Capacitor Calculator

Calculate the charge and stored energy of a capacitor from its capacitance and voltage (Q = CV, E = ½CV²), and the time constant with a resistor.

Capacitor Calculatorمباشر

كيفية استخدام هذه الحاسبة

1Enter the capacitance and choose its unit (microfarads are common).
2Enter the voltage across the capacitor.
3Optionally add a series resistance for the charging time constant.
4Read the charge and energy stored, and the RC time constant.

طريقة الحساب

Capacitor charge and energy

charge: Q = C × V
energy: E = ½ C V²
time constant: τ = R × C
capacitance in farads, voltage in volts

A capacitor stores electrical energy by holding separated charge on two conductive plates, with the amount of charge it can hold per volt defined as its capacitance, measured in farads. The charge stored is simply the capacitance times the voltage across it — a larger capacitor or a higher voltage holds more charge. The energy stored in the capacitor's electric field, however, grows with the square of the voltage: it is one-half the capacitance times the voltage squared. This squared relationship means voltage matters much more than it might seem — doubling the voltage stores four times the energy. When a capacitor is charged or discharged through a resistor, the process is not instant but follows an exponential curve governed by the time constant, the product of the resistance and the capacitance. One time constant is the time to reach about 63% of the final voltage, and after about five time constants the capacitor is effectively fully charged or discharged.

مثال محلول

A 100 microfarad capacitor charged to 12 volts holds a charge of Q = 0.0001 × 12 = 0.0012 coulombs (1.2 mC) and stores an energy of E = ½ × 0.0001 × 12² = 0.0072 joules (7.2 mJ). Through a 1,000 ohm resistor, its time constant would be 1,000 × 0.0001 = 0.1 seconds.

Capacitor Calculator: الدليل الكامل

How a capacitor stores charge

A capacitor is one of the most fundamental components in electronics, and its job is to store electrical charge and energy. In its simplest form it is two conductive plates separated by an insulator; when a voltage is applied, positive charge accumulates on one plate and negative on the other, held in place by their mutual attraction across the gap. The capacitance measures how much charge the device stores for each volt applied — a one-farad capacitor holds one coulomb per volt, though a farad is a very large unit, which is why real capacitors are usually rated in microfarads, nanofarads, or picofarads.

The relationship Q equals C times V is the defining equation of a capacitor. It says the charge stored is directly proportional to the voltage: raise the voltage and the capacitor holds proportionally more charge, up to its rated limit. This proportionality is what makes a capacitor's behaviour predictable and useful. Unlike a battery, which stores energy chemically and delivers it at a roughly constant voltage, a capacitor stores charge physically and its voltage falls as it discharges, which suits it to different tasks — rapid bursts of energy, smoothing, and timing rather than sustained power delivery.

Energy and the square of voltage

While the charge on a capacitor is proportional to voltage, the energy it stores grows with the square of the voltage, and this distinction has important consequences. The energy formula, one-half times capacitance times voltage squared, means that voltage is a powerful lever on stored energy. Doubling the voltage on a capacitor quadruples the energy it holds; tripling it stores nine times as much. This is why high-energy capacitor applications run at high voltages, and why the voltage rating of a capacitor is a critical specification — exceed it and the insulator breaks down, often dramatically.

This concentrated energy storage makes capacitors capable of delivering very rapid, powerful bursts. A charged capacitor can dump its energy almost instantaneously, far faster than a battery, which is exploited in camera flashes, defibrillators, and pulsed lasers. Large capacitors charged to high voltages store enough energy to be genuinely dangerous, retaining a lethal charge even after the power is disconnected, which is why equipment like televisions and power supplies carries warnings about discharging capacitors before servicing. The squared voltage relationship is the reason a physically small capacitor at high voltage can hold a surprising and hazardous amount of energy.

The RC time constant and timing

Capacitors rarely act alone; paired with a resistor, they form the RC circuit that underlies an enormous range of electronic timing and filtering. When a capacitor charges or discharges through a resistor, it does not do so instantly but follows a smooth exponential curve, and the pace of that curve is set by the time constant — the resistance multiplied by the capacitance. After one time constant the capacitor has charged to about 63% of the supply voltage; after two, about 86%; and after roughly five, it is more than 99% charged, treated as effectively complete. The same curve, in reverse, governs discharge.

This predictable timing makes the RC combination the basis of countless circuits. It sets the delay in timers and the frequency of oscillators that generate clock signals and tones. It smooths the ripple in power supplies, letting the capacitor fill in the gaps between pulses of rectified voltage. It filters signals, passing or blocking frequencies depending on the time constant, which is the foundation of tone controls and radio tuning. By choosing the resistance and capacitance, a designer sets the time constant to whatever the application needs, from microseconds to seconds. Understanding that τ equals R times C, and that five time constants means fully charged, is the key to reasoning about how any capacitor-based circuit behaves over time.

الأسئلة الشائعة

How do I calculate the charge on a capacitor?

Multiply capacitance by voltage: Q = C × V. A 100 µF capacitor (0.0001 F) at 12 V holds 0.0001 × 12 = 0.0012 coulombs, or 1.2 millicoulombs. Charge is directly proportional to the voltage applied.

How much energy does a capacitor store?

E = ½ × C × V². A 100 µF capacitor at 12 V stores ½ × 0.0001 × 144 = 0.0072 joules (7.2 mJ). Energy grows with the square of voltage, so doubling the voltage quadruples the stored energy — which is why voltage rating matters so much.

What is the RC time constant?

The time constant τ = R × C sets how fast a capacitor charges or discharges through a resistor. After one time constant it reaches about 63% of the final voltage; after five, it's essentially fully charged. A 100 µF capacitor with a 1,000 Ω resistor has a time constant of 0.1 seconds.

Why can charged capacitors be dangerous?

Because energy grows with the square of voltage, a small capacitor at high voltage can store a lot of energy — and it can deliver that energy almost instantly. Large capacitors in TVs and power supplies retain a potentially lethal charge even after being unplugged, which is why they must be discharged before servicing.