Capacitance Calculator

About the Capacitance Calculator

A capacitor stores electric charge. At its simplest it is two conducting plates separated by an insulator; apply a voltage and charge builds up on the plates, storing energy in the electric field between them. Capacitors smooth power supplies, filter noise, set the timing of circuits, store energy for camera flashes and even help tune radios. Their capacitance, measured in farads, tells you how much charge they hold for each volt.

This capacitance calculator covers the four calculations you need most. It finds the charge and stored energy from capacitance and voltage, the capacitance from a measured charge, the RC time constant of a resistor–capacitor circuit, and the total of several capacitors connected in series or in parallel. Capacitances can be entered in picofarads, nanofarads, microfarads, millifarads or farads.

How to Use the Capacitance Calculator

Choose Charge and energy, Capacitance from charge, RC time constant or Series and parallel.

Enter the values asked for, and choose the capacitance unit — µF for most electrolytic capacitors, nF or pF for small ceramic ones.

For series and parallel, list two or more capacitances separated by commas.

The Formulas

  charge            Q = C × V
  capacitance       C = Q ÷ V
  stored energy     E = ½ × C × V²
  time constant     τ = R × C
  charging          V(t) = V × (1 − e^(−t/τ))

  parallel          C = C1 + C2 + C3 + …
  series            1/C = 1/C1 + 1/C2 + 1/C3 + …

Step-by-Step Examples

100 µF at 12 V.

  Q = 0.0001 × 12 = 0.0012 C = 1.2 mC
  E = ½ × 0.0001 × 12² = 0.0072 J = 7.2 mJ

RC time constant of 10 kΩ and 100 µF.

  τ = 10,000 × 0.0001 = 1 s
  after 1τ: 63.2%   after 3τ: 95%   after 5τ: 99.3%

10, 22 and 47 µF combined.

  parallel  10 + 22 + 47 = 79 µF
  series    1 ÷ (1/10 + 1/22 + 1/47) = 5.9977 µF

A 1 F supercapacitor at 2.7 V stores ½ × 1 × 2.7² = 3.645 J.

Capacitance from charge: 1,200 µC at 12 V means C = 1,200 ÷ 12 = 100 µF.

How Capacitors Charge and Discharge

A capacitor charging through a resistor does not fill up at a steady rate. At first, with no charge on the plates, current flows easily; as the voltage builds, it opposes the supply and the current falls. The result is an exponential curve described by the time constant τ = RC. After one time constant the capacitor reaches about 63.2 percent of the supply voltage, after three about 95 percent and after five about 99.3 percent — effectively full. Discharging follows the mirror-image curve. This predictable timing is used in delay circuits, oscillators, debouncing switches and the classic 555 timer.

Series and Parallel

Capacitors combine the opposite way to resistors. In parallel, the plate areas effectively add, so the capacitances simply add: 10, 22 and 47 µF make 79 µF. In series, the plates are effectively further apart, and the total is found by adding reciprocals; the result is always smaller than the smallest capacitor, about 6 µF here. Capacitors are put in parallel to increase capacitance and in series to share a higher voltage between several parts.

Energy Stored in a Capacitor

The energy stored, ½CV², grows with the square of the voltage: doubling the voltage stores four times the energy. Ordinary capacitors store little energy — a 100 µF capacitor at 12 V holds only a few millijoules — but they can release it very quickly, which is why they power camera flashes and defibrillators. Supercapacitors, with capacitances of farads or even thousands of farads at low voltages, store enough energy to back up memory, smooth power in hybrid vehicles and capture braking energy in some buses and trams.

Units of Capacitance

The farad is a very large unit, named after Michael Faraday. Most capacitors are measured in fractions of it: microfarads (µF, millionths) for electrolytic capacitors in power supplies and audio circuits; nanofarads (nF) and picofarads (pF) for small ceramic and film capacitors in radio, timing and decoupling. One microfarad is 1,000 nanofarads or a million picofarads. Ceramic capacitors are often marked with a three-digit code in picofarads, so 104 means 10 × 10⁴ pF = 100 nF.

Safety

Large capacitors can hold a dangerous charge long after a circuit is switched off, particularly in power supplies, microwave ovens and flash units. Always discharge them safely through a suitable resistor before handling. Respect the voltage rating printed on a capacitor, and observe the polarity of electrolytic capacitors: connecting one backwards or over its rated voltage can make it overheat, bulge or burst.

Capacitors in Everyday Devices

Nearly every electronic device contains dozens or hundreds of capacitors. Small ceramic capacitors sit beside each chip on a circuit board, supplying quick bursts of current and absorbing electrical noise. Large electrolytic capacitors in chargers and power supplies smooth the pulsing output of a rectifier into steady direct current. Touchscreens detect fingers by the tiny change in capacitance they cause, and capacitor microphones turn sound into a varying capacitance and then into an electrical signal.

Understanding Your Result

The headline is the charge, capacitance, time constant or combined capacitance.

The charge and energy lines give the charge in coulombs and the stored energy.

The charging line shows the percentage charged after one to five time constants.

The parallel and series lines show how combined capacitances are worked out.

When Should You Use This Calculator?

Use it for physics and electronics homework on capacitors.

Use it to design RC timing and filter circuits.

Use it to combine capacitors to reach a value you do not have.

Common Mistakes

Mixing µF and nF. 1 µF is 1,000 nF.

Adding series capacitors directly. In series, add the reciprocals.

Ignoring the voltage rating. Exceeding it can destroy the capacitor.

Assuming a capacitor is fully charged after one time constant. It takes about five.