Capacitor Reactance & RC Circuit Calculator
Enter capacitance, frequency, and resistance to get capacitive reactance (Xc), RC time constant, and -3dB cutoff frequency. pF through mF units. Nothing uploaded.
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Learn more: capacitive reactance and RC circuits
What capacitive reactance measures
Reactance is the opposition a capacitor puts up against alternating current, and the calculator works it out as Xc = 1 / (2πfC). Because frequency sits in the denominator, the same part behaves very differently at mains frequency and at radio frequency.
A 1µF capacitor has a reactance of about 3,183Ω at 50Hz, which the tool displays as 3.18kΩ. Push the same part to 10kHz and it drops to roughly 15.9Ω. That is what makes capacitors useful for AC coupling: the signal gets through while the DC bias behind it does not.
Reading the RC time constant
The time constant is resistance multiplied by capacitance (τ = R x C). At the values the app starts with, 100nF and 1kΩ, that works out to 100µs.
One time constant brings a charging capacitor to 63.2% of its final voltage. That figure comes from 1 - 1/e in the exponential charging curve, so it holds for any R and C you pick. Five time constants reaches 99.33%, which is where most designs treat the capacitor as charged.
Cutoff frequency, and a check for unit mistakes
The -3dB cutoff is fc = 1 / (2πRC), the frequency where an RC filter's output power has halved and its amplitude has fallen to about 70.7% of the input. With the default 100nF and 1kΩ, the tool reports 1.592kHz.
The reactance and cutoff formulas are the same expression, with resistance standing in for frequency. So if you type the cutoff back into the frequency box, the reactance should read your resistor value exactly: 1.592kHz against 100nF returns 1000Ω. A different answer usually means one of the unit dropdowns is set wrong.
Series and parallel banks
The calculator takes a single capacitance, so work out a bank before you enter it. Capacitors in parallel add up (C1 + C2 + ...), while capacitors in series use the reciprocal form, 1 / (1/C1 + 1/C2 + ...).
Resistors behave the other way round, which catches people out. Two 100nF capacitors in parallel give 200nF, and the same pair in series gives 50nF.
FAQ
What does the -3dB cutoff frequency actually mean?
At that frequency the capacitor's reactance equals the resistance, so the filter's output amplitude has fallen to about 70.7% of the input and its power to half. In a low-pass arrangement the frequencies below it pass more or less untouched, and the ones above it are cut back progressively.
Why does a capacitor block DC?
Reactance is inversely proportional to frequency, and DC sits at zero frequency, so the opposition is unbounded. Once the capacitor has charged to the supply voltage, current stops flowing through it.
Why does the reactance result show a dash?
Reactance needs both a frequency and a capacitance above zero, so with either one at zero the calculator prints a dash rather than dividing by zero. The frequency box has no effect on the other two results, which use only resistance and capacitance.