Series RLC Impedance Calculator
Find the impedance, reactances and phase angle of a series RLC circuit at a given frequency from R, L and C.
How it works
Xʟ = 2πf·L · Xᴄ = 1 ÷ (2πf·C) · Z = √(R² + (Xʟ − Xᴄ)²) · φ = atan((Xʟ − Xᴄ) ÷ R)
In a series RLC circuit the total opposition to AC is impedance, combining resistance with the two frequency-dependent reactances. Inductive reactance rises with frequency while capacitive reactance falls, so they subtract; the impedance is the vector sum √(R² + X²). When the two reactances are equal the circuit is at resonance, X cancels to zero and impedance drops to just R — the current peaks.
Worked example
With R = 10 Ω, L = 10 mH, C = 10 µF at 60 Hz: ω = 2π×60 ≈ 376.99 rad/s. Xʟ = 376.99 × 0.01 ≈ 3.77 Ω. Xᴄ = 1/(376.99 × 10⁻⁵) ≈ 265.26 Ω. Net X ≈ −261.5 Ω, so Z = √(10² + 261.5²) ≈ 261.7 Ω, dominated by the capacitor.
Sources: RLC circuit — Wikipedia
Frequently asked questions
Why do the reactances subtract instead of add?
Inductor and capacitor voltages are 180° out of phase with each other, so their reactances oppose. The circuit behaves inductively when Xʟ > Xᴄ and capacitively when Xᴄ > Xʟ.
What happens at the resonant frequency?
Xʟ equals Xᴄ, the net reactance is zero, and impedance falls to the resistance alone. Current is maximum and the phase angle is zero. Use the LC resonant frequency calculator to find that frequency.
What does the phase angle sign mean?
A positive angle means the circuit is inductive and current lags voltage; a negative angle means it is capacitive and current leads. Zero means purely resistive.
Related calculators
This calculator is for educational purposes. Double-check important results before acting on them.