🦾 Capacitor Energy Calculator

A capacitor stores electrical energy in an electric field between its plates. When charged to a voltage V, a capacitor with capacitance C stores energy equal to E = ½ × C × V², holds a charge of Q = C × V, and can deliver that energy back to a circuit when discharged. This ability to store and release energy rapidly makes capacitors essential in power supplies (smoothing ripple), camera flashes (delivering a burst of energy), timing circuits (RC oscillators), and energy harvesting systems.

When a capacitor C charges through a resistor R, the voltage across the capacitor follows V(t) = V_max × (1 - e^-t/RC). The product RC is the time constant τ: after one time constant (τ = RC), the capacitor reaches 63.2% of its final voltage; after 5τ, it is over 99% charged. During discharge, V(t) = V₀ × e^-t/RC, falling to 36.8% after one time constant.

The calculator computes three key values: stored energy E = ½CV² (joules), stored charge Q = CV (coulombs), and the RC time constant τ = RC (seconds). It also shows the voltage at 1τ, 2τ, 3τ, and 5τ to illustrate the exponential charging behavior.

The energy stored in a capacitor is proportional to the square of voltage, meaning doubling the voltage quadruples the stored energy. This is why high-voltage capacitors can store surprisingly dangerous amounts of energy—a 1 mF capacitor at 300 V stores 45 joules, enough to cause serious shock. The maximum current during discharge is I₀ = V₀ / R, which can be enormous if R is small (e.g., a short circuit).

1. Enter the capacitance (C) in farads, microfarads, or picofarads.
2. Enter the voltage (V) across the capacitor.
3. Optionally enter the series resistance (R) for time constant calculations.
4. Click Calculate to get stored energy, charge, and RC time constant.
5. Review the charging/discharging table for the time to reach each threshold.

How much energy can a typical capacitor store?

A 100 µF capacitor at 12 V stores 0.0072 joules—barely enough to light an LED for a fraction of a second. A 1 F supercapacitor at 2.7 V stores 3.65 joules. Compare this to an AA battery, which stores about 10,000 joules. Capacitors excel at delivering energy quickly, not storing large amounts.

What is the RC time constant and why does it matter?

The time constant τ = RC tells you how fast a capacitor charges or discharges through a resistor. After one τ, the capacitor reaches 63.2% of its final voltage; after 5τ, it is over 99%. The time constant determines the bandwidth of filters, the speed of timing circuits, and the ripple in power supplies.

Why is the stored energy E = ½CV² and not CV²?

The factor of ½ comes from the integration of power over time during charging. As the capacitor charges, the voltage rises linearly with charge (V = Q/C), so the average voltage during charging is V_max/2. The energy equals charge × average voltage = CV × V/2 = ½CV².

What happens if I short-circuit a charged capacitor?

The discharge current is initially I₀ = V₀/R, where R is the resistance of the short. For a capacitor at high voltage with very low internal resistance (like a screwdriver across the terminals), the peak current can be thousands of amperes for microseconds. This can vaporize metal, cause burns, and damage the capacitor.

How do I choose a resistor for safe discharge?

Select R so that 5τ (5 × R × C) is an acceptable wait time (e.g., 5-30 seconds for manual discharge). Ensure the resistor power rating exceeds V²/R. For a 470 µF capacitor at 300 V, a 2 kΩ 50 W resistor discharges it to safe levels in about 5 seconds (5τ = 5 × 2000 × 470e-6 = 4.7 s).

What is the difference between a capacitor and a battery?

A battery stores energy chemically and releases it slowly (hours), while a capacitor stores energy electrostatically and releases it almost instantly (microseconds to milliseconds). Batteries have much higher energy density (joules per kg), but capacitors have much higher power density (watts per kg). Supercapacitors sit in between.

Supercapacitors (ultracapacitors) bridge the gap between regular capacitors and batteries: a 1 F supercapacitor at 2.7 V stores 3.65 joules—tiny compared to a battery but far more than any conventional capacitor. In camera flash circuits, a capacitor is charged to 300 V over several seconds, then discharged through the xenon tube in under a millisecond, amplifying the power by 1000-fold. When sizing a smoothing capacitor for a rectifier, aim for a ripple of less than 10% of V_dc: the rule of thumb is C ≥ 1 / (2 × f × R_load × ripple_fraction) for full-wave rectification at frequency f. Always discharge capacitors before handling: a resistor across the terminals bleeds the charge over several time constants. Large electrolytic capacitors can retain dangerous voltage for minutes or hours after power is removed.