What capacitive reactance actually is
Capacitive reactance is the opposition a capacitor offers to alternating current, and you measure it in ohms exactly as you measure resistance. The difference is that reactance stores energy instead of burning it. A resistor turns every watt it sees into heat; a capacitor takes charge in on one quarter-cycle and gives it straight back on the next, so over a full cycle an ideal capacitor consumes nothing.
Because the mechanism is charge storage rather than collision, the ohms you get depend on how fast the voltage is changing. Current into a capacitor is i = C · dv/dt: the steeper the voltage slope, the more current flows. Double the frequency of a sine wave of fixed amplitude and you double its slope everywhere, so you double the current and halve the reactance. That single fact explains everything a capacitor is used for. It blocks DC absolutely, passes audio poorly, and passes radio frequencies almost as though it were a wire.
The practical consequence is that a capacitor has no single “impedance” you can write on a schematic. The 0.1 µF decoupling capacitor beside a logic chip is 1.6 kΩ at 1 kHz and 1.6 Ω at 1 MHz. You must always state the frequency alongside the number, and this calculator makes you enter it for that reason.
The formula, term by term
The working equation is XC = 1 ÷ (2πfC). Read it as three separate ideas stacked together.
The 2πf is angular frequency ω, in radians per second. A 60 Hz sine wave sweeps 2π radians sixty times a second, so ω = 376.99 rad/s. Every reactance formula in AC theory is really written in ω; the 2π only appears because engineers prefer to quote frequency in cycles.
The product ωC is susceptance, measured in siemens, and it is the quantity that is genuinely linear. Susceptance rises in direct proportion to both frequency and capacitance. Reactance is its reciprocal, which is why the reactance curve is a hyperbola rather than a straight line, and why a plot of reactance against frequency looks so steep at the low end.
The reciprocal converts susceptance back into ohms so you can use it in Ohm's law. With no losses, I = V ÷ XC, and the reactive power the capacitor swaps with the supply is Q = V2 ÷ XC volt-amperes reactive.
Real capacitors add a small series loss resistance, the ESR, from the foil, leads, terminations and dielectric. Once ESR is present the impedance is a vector sum, |Z| = √(R2 + XC2), the current becomes V ÷ |Z|, and the correct reactive power is I2XC, not V2 ÷ XC. The calculator uses the I2XC form throughout, which reduces to the familiar one whenever you leave ESR at zero. The ratio R ÷ XC is the dissipation factor, and its reciprocal is the capacitor's quality factor Qf.
The phase angle of the impedance is θ = −arctan(XC ÷ R). With no ESR that is exactly −90°, the textbook statement that current leads voltage by a quarter cycle. The same vector arithmetic scales up to a full network in the RLC impedance calculator.
Worked example: 10 µF motor-run capacitor on 120 V, 60 Hz
Take a 10 µF capacitor across a 120 V, 60 Hz supply, with ESR neglected. Every step below can be checked on a pocket calculator.
- Convert the capacitance to farads. 10 µF = 10 × 10−6 = 1.0 × 10−5 F.
- Find the angular frequency. ω = 2π × 60 = 376.991 rad/s.
- Multiply to get susceptance. ωC = 376.991 × 1.0 × 10−5 = 3.76991 × 10−3 S.
- Invert for reactance. XC = 1 ÷ 3.76991 × 10−3 = 265.26 Ω.
- Apply Ohm's law for current. I = 120 ÷ 265.26 = 0.4524 A, or 452.4 mA.
- Compute the reactive power. Q = 1202 ÷ 265.26 = 14,400 ÷ 265.26 = 54.29 VAR leading.
- Size the conductor to code. NEC 460.8(A) asks for at least 135% of rated current: 1.35 × 0.4524 = 0.611 A, so the smallest conductor permitted by the rest of the Code is ample here.
Now change one thing. Run the same capacitor at 400 Hz, the frequency used in aircraft and some industrial drives. Frequency rises by a factor of 400 ÷ 60 = 6.667, so reactance falls by the same factor: 265.26 ÷ 6.667 = 39.79 Ω. Current rises to 120 ÷ 39.79 = 3.016 A, and reactive power to 14,400 ÷ 39.79 = 362 VAR. The part has not changed; only the slope of the voltage waveform has.
Finally, look at the peaks. A 120 V RMS sine peaks at 120√2 = 169.7 V, so the charge sloshing in and out each half cycle is q = CVpk = 1.0 × 10−5 × 169.7 = 1.70 mC, and the peak current is 0.4524 × √2 = 0.640 A. Those peak figures, not the RMS ones, are what a capacitor's voltage rating and a semiconductor's current rating must survive.
How to read the number you get
Compare the reactance with the other impedances in the same loop; on its own the ohm figure means nothing. A capacitor is doing its job as a coupling or bypass element when its reactance at the lowest frequency of interest is small relative to the load resistance it works into — one tenth is the usual design target, which costs you about 0.04 dB of amplitude and roughly 6° of phase shift. It is doing its job as a blocking element when its reactance is large relative to the same resistance.
For power-factor and motor work the useful reading is the current and the VAR. A capacitor connected across the line draws leading current continuously, and that current is what the conductors, the contactor and the fuse have to carry. The VAR figure is what you compare against a motor's lagging reactive demand when you size correction, which is the job of the power-factor correction capacitor calculator.
Once ESR is entered, watch the real-power output. A capacitor dissipates I2R internally, and because that heat has to leave through a small package, ripple current rather than voltage is usually what kills electrolytics in switching supplies. A dissipation factor below about 0.05 at the working frequency is typical of film and ceramic parts; aluminium electrolytics commonly sit several times higher, and higher again when cold.
Be sceptical when the calculated reactance is very small. Below roughly one ohm you are usually in a region where the capacitor's own lead inductance matters, the self-resonant frequency is close, and the part stops behaving like a capacitor at all. Above self-resonance a capacitor is an inductor; see the inductive reactance calculator for the term that takes over.
Capacitive reactance in ohms at common frequencies
| Capacitance | 50 Hz | 60 Hz | 400 Hz | 1 kHz | 10 kHz | 100 kHz |
|---|---|---|---|---|---|---|
| 100 pF | 31.83 MΩ | 26.53 MΩ | 3.979 MΩ | 1.592 MΩ | 159.2 kΩ | 15.92 kΩ |
| 1 nF | 3.183 MΩ | 2.653 MΩ | 397.9 kΩ | 159.2 kΩ | 15.92 kΩ | 1.592 kΩ |
| 10 nF | 318.3 kΩ | 265.3 kΩ | 39.79 kΩ | 15.92 kΩ | 1.592 kΩ | 159.2 Ω |
| 100 nF | 31.83 kΩ | 26.53 kΩ | 3.979 kΩ | 1.592 kΩ | 159.2 Ω | 15.92 Ω |
| 1 µF | 3.183 kΩ | 2.653 kΩ | 397.9 Ω | 159.2 Ω | 15.92 Ω | 1.592 Ω |
| 10 µF | 318.3 Ω | 265.3 Ω | 39.79 Ω | 15.92 Ω | 1.592 Ω | 0.1592 Ω |
| 100 µF | 31.83 Ω | 26.53 Ω | 3.979 Ω | 1.592 Ω | 0.1592 Ω | 0.01592 Ω |
| 1000 µF | 3.183 Ω | 2.653 Ω | 0.3979 Ω | 0.1592 Ω | 0.01592 Ω | 0.001592 Ω |
Every row is the row above divided by ten, and every column is derived from its neighbour by the frequency ratio, because reactance is inversely proportional to both quantities. Values below about one ohm are theoretical: a real capacitor's series inductance dominates long before you get there.
The code rules that use this number
Two documents govern capacitors in North American electrical installations, and both are written in terms of the rated current this calculator produces. NEC (NFPA 70) Article 460, assumed here at the 2023 edition, covers capacitors used for power-factor correction and surge work; 460.8(A) requires that circuit conductors have an ampacity of not less than 135% of the capacitor's rated current, and 460.8(B) sets the overcurrent-device rules. IEEE Std 18, IEEE Standard for Shunt Power Capacitors, defines the ratings and test conditions that manufacturers publish against. Neither document changes the physics on this page; they set the margins you apply to the answer.
Mistakes that produce a wrong reactance
- Leaving the capacitance in microfarads. The formula needs farads. A 10 µF part entered as 10 gives an answer a million times too small. The unit selector on this page exists to remove that error.
- Using the marked value at a frequency the datasheet never claimed. Class 2 ceramics such as X7R and Y5V lose a large fraction of their capacitance under DC bias and with age, and the loss is specified in the manufacturer's curves, not on the part.
- Ignoring self-resonance. Every capacitor has series inductance. Above its self-resonant frequency it presents rising, inductive impedance, and the 1/(2πfC) curve no longer describes it. Check the datasheet impedance plot before trusting a reactance below an ohm.
- Treating reactive power as consumption. The VAR figure is energy borrowed and returned each cycle. It loads the conductors and the transformer but it does not turn the utility's energy meter, which is why a capacitor is used to correct power factor rather than to supply it.
- Mixing RMS and peak. Enter RMS voltage and you get RMS current. Voltage ratings, creepage clearances and semiconductor stress are all peak quantities: multiply by √2.
- Assuming the source is a clean sine. Reactance falls with frequency, so harmonics see far less opposition than the fundamental. On a distorted supply a power capacitor can draw substantially more current than this single-frequency calculation predicts, which is the mechanism behind harmonic resonance in capacitor banks.
Where this fits among the other AC tools
Reactance is the first step of nearly every AC calculation, not the last one. If your capacitor sits in series or parallel with a resistor, the quantity you actually want is the corner frequency, where reactance equals resistance and the response is 3 dB down; that is the RC filter cutoff frequency calculator. If you care about how long the capacitor takes to charge through that resistor rather than how it responds to a sine wave, work in the time domain with the RC time constant calculator — the two views are the same physics, linked by fc = 1 ÷ (2πRC).
Add an inductor and the two reactances subtract, because they are 180° apart. They cancel exactly at the resonant frequency given by the RLC resonant frequency calculator, leaving only resistance; that cancellation is what makes tuned circuits, and what makes an unlucky capacitor bank resonate with the supply transformer at a harmonic. When you need to combine several capacitors before you start, note that they add in parallel and combine reciprocally in series, the opposite of resistors — use the capacitor series and parallel calculator for the equivalent value, then bring it back here.
This page assumes a single sinusoidal frequency and linear components. It does not model dielectric absorption, temperature coefficients, DC-bias derating, or the distributed inductance of the mounting. For any of those, the manufacturer's impedance-versus-frequency plot is the authority.
Key terms
- Reactance (X)
- The ohms of opposition an ideal capacitor or inductor presents to sinusoidal current. Reactance stores and returns energy; resistance dissipates it.
- Susceptance (B)
- The reciprocal of reactance, in siemens. For a capacitor B = ωC, which is the quantity that rises linearly with frequency.
- Impedance (Z)
- The complex sum of resistance and reactance, Z = R − jXc for a capacitor. Its magnitude is √(R² + Xc²) and its angle is the phase between voltage and current.
- ESR
- Equivalent series resistance: all of a capacitor's loss mechanisms lumped into one series resistor. It is frequency-dependent and is read from a datasheet curve, not from a single number.
- Dissipation factor (DF, tan δ)
- The ratio ESR ÷ Xc. Its reciprocal is the quality factor Q. A low dissipation factor means the part is close to a pure reactance.
- Self-resonant frequency
- The frequency at which a capacitor's own series inductance cancels its capacitance. Below it the part is capacitive; above it the part is inductive.