How this instrument works
Reactance is opposition that never gets warm. Drive alternating current through any capacitor and voltage still appears across it, but that voltage arrives a quarter cycle late — current peaks while voltage sits at zero, so their product averages to nothing; no energy is consumed. Each half cycle charges dielectric; next half cycle hands that energy back. Raise frequency and each half cycle grows shorter, so less charge piles up before polarity flips, so less voltage develops for a given current. Hence 2πfC sits in a denominator: reactance and frequency move opposite ways, decade for decade.
Alternating current arrived faster than mathematics fit to describe it. Oliver Heaviside supplied operational calculus and named impedance in 1886; Charles Proteus Steinmetz demonstrated complex-number phasors at Chicago's International Electrical Congress in 1893, turning differential equations into arithmetic an engineer could finish at his desk. That same year French engineer M. Hospitalier proposed calling this quadrature component reactance, writing in L'Électricien, and American practice took up his word almost at once. Inside ten years X_C = 1/(2πfC) had become as routine as Ohm's law.
One frequency, one sine wave, one ideal part — those are this formula's assumptions, and hardware honours them only approximately. Equivalent series resistance and lead inductance mean measured impedance magnitude stops falling at self-resonance and climbs beyond it, where bulk electrolytics already behave inductively below 1 MHz. Class II ceramics shed capacitance under DC bias, pushing true reactance well above whatever printed markings predict. And for square waves, switching edges or any transient, no single reactance exists at all: break your signal into harmonics, or abandon phasors and work in time with i = C·dv/dt.
- Put your part value into Capacitance, using pF, nF, µF, mF or F — whichever unit the marking or datasheet uses.
- Set Frequency to the operating point you care about: 50 or 60 Hz for mains, 20 kHz for switching ripple, MHz for radio work.
- Read Capacitive reactance in ohm, kohm or Mohm. Small answers mean this part passes that frequency; large answers mean it blocks.
- Step frequency by tens and watch reactance drop by tens — plotted on log axes, the response is a straight line of slope minus one.
- Sizing a coupling capacitor? Choose C so reactance stays below a tenth of load resistance at your lowest frequency of interest.
Worked example — a 10 µF run capacitor on 50 Hz mains
A single-phase pump motor carries a 10 µF run capacitor across its auxiliary winding, fed from 230 V 50 Hz mains. Enter 10 µF into Capacitance and 50 into Frequency: X_C = 1 ⁄ (2π × 50 × 1×10⁻⁵) = 1 ⁄ (3.14159 × 10⁻³) = 318.309886 ohm. Call it 318 ohm on the bench; six decimal places matter only when you are checking arithmetic.
That figure does real work. Winding current comes to 230 ⁄ 318.31 = 0.72 amperes, and reactive power to 230² ⁄ 318.31 = 166 VAr — shuttled back and forth every cycle rather than burned. Ship the same motor somewhere running at 60 Hz and reactance drops to 265.26 ohm, so this capacitor forces 20% more current through a winding never sized for it. Run capacitors print a frequency beside their voltage rating for exactly that reason.
Questions
Why does capacitive reactance fall as frequency rises?
Because reactance measures how much voltage builds for a given current, and faster alternation leaves less time for charge to accumulate. Capacitor current obeys i = C·dv/dt, so at fixed current amplitude voltage amplitude scales as 1/(ωC). Ten times the frequency, one tenth the reactance. A 10 µF part shows 318 ohm at 50 Hz, 31.8 ohm at 500 Hz and 3.18 ohm at 5 kHz — which is precisely why capacitors get used to pass signal while blocking steady current.
Is reactance the same thing as resistance?
No, although both are quoted in ohms. Resistors turn electrical energy into heat; capacitive reactance parks energy in an electric field and returns it a quarter cycle later, dissipating nothing on average. Reactance also carries phase information — current leads voltage by 90° in an ideal capacitor — where resistance carries none. Only loss inside a real part, its equivalent series resistance, actually warms anything.
Why do textbooks write capacitive reactance as a negative number?
That sign comes from complex impedance: Z_C = 1/(jωC) = −j/(ωC). Written as Z = R + jX, capacitive X is negative while inductive X is positive, which keeps phasor bookkeeping honest and lets the two cancel at resonance. This sheet reports magnitude — the positive figure you want when dividing voltage by reactance to get current. Keep the minus sign when summing reactances in a branch; drop it for magnitude arithmetic.
How do I combine reactance with a resistor in series?
In quadrature, never by simple addition: |Z| = √(R² + X_C²). Put 318 ohm of reactance in series with 318 ohm of resistance: impedance comes to 450 ohm, not 636, at a phase angle of −45°. Adding them straight is the single most common blunder made with this quantity, and it overstates impedance by up to 41%. Series RC also sets a corner frequency where R and X_C match, the point every passive filter is designed around.
What is the reactance at DC?
Infinite, ideally. Set f = 0 and 1/(2πfC) has no finite value, which is arithmetic agreeing that a charged capacitor stops steady current. This sheet rejects zero frequency for that reason. Real parts leak slightly: insulation resistance of good film capacitors runs into gigohms, while large aluminium electrolytics might show only hundreds of kilohms, so DC blocking is excellent rather than perfect.
How does this relate to inductive reactance?
They are mirror images. Inductive reactance X_L = 2πfL climbs with frequency while X_C falls, and their phase shifts have opposite signs, so in series they subtract from one another. Where the two match, a circuit resonates at f = 1/(2π√(LC)) and only resistance remains to limit current. Pair 10 µF with 1 H and that balance lands near 50.3 Hz — close enough to mains that power engineers watch for it.