Capacitor Energy Calculator
This calculator finds the energy stored in a capacitor, the charge on its plates, and the discharge time constant if you also enter a load resistance. Capacitors store energy in an electric field between their plates, and the amount of energy depends on both the capacitance and the square of the voltage across the capacitor. Doubling the voltage quadruples the stored energy. The formula is E = 0.5 x C x V squared, where C is in farads and V is in volts, giving energy in joules. For a 1000 microfarad capacitor charged to 12 V, the stored energy is 0.5 x 0.001 x 144 = 72 millijoules. That is enough energy to spark or cause an electric shock in certain contexts, which is why large capacitors in power supplies and motor drives carry safety warnings. The charge stored on the plates is Q = C x V in coulombs. For the same capacitor, Q = 0.001 x 12 = 12 millicoulmbs. When you discharge a capacitor through a resistor, the voltage decays exponentially with a time constant tau = R x C seconds. After one time constant, the voltage has dropped to about 36.8 percent of its starting value. After five time constants, the capacitor is for practical purposes fully discharged. This calculator is useful when designing flash circuits, energy storage systems, motor start capacitors, power supply filter stages, and any circuit where you need to know how much energy a capacitor holds or how quickly it will discharge. Enter the capacitance, voltage, and optionally the discharge resistance below.
C input is in microfarads. Tau = RC in seconds; after 5 tau the capacitor is considered fully discharged. Large capacitors can store dangerous amounts of energy; discharge safely before handling.
How it works
Capacitance is converted from microfarads to farads by dividing by 1,000,000. Energy is E = 0.5 x C x V squared joules. Charge is Q = C x V coulombs. If a discharge resistance R is provided, the time constant is tau = R x C seconds and the practical full-discharge time is 5 x tau. At t = tau, voltage has dropped to V x exp(-1) = V x 0.368. At t = 5 tau, voltage is V x exp(-5) = V x 0.0067, which is less than 1 percent of the initial value.
Worked example
A 1000 uF (0.001 F) electrolytic capacitor is charged to 12 V. Stored energy is E = 0.5 x 0.001 x 12 squared = 0.5 x 0.001 x 144 = 0.072 J = 72 mJ. Stored charge is Q = 0.001 x 12 = 0.012 C = 12 mC. If it discharges through a 100 ohm load, the time constant is tau = 100 x 0.001 = 0.1 s and the practical discharge time is 5 x 0.1 = 0.5 s. These match the default capacitance and voltage values above.
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