Capacitor Calculator
Choose a calculation mode, enter your values, and get instant results with full worked steps. The Charge and Energy mode solves Q = C·V and E = 0.5·C·V². The RC Time Constant mode gives the time constant and the voltage at any point during charging. The Capacitive Reactance mode computes how a capacitor opposes AC current at a given frequency. The Series and Parallel mode finds the equivalent capacitance for two capacitors in either configuration.
Formula
Worked example
A 100 uF capacitor charged to 12 V stores Q = 100e-6 x 12 = 1.2 mC and E = 0.5 x 100e-6 x 144 = 7.2 mJ. Through a 10 kOhm resistor, tau = 10000 x 100e-6 = 1.0 s. At t = 1 s the capacitor is at 63.2% of 12 V = 7.58 V. At 1 kHz the reactance is Xc = 1 / (2 x pi x 1000 x 100e-6) = 1.59 Ohm.
What is a capacitor and why does it store energy?
A capacitor is a passive electronic component that stores electrical energy in an electric field between two conductive plates separated by an insulating material called a dielectric. When connected to a voltage source, positive charge builds up on one plate and negative charge on the other. The ability to store this charge is measured in farads (F). Because the charge and energy are proportional to the applied voltage, capacitors are used in power-supply smoothing, timing circuits, signal coupling, and energy hold-up applications. The fundamental equations are Q = C times V for charge and E = 0.5 times C times V squared for stored energy, where C is capacitance in farads and V is voltage in volts.
RC time constant: charging and discharging
When a capacitor charges through a resistor, it does not charge instantly. The voltage rises exponentially according to V(t) = Vs times (1 minus e to the power of minus t divided by tau), where tau = R times C is the time constant. After one tau, the capacitor reaches 63.2% of the supply voltage. After five time constants (5 tau) it is considered fully charged at 99.3%. The same formula applies to discharging: the voltage falls from its initial value toward zero with the same time constant. Engineers use the RC product to set the timing of oscillators, debouncing circuits, and integrators. A 100 uF capacitor with a 10 kOhm resistor gives tau = 1 second; switching to 100 kOhm makes tau = 10 seconds.
Capacitive reactance in AC circuits
In a DC circuit a capacitor eventually blocks all current. In an AC circuit it presents an impedance called capacitive reactance, given by Xc = 1 divided by (2 times pi times f times C). This reactance falls as frequency rises: at high frequencies the capacitor passes current easily, at low frequencies it resists it. This property is exploited in low-pass and high-pass RC filters, audio crossover networks, and coupling capacitors that pass AC signals while blocking DC bias. The reactance is purely imaginary in the complex impedance sense, meaning current through a capacitor leads the voltage across it by 90 degrees.
Series and parallel combinations
Two capacitors in parallel add their capacitances directly: Ceq = C1 + C2. This increases total charge storage and is used when a single capacitor of the required value is unavailable. Two capacitors in series combine reciprocally: 1 divided by Ceq equals 1 divided by C1 plus 1 divided by C2, giving a total capacitance smaller than either individual value. Series connections increase the effective voltage rating of the combination, since each capacitor sees only a fraction of the total voltage. For equal capacitors in series, Ceq = C divided by 2; in parallel, Ceq = 2C.
RC charging milestones
| Time elapsed | Charge level (% of Vs) | tau multiples |
|---|---|---|
| 0.5 tau | 39.3% | 0.5x |
| 1 tau | 63.2% | 1x |
| 2 tau | 86.5% | 2x |
| 3 tau | 95.0% | 3x |
| 4 tau | 98.2% | 4x |
| 5 tau | 99.3% | 5x |
How long it takes the capacitor voltage to reach key percentages during charging.
Frequently asked questions
What unit is capacitance measured in?
Capacitance is measured in farads (F), named after Michael Faraday. A farad is a very large unit; practical capacitors are usually rated in microfarads (uF, 1e-6 F), nanofarads (nF, 1e-9 F), or picofarads (pF, 1e-12 F). Large electrolytic capacitors used in power supplies are typically 100 uF to several thousand uF, while small ceramic capacitors for high-frequency decoupling are often in the picofarad range.
How much energy does a capacitor store?
The energy stored is E = 0.5 times C times V squared, in joules. For example, a 1000 uF capacitor charged to 50 V stores 0.5 times 0.001 times 2500 = 1.25 J. The energy grows with the square of voltage, so doubling the voltage quadruples the stored energy. This is why high-voltage capacitors store enormous energy even at modest capacitance.
What is the RC time constant and how is it used?
The RC time constant (tau) equals resistance times capacitance and has units of seconds. It sets the speed of charging and discharging: after one tau the capacitor is at 63.2% of the supply voltage, after five tau it is considered fully charged. Designers choose R and C to set delays, oscillation periods, and filter cutoff frequencies. A 10 kOhm resistor with a 100 uF capacitor gives tau = 1 second; a 1 kOhm resistor with 1 uF gives tau = 1 ms.
Does a capacitor block DC?
Yes. Once fully charged to the applied DC voltage, a capacitor stops passing current. In AC circuits, however, the continuously changing voltage means the capacitor constantly charges and discharges, so AC current flows through it. The opposition to this current is the capacitive reactance Xc = 1 divided by (2 times pi times f times C). This property is used in coupling capacitors, which pass AC audio signals while blocking any DC offset.
What is the difference between series and parallel capacitors?
Parallel capacitors add directly (Ceq = C1 + C2), increasing total capacitance and charge storage while keeping the same working voltage. Series capacitors combine reciprocally (1/Ceq = 1/C1 + 1/C2), reducing total capacitance below the smallest value but effectively increasing the voltage rating because the voltage divides across them. Parallel is used when you need more capacitance; series is used when you need to handle a higher voltage than a single capacitor can withstand.