Capacitor Calculator
Free Capacitor Calculator for electricity. Enter variables to compute results with formulas and detailed steps. Get results you can export or share.
Reviewed for accuracy by Manoj Kumar, Mathematics Educator
Capacitor Calculator
Calculator
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Formula: Series: 1/Ct = 1/C1 + 1/C2 + ... | Parallel: Ct = C1 + C2 + ...
Worked example — Total Capacitance: 59.98 uF | Energy: 4.319 mJ | Charge: 719.7 uC
Formula
Series: 1/Ct = 1/C1 + 1/C2 + ... | Parallel: Ct = C1 + C2 + ...
For series connections, the reciprocal of total capacitance equals the sum of reciprocals of individual capacitances. For parallel connections, total capacitance is the sum of all individual capacitances. Energy stored: E = 0.5CV2. Charge: Q = CV.
Worked Examples
Example 1: Series Capacitor Combination
Problem:Three capacitors of 100 uF, 220 uF, and 470 uF are connected in series across a 12V supply. Find the total capacitance and stored energy.
Solution:1/Ctotal = 1/100 + 1/220 + 1/470 1/Ctotal = 0.01 + 0.004545 + 0.002128 1/Ctotal = 0.016673 Ctotal = 59.98 uF Energy = 0.5 x 59.98e-6 x 12^2 Energy = 0.5 x 59.98e-6 x 144 Energy = 4.319 mJ
Result:Total Capacitance: 59.98 uF | Energy: 4.319 mJ | Charge: 719.7 uC
Example 2: Parallel Capacitor Combination
Problem:The same three capacitors (100 uF, 220 uF, 470 uF) are connected in parallel across 12V. Find total capacitance and stored energy.
Solution:Ctotal = 100 + 220 + 470 = 790 uF Energy = 0.5 x 790e-6 x 12^2 Energy = 0.5 x 790e-6 x 144 Energy = 56.88 mJ Charge = 790e-6 x 12 = 9,480 uC
Result:Total Capacitance: 790 uF | Energy: 56.88 mJ | Charge: 9,480 uC
Frequently Asked Questions
What is a capacitor and how 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 a dielectric material. When voltage is applied across the plates, opposite charges accumulate on each plate, creating an electric field that stores energy. The amount of energy stored is given by the formula E = 0.5 times C times V squared, where C is the capacitance and V is the voltage. Capacitors can release their stored energy very quickly, which makes them useful for applications requiring rapid bursts of power such as camera flashes, defibrillators, and power supply filtering in electronic circuits.
What is the difference between series and parallel capacitor connections?
In a series connection, capacitors are connected end to end so the same charge flows through each one, and the total capacitance decreases according to the reciprocal formula: 1/Ctotal = 1/C1 + 1/C2 + 1/C3. In a parallel connection, capacitors share the same voltage across their terminals, and the total capacitance simply adds up: Ctotal = C1 + C2 + C3. This is the opposite behavior of resistors, where series resistances add and parallel resistances use the reciprocal formula. Series connections are used when higher voltage ratings are needed, while parallel connections increase the total storage capacity of the circuit.
What units are used to measure capacitance?
Capacitance is measured in farads (F), named after Michael Faraday. One farad is an extremely large capacitance, so practical capacitors are measured in smaller units: microfarads (uF, one millionth of a farad), nanofarads (nF, one billionth), and picofarads (pF, one trillionth). Electrolytic capacitors commonly range from 1 uF to 10,000 uF and are used in power supplies. Ceramic capacitors typically range from 1 pF to 100 uF and are used for high-frequency filtering. Film capacitors fall between these ranges and offer excellent stability and low losses for precision applications.
What is capacitive reactance and why does it matter?
Capacitive reactance is the opposition that a capacitor presents to alternating current, measured in ohms and calculated as Xc = 1 divided by (2 times pi times f times C), where f is frequency and C is capacitance. Unlike resistance, reactance varies with frequency: at low frequencies capacitors block current flow (high reactance), and at high frequencies they pass current easily (low reactance). This frequency-dependent behavior makes capacitors essential for filtering circuits, where they can block DC while passing AC signals. Understanding reactance is crucial for designing audio crossover networks, radio frequency filters, and power factor correction systems.
How do you choose the right capacitor for a circuit?
Choosing the right capacitor involves considering several key parameters: capacitance value for the required energy storage or filtering, voltage rating that exceeds the maximum expected voltage by at least 20 percent for safety margin, temperature rating for the operating environment, and equivalent series resistance (ESR) for power applications. The dielectric type also matters significantly because it affects temperature stability, voltage coefficient, and frequency response. Ceramic capacitors work well for high-frequency decoupling, electrolytic capacitors suit bulk energy storage in power supplies, and film capacitors are preferred for audio and precision applications due to their low distortion and excellent stability.
What is the energy stored in a capacitor and how is it calculated?
The energy stored in a capacitor is calculated using the formula E = 0.5 times C times V squared, where C is the capacitance in farads and V is the voltage across the capacitor. This quadratic relationship with voltage means doubling the voltage quadruples the stored energy, while doubling the capacitance only doubles the stored energy. A typical 1000 uF capacitor charged to 50 volts stores 1.25 joules of energy. While this seems small compared to batteries, capacitors can deliver this energy in microseconds, producing enormous instantaneous power. Supercapacitors with capacitances of hundreds of farads can store enough energy to briefly power electronic devices.
What is the charge stored on a capacitor?
The charge stored on a capacitor is calculated using Q = C times V, where Q is charge in coulombs, C is capacitance in farads, and V is voltage in volts. This linear relationship means doubling either the capacitance or the voltage will double the stored charge. In a series circuit, each capacitor holds the same charge regardless of its individual capacitance value, because the same current flows through all components. In a parallel circuit, each capacitor can hold a different charge proportional to its capacitance, but all share the same voltage. The total charge in a parallel combination equals the sum of individual charges on each capacitor.
What are common capacitor failure modes and how to prevent them?
Capacitors can fail due to several mechanisms including overvoltage breakdown, excessive temperature, ripple current heating, and electrolyte drying in electrolytic types. Overvoltage causes dielectric breakdown, permanently damaging the insulating layer between plates. Electrolytic capacitors are particularly susceptible to aging because their liquid or polymer electrolyte gradually dries out, reducing capacitance and increasing ESR over time. To prevent failures, always derate voltage by at least 20 percent, ensure adequate ventilation for heat dissipation, use capacitors rated for the expected ripple current, and replace electrolytic capacitors in critical applications every 5 to 10 years as part of preventive maintenance.
How do capacitors behave in DC versus AC circuits?
In DC circuits, a capacitor initially allows current to flow as it charges, but once fully charged it blocks all direct current and acts as an open circuit. The time to charge depends on the RC time constant (resistance times capacitance). In AC circuits, capacitors continuously charge and discharge with the alternating voltage, allowing alternating current to flow through the circuit. The amount of AC current depends on the capacitive reactance, which decreases at higher frequencies. This dual behavior makes capacitors invaluable for separating AC and DC components in signals, coupling audio signals between amplifier stages, and filtering unwanted noise from power supplies.
What is the RC time constant and how does it relate to capacitors?
The RC time constant (tau) equals resistance times capacitance and represents the time for a capacitor to charge to approximately 63.2 percent of the applied voltage or discharge to 36.8 percent of its initial voltage. After five time constants, the capacitor is considered fully charged or discharged at 99.3 percent. For example, a 100 uF capacitor with a 10 kilohm resistor has a time constant of 1 second, meaning it takes about 5 seconds to fully charge. The RC time constant is fundamental to timing circuits, filters, and signal processing. It determines the cutoff frequency of RC low-pass and high-pass filters using the formula fc = 1 divided by (2 times pi times R times C).
References
Background & Theory
Series vs. Parallel: Why the Rules Are Opposite
Capacitors combine in the opposite way that resistors do: capacitors in parallel simply add (Ctotal = C1 + C2 + ...) because each capacitor's plates effectively become larger, while capacitors in series combine by reciprocal sum (1/Ctotal = 1/C1 + 1/C2 + ...) because stacking capacitors effectively increases the total plate separation, always yielding a lower total capacitance than the smallest individual value.
| Configuration | Rule | Typical use |
|---|---|---|
| Parallel | Ctotal = C1 + C2 + ... | Increasing total capacitance / energy storage |
| Series | 1/Ctotal = 1/C1 + 1/C2 + ... | Increasing voltage rating (splitting voltage across capacitors) |
A common real-world reason to use series capacitors is voltage handling: putting two 250V-rated capacitors in series lets the pair withstand up to roughly 500V total (shared evenly if capacitances match), at the cost of halving the usable capacitance — a tradeoff engineers make deliberately when a single capacitor rated for the full voltage isn't available or is too expensive.
Reviewed for accuracy by Manoj Kumar, Mathematics Educator · Editorial policy
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