Capacitive and Inductive Reactance Calculator
Capacitive and Inductive Reactance Calculator
Reactance of a capacitor or an inductor at any frequency — X_C = 1/(2πfC), X_L = 2πfL — with the current it allows at a stated voltage, the 90° phase shift, and the net reactance when both are in series.
Reactance at a frequency
A 100 nF decoupling capacitor at 1 MHz, 1 V RMS across it
Reactance
- XC
- capacitive reactance in ohms; halve the frequency and it doubles
- XL
- inductive reactance in ohms; double the frequency and it doubles
- phase
- current leads the voltage by 90° in a capacitor and lags by 90° in an inductor, so neither dissipates power
- X = 0
- where XL = XC: that is resonance
Worked example
A 100 nF decoupling capacitor at 1 MHz, 1 V RMS across it
2πfC = 2π × 1,000,000 × 100 × 10⁻⁹ = 0.6283 S
XC = 1 ÷ 0.6283 = 1.592 Ω
At 1 V RMS that passes 628.3 mA, with the current leading by 90°
The same capacitor at 1 kHz is 1.592 kΩ and at 50 Hz 31.83 kΩ — which is why it decouples high frequencies and does nothing at mains frequency
A 100 nF capacitor and a 100 µH inductor across the spectrum
| Frequency | XC of 100 nF | XL of 100 µH |
|---|---|---|
| 50 Hz | 31.83 kΩ | 31.42 mΩ |
| 1 kHz | 1.592 kΩ | 628.3 mΩ |
| 100 kHz | 15.92 Ω | 62.83 Ω |
| 1 MHz | 1.592 Ω | 628.3 Ω |
| 100 MHz | 15.92 mΩ | 62.83 kΩ |
What reactance is, and what it is not
Reactance is what a capacitor or an inductor offers instead of resistance. It is measured in ohms and it divides voltage into current exactly as a resistance does, I = V ÷ X, but it depends on frequency and it does not turn energy into heat. A capacitor stores charge and gives it back; an inductor stores energy in its magnetic field and gives that back. The current is a quarter of a cycle out of step with the voltage, and because power is the product of the two, the energy that flows in on one quarter-cycle flows straight back out on the next. Averaged over a cycle a perfect reactance dissipates nothing.
They go opposite ways. XC = 1/(2πfC) falls as the frequency rises, so a capacitor blocks DC completely and looks more and more like a short circuit the higher you go. XL = 2πfL does the reverse: an inductor is a piece of wire at DC and an obstacle at high frequency. That is the whole basis of filtering, decoupling and tuning.
Check it against something real. The 100 nF ceramic next to every logic chip on a board is there to supply the current the chip demands when it switches. At 1 MHz its reactance is 1.592 Ω — low enough to be the chip’s local supply for a fast edge. At 1 kHz the same part is 1.592 kΩ and at mains frequency 31.83 kΩ, which is why it does nothing about slow ripple and why a bulk electrolytic sits alongside it. The table above runs the same capacitor and a 100 µH inductor across five decades; note that the inductor’s reactance at 50 Hz is only 31.42 mΩ, less than the resistance of its own winding.
Both together. In series the reactances add with their signs: X = XL − XC. Below the frequency where they are equal the capacitor dominates and the pair is net capacitive; above it the inductor dominates. At 50.33 kHz for these two they cancel exactly and nothing is left but the real resistance in the loop — that is resonance, and the LC resonant frequency calculator covers what happens there in full. This page tells you the net reactance at any one frequency, which is the useful thing when you are not at resonance.
What the model leaves out. One sine wave at one frequency, and ideal parts. A real capacitor has equivalent series resistance and series inductance, so its impedance stops falling somewhere in the tens of megahertz and starts rising: that is its self-resonance, and above it the part is an inductor. A real inductor has winding resistance, core loss and self-capacitance and does the same thing in reverse. For a square wave or any other non-sine signal, reactance applies to each Fourier component separately — for switching edges the RC time constant calculator is often the more useful picture. To combine a reactance with a resistance into a filter with a defined corner, use the RC and RLC filter calculator; for the plain resistive case, the Ohm’s law calculator; and to get the capacitor value into the units this page wants, the capacitance converter.
Frequently asked questions
What is the formula for capacitive reactance?
XC = 1 ÷ (2πfC), in ohms, with f in hertz and C in farads. 100 nF at 1 MHz is 1.592 Ω.
What is the formula for inductive reactance?
XL = 2πfL, in ohms, with L in henries. 100 µH at 1 MHz is 628.3 Ω.
Is reactance the same as resistance?
No. Both are in ohms and both limit current, but a resistance turns the energy into heat and keeps voltage and current in step, while a reactance stores the energy and returns it, with the current 90° out of phase. Together they make impedance.
Does a capacitor block high or low frequencies?
It blocks low ones. Its reactance is inversely proportional to frequency, so it is an open circuit at DC and nearly a short at high frequency — 31.83 kΩ at 50 Hz but 15.92 mΩ at 100 MHz for a 100 nF part.
Does a capacitor dissipate power?
An ideal one does not: the current leads the voltage by 90°, so the average of their product over a cycle is zero. A real one loses a little in its equivalent series resistance and dielectric, which is what the dissipation factor measures.
What is the net reactance of an inductor and capacitor in series?
XL − XC, taking the sign. It is positive (inductive) above their resonant frequency and negative (capacitive) below it, and zero at resonance.
Related calculators
References
- Horowitz P, Hill W. The Art of Electronics, 3rd ed. Cambridge University Press, 2015. Chapter 1 (resistors in series and parallel, reactance, resonance, zener regulators) and Chapter 9 (voltage regulators).
- IEC 60063:2015. Preferred number series for resistors and capacitors (the E6, E12, E24, E48, E96 and E192 series). International Electrotechnical Commission.