Reactance and Impedance Calculator
Calculate inductive and capacitive reactance, series or parallel RLC impedance with phase angle, plus resonant frequency, Q factor and bandwidth at any frequency.
The interactive tool loads here when JavaScript runs.
About this toolWhat is the Reactance and Impedance Calculator?
A resistor opposes current the same way at every frequency. Inductors and capacitors do not: an inductor pushes back harder as frequency rises and a capacitor pushes back less. That frequency-dependent opposition is reactance, and the combination of resistance and reactance is impedance. This reactance and impedance calculator gives XL = 2πfL and XC = 1 ÷ (2πfC), then combines any mix of a resistor, an inductor and a capacitor, in series or in parallel, into a single impedance with its magnitude in ohms and its phase angle.
When both L and C are present it also finds the resonant frequency, the Q factor, the −3 dB bandwidth with its exact upper and lower edges, and the characteristic impedance √(L/C). Add an applied voltage to get the current and the real power, and a log-log chart shows how the impedance dips (series) or peaks (parallel) around resonance, two decades either side.
- XL and XC at any frequency, with unit pickers from nH to H and pF to mF
- Series or parallel combinations of R, L and C, any subset
- Magnitude, phase, rectangular form, admittance and power factor
- Resonant frequency, Q, bandwidth and exact band edges
- Current and real power from an applied voltage
- Log-log impedance chart around resonance
How to use the Reactance and Impedance Calculator
- Choose Series or Parallel and tick the components that are in the circuit.
- Enter the frequency and the values of R, L and C, each with a unit.
- Optionally enter the applied RMS voltage to see the current and real power.
- Read XL, XC, the impedance magnitude and phase, the rectangular form and the power factor.
- With both L and C included, read f0, Q and bandwidth, and use the chart to see how the impedance changes with frequency.
Worked examples
Series RLC below resonance
Input
Series, R 100 Ω, L 10 mH, C 1 µF, 1 kHz
Output
XL 62.83 Ω, XC 159.15 Ω, |Z| 138.85 Ω at −43.93°, power factor 0.7202
At 1 kHz the capacitor dominates, so the net reactance is −96.32 Ω and the circuit is capacitive. Resonance is at 1.5915 kHz with Q = 1, a very broad response.
The same parts as a parallel tank with 1 kΩ
Input
Parallel, R 1 kΩ, L 10 mH, C 1 µF, 1 kHz, 10 V
Output
|Z| 103.26 Ω at +84.07°, 96.84 mA, Q 10, bandwidth 159.2 Hz (1.514 to 1.673 kHz)
Below resonance the inductor's lower reactance carries most of the current, so the parallel circuit looks inductive. Only the resistor dissipates power: 10² ÷ 1000 = 100 mW.
Reactance of a mains inductor
Input
Series, L only, 100 mH, 60 Hz
Output
XL 37.70 Ω, phase +90°
A pure reactance draws current a quarter cycle behind the voltage and consumes no real power; the power factor is zero.
Resonant tank at 50 kHz
Input
Series, R 10 Ω, L 100 µH, C 100 nF
Output
f0 50.33 kHz, Q 3.162, bandwidth 15.92 kHz (43.00 to 58.91 kHz)
The characteristic impedance √(L/C) is 31.62 Ω, so with 10 Ω of loss Q is about 3. Notice the band edges are not equally spaced around f0 in hertz.
Background and insight
The arithmetic is complex numbers, with j standing for the square root of −1 to mark a 90° phase shift. An ideal inductor has impedance +jXL, an ideal capacitor −jXC and a resistor R. In series the impedances add: Z = R + j(XL − XC). In parallel the admittances add: Y = 1/R + j(1/XC − 1/XL), and Z = 1/Y. The magnitude is √(re² + im²) and the phase is atan(im ÷ re). A positive phase means the circuit looks inductive and the current lags the voltage; a negative phase means capacitive, with current leading. The cosine of the phase is the power factor.
At f0 = 1 ÷ (2π√(LC)) the two reactances are equal and cancel. A series circuit then presents only R, its minimum, and a parallel one presents only R, its maximum (infinite for ideal parts with no resistor). The sharpness of that dip or peak is Q: (1/R)√(L/C) for series and R√(C/L) for parallel, and the bandwidth between the half-power points is f0 ÷ Q. The two edges are not symmetric in hertz; they sit symmetrically on a log scale around f0, which the calculator accounts for.
Real parts depart from the ideal. An inductor has winding resistance and self-capacitance, so it resonates on its own somewhere above its useful range; a capacitor has equivalent series resistance (ESR) and inductance (ESL). For a quick estimate of a real coil in a series circuit, add its DC resistance to R. These are the textbook relations found in any circuit theory text, such as Hayt and Kemmerly or the ARRL Handbook.
Common use cases
Filter and tank design
Find where an LC network resonates and how selective it is before choosing parts for an RF or audio filter.
AC circuit homework
Check phasor answers for series and parallel RLC problems, including phase angle and power factor.
Power-supply and EMI work
See the impedance of a decoupling capacitor or a choke at the switching frequency and its harmonics.
Loudspeaker and crossover estimates
Estimate the reactance of crossover inductors and capacitors at the crossover frequency.
Tips and limitations
- XL and XC are equal only at f0. Below it the capacitor's reactance is larger; above it the inductor's is.
- A high Q gives a narrow, tall response but also a large circulating current in a parallel tank and a large voltage across L and C in a series circuit, Q times the applied voltage at resonance.
- Electrolytic and large ceramic capacitors stop behaving like capacitors above their self-resonant frequency, where ESL takes over; check the impedance curve in the datasheet.
- Impedance magnitudes do not add in series unless the phases are equal. Always combine in complex form, as the calculator does.
- Power factor here is purely displacement (phase) power factor for a sine wave. Harmonic currents from rectifiers need a separate distortion factor.
Frequently asked questions
What is the difference between reactance and impedance?
Reactance is the opposition from an inductor or capacitor alone, and it depends on frequency. Impedance combines resistance and reactance into one complex quantity with a magnitude in ohms and a phase angle.
How do you calculate capacitive reactance?
XC = 1 ÷ (2πfC). A 10 µF capacitor at 60 Hz has XC = 1 ÷ (2π × 60 × 10 × 10⁻⁶) = 265.3 Ω. Double the frequency and the reactance halves.
How do you calculate inductive reactance?
XL = 2πfL. A 100 mH inductor at 60 Hz has XL = 2π × 60 × 0.1 = 37.70 Ω, and the reactance rises in proportion to frequency.
What is the impedance of a series RLC circuit at resonance?
Just R. The inductive and capacitive reactances are equal and opposite, so they cancel and the circuit draws the largest current, in phase with the voltage.
How is Q factor related to bandwidth?
Bandwidth = f0 ÷ Q, measured between the two frequencies where the power falls to half (−3 dB). A circuit resonating at 1.59 kHz with Q = 10 has a bandwidth of about 159 Hz.
Why does a parallel LC circuit have high impedance at resonance?
At f0 the inductor and capacitor currents are equal and opposite, so they circulate between the two parts and the source supplies almost nothing. With ideal parts the impedance would be infinite; in practice losses limit it to R, or to Q² times the coil resistance.
What does a negative phase angle mean?
The circuit is capacitive: current leads voltage. A positive angle means inductive, with current lagging. Zero means the circuit behaves as a pure resistance at that frequency.
Is there an in-depth guide to the Reactance and Impedance Calculator?
Yes. “Reactance, Impedance and RLC Resonance: The Phasor View” covers the background, how it works, common pitfalls and worked examples. Read the full guide.
Related Tools You May Like
Free, in-browser tools that pair well with this one.