Capacitive Reactance Calculator
Calculate how strongly an ideal capacitor opposes sinusoidal alternating current at a selected frequency. Add RMS voltage to see current, reactive power, peak stored energy, and the 90-degree current-leading-voltage relationship in one coherent result.
Ideal AC result
Calculation trace
Equivalent C = 10.000 µF Xc = 1 ÷ (2π × 60 Hz × 0.000010000 F) = 265.258 Ω Irms = 120 V ÷ 265.258 Ω = 0.4524 A
What capacitive reactance tells you
AC opposition in ohms
Capacitive reactance is the magnitude of an ideal capacitor’s opposition to sinusoidal alternating current. It is measured in ohms, but it is not ordinary resistance: an ideal capacitor exchanges energy with the electric field rather than turning the same amount into heat each cycle.
Frequency changes the path
Reactance is inversely proportional to frequency. Raise frequency while capacitance stays constant and XC falls, allowing more ideal AC current at the same voltage. Lower the frequency and the capacitor presents a larger magnitude of opposition.
Capacitance changes the path
Reactance is also inversely proportional to capacitance. A larger effective capacitance produces lower XC at the same frequency. Identical capacitors in parallel add capacitance; identical capacitors in series divide the single-unit capacitance by the count.
The formula requires capacitance in farads. The unit menu converts picofarads, nanofarads, microfarads, and millifarads before the calculation. A 10 µF value becomes 0.000010 F. Keeping the conversion visible in the trace helps catch the most common error in hand calculations: entering the printed number without its metric prefix.
At zero frequency, an ideal steady-state capacitor is an open circuit after charging, so the reactance expression approaches infinity. This calculator requires a positive frequency because it is designed for sinusoidal AC. Transient charging from a DC step is a different time-domain problem involving circuit resistance and the RC time constant.
Worked example: 10 µF at 60 Hz and 120 V RMS
Convert 10 microfarads to farads: 10 × 10−6 F equals 0.000010 F. Angular frequency is 2π times 60 Hz, or about 376.991 radians per second. Multiplying angular frequency by capacitance gives a susceptance magnitude of about 0.00376991 siemens. Its reciprocal is 265.258 ohms of capacitive reactance.
With 120 V RMS across the ideal capacitor, RMS current is 120 divided by 265.258, or approximately 0.4524 A. For a sine wave, peak current is RMS current multiplied by the square root of two, approximately 0.6398 A. The reactive-power magnitude is 120 squared divided by 265.258, about 54.286 var. An ideal capacitor has zero average real power, although current still flows and real components have losses.
Peak voltage is 120 times the square root of two. Applying one-half C Vpeak2 gives 0.144 J of maximum stored electric-field energy. The energy returns to the circuit later in the cycle in the ideal model. The 60 Hz period is one-sixtieth of a second, or 16.667 milliseconds.
See the inverse-frequency relationship
For the same 10 µF capacitance, changing frequency alone changes the reactance substantially. The bars below represent reactance magnitude, so a shorter bar at higher frequency means a lower AC opposition. These values use the ideal formula and are not a frequency-rating recommendation for a real capacitor.
This relationship explains why a coupling or bypass capacitor can behave very differently across a signal band. It also explains why a power-frequency correction capacitor must be studied at harmonic frequencies, where its reactance is lower. A simple single-frequency calculation cannot determine resonance, harmonic amplification, switching transients, or safe capacitor-bank operation.
Using the identical-capacitor bank control
All in parallel
For identical capacitors connected in parallel, effective capacitance is the single-unit capacitance multiplied by the count. Two 10 µF capacitors ideally make 20 µF. At the same frequency, the bank reactance is half the single-capacitor value and the total ideal current doubles.
Real parallel banks require current sharing, fuse or protection decisions, discharge paths, tolerances, thermal review, and layout appropriate to the application.
All in series
For identical capacitors connected in series, effective capacitance is the single-unit capacitance divided by the count. Two 10 µF capacitors ideally make 5 µF, doubling reactance at the same frequency. Voltage does not necessarily divide equally in real parts without proper balancing and matched behavior.
The control assumes identical units and calculates only the ideal equivalent capacitance. It does not increase a bank voltage rating or approve a series design.
Why a real capacitor differs from the ideal model
Real capacitors include equivalent series resistance, equivalent series inductance, leakage, dielectric absorption, and capacitance that can vary with temperature, frequency, bias, age, and tolerance. At low and moderate frequencies, the ideal reactance may dominate. Near self-resonance, parasitic inductance becomes important; above it, the part can behave more inductively than capacitively. The simple formula has no way to locate that boundary.
Current calculated from V ÷ XC is an ideal sinusoidal magnitude. In a rectifier input, switching converter, pulse circuit, or distorted power waveform, current may be highly non-sinusoidal and have large peaks. RMS current, heating, harmonic spectrum, and manufacturer ripple-current limits need waveform-aware analysis or measurement.
Reactive power in this calculator is reported as a positive magnitude for clarity. Under a common power-system sign convention, capacitive reactive power may be shown with a negative sign because it is opposite inductive reactive power. Always state the sign convention when exchanging results with engineers or software.
These are separate models with different assumptions.
A careful component-screening workflow
- Define the waveform. Confirm whether the applied voltage is approximately sinusoidal and identify the relevant fundamental and harmonic frequencies.
- Use effective capacitance. Account for tolerance and any bias, temperature, or frequency dependence shown in the manufacturer data.
- Calculate reactance and current. Use the expected RMS voltage at each relevant frequency, not merely the nominal supply label.
- Compare with ratings. Check working voltage, ripple current, dissipation, temperature rise, polarity, safety class, and life expectancy.
- Examine resonance. Include source, wiring, and component inductance when the operating band could approach self-resonance or system resonance.
- Validate on hardware safely. Follow appropriate electrical safety procedures and use instruments rated for the circuit energy and category.
Document whether each number is nominal, worst case, or measured. A useful design review might calculate reactance at minimum capacitance and maximum frequency for one limit, then maximum capacitance and minimum frequency for another. One nominal result rarely captures every stress.
Frequently asked questions
Is capacitive reactance the same as resistance?
No. Both are expressed in ohms, but ideal resistance dissipates real power while ideal capacitive reactance represents energy storage and return with a phase shift between voltage and current. Real capacitors also contain resistive loss, so an impedance model may include both parts.
Why does current lead voltage by 90 degrees?
For an ideal capacitor, current is proportional to how quickly voltage changes. In a sine wave, the maximum rate of change occurs one-quarter cycle before the voltage reaches its peak, producing a 90-degree leading current relationship. Real losses and parasitics shift the phase away from exactly 90 degrees.
What happens to Xc when frequency doubles?
It halves when capacitance stays constant because Xc is inversely proportional to frequency. Current magnitude therefore doubles at the same applied RMS voltage in the ideal model. Component frequency limits and parasitics can prevent that simple relationship from remaining accurate at high frequency.
Can I enter microfarads directly?
Yes. Select µF and enter the printed microfarad value. The script converts it to farads internally. The calculation trace shows the equivalent capacitance and denominator so the unit conversion can be reviewed.
Does the result include ESR or ESL?
No. The calculator uses an ideal capacitor. Equivalent series resistance adds loss and changes impedance magnitude and phase. Equivalent series inductance becomes increasingly important with frequency and creates self-resonance. Use manufacturer impedance curves or a complete RLC model when those effects matter.
Can this size a motor-run or power-factor-correction capacitor?
Not by itself. It can provide an ideal reactance and current cross-check, but application-specific voltage, kvar, harmonic, switching, discharge, protection, temperature, enclosure, fault, and listing requirements must be addressed. Use qualified design methods and the manufacturer’s application data.
References
- U.S. Department of Energy, DOE Fundamentals Handbook: Electrical Science, Volume 3, Basic AC Reactive Components
- National Institute of Standards and Technology, Special Publication 811, Guide for the Use of the International System of Units
Educational ideal-circuit estimate only. Follow manufacturer specifications, applicable electrical codes, laboratory safety practices, and qualified engineering review.