1/(jXL) + 1/(-jXC)
Example Problems & Step-by-Step Solutions
Example 1: Series RLC impedance
Suppose R = 100 Ω, L = 50 mH, C = 10 µF, and f = 60 Hz.
First calculate XL = 2πfL and XC = 1/(2πfC).
Then find net reactance with X = XL − XC.
Finally, calculate |Z| = √(R² + X²) and the phase angle φ = atan2(X, R).
Example 2: RC circuit
For an RC circuit, set L = 0. The calculator treats the circuit as having resistance and capacitive reactance only.
Because capacitive reactance contributes negative net reactance in a series circuit, the phase angle is usually negative.
A negative phase angle means the circuit is net capacitive, so current leads voltage.
Example 3: Resonance in an RLC circuit
At resonance, inductive and capacitive reactance are equal in magnitude.
XL = XC
The resonance helper uses f0 = 1/(2π√(LC)) to find the frequency where cancellation occurs.
In a series RLC circuit near resonance, the impedance is mostly resistive and the phase angle is close to 0°.
Common mistakes to avoid
- Do not add resistance and reactance as simple scalar values. They are perpendicular parts of complex impedance.
- Do not forget unit conversions: mH, µF, kHz, and MHz can change the answer by large factors.
- For series circuits, use X = XL − XC, not XL + XC.
- For parallel circuits, add admittances first. Do not add component impedances directly.
- Do not calculate capacitive reactance with C = 0. If there is no capacitor, leave it as 0 and treat the capacitor as not present.
Frequently Asked Questions
What is impedance?
Impedance is the total opposition to alternating current. It includes ordinary resistance plus frequency-dependent reactance from inductors and capacitors.
What is the difference between resistance and impedance?
Resistance is the real part of impedance. Impedance can also include an imaginary reactance part, which represents energy storage effects from capacitors and inductors.
What does a negative phase angle mean?
A negative phase angle means the circuit is net capacitive. In that case, current leads voltage.
What does a positive phase angle mean?
A positive phase angle means the circuit is net inductive. In that case, current lags voltage.
What happens at resonance?
At resonance, inductive reactance and capacitive reactance cancel. In a series RLC circuit, the impedance becomes mostly resistive and the phase angle is close to 0°.
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