Capacitor Size Calculator - C = 2E/V^2 Energy Solver

A capacitor size calculator is a physics tool that turns a target start-up energy and an operating voltage into the capacitance value a circuit must hold, using the capacitor size formula C = 2 E / V^2. It is the right starting point when you are sizing a motor-start reservoir, a defibrillator capacitor bank, a DC-link bulk capacitor, or any other design where the deliverable energy matters more than the printed capacitance.

• • Motor start-up sizing: Pick a reservoir capacitor that delivers the joules a small DC motor needs during the first few milliseconds of motion.
• • DC-link bulk capacitance: Choose the bulk capacitor on a 400 V bus that has to ride through an 8 J brownout without sagging below the logic rail.
• • Defibrillator and pulse capacitor sizing: Estimate the capacitance needed to deliver hundreds of joules through a high-voltage pulse.
• • Battery backup on a low-voltage rail: Reserve enough capacitance on a 3.3 V or 5 V rail so a brief load step does not collapse the supply.

The word 'size' in this context means capacitance in farads, not the physical dimensions of the part. A capacitor with higher capacitance stores more charge at the same voltage and therefore more energy.

The result is often quoted in microfarads, nanofarads, or picofarads because practical components rarely sit above one farad. The calculator picks the prefix automatically so the printed number lands between 1 and 999.

When you already know the printed capacitance and want to decode a 3-digit marking instead, Capacitor Calculator handles the reverse direction in the same capacitor cluster.

The calculator takes a target start-up energy E in joules and an operating voltage V in volts, then solves the stored-energy equation for C. The only assumptions are that V is positive and that E is non-negative, both of which the form enforces before the math runs.

• E: Start-up energy the capacitor must deliver, in joules (J). Same unit as watt-seconds.
• V: Voltage across the capacitor in volts (V). Use the rated supply or motor operating voltage, not the ripple peak.
• C: Required capacitance in farads (F), returned by the calculator in mF, uF, nF, pF, or fF.

C = 2 E / V^2 is just E = 1/2 C V^2 rearranged. If you would rather solve for energy from a known capacitance, multiply C by V squared and divide by two; for voltage, take the square root of 2 E / C.

The calculator prefixes the capacitance so the displayed value stays between 1 and 999 in the chosen unit. A 5e-7 F result is reported as 500 nF and a 1e-4 F result as 100 µF; the underlying farad value is unchanged.

According to Hyperphysics, Georgia State University, the energy stored in a charged capacitor is E = 1/2 C V^2, and solving for C gives the capacitor size formula C = 2 E / V^2.

Once you know the required capacitance and want to verify it against plate geometry, Capacitance Calculator solves the parallel-plate form C = ε A / d for the same kind of part.

Four ideas show up in every capacitor-sizing problem: the stored-energy equation, the V squared dependence, the SI prefix system, and the 3-digit capacitor code.

The 3-digit code is convenient when you are at a parts bench comparing unmarked ceramic or film parts. The calculator prints the code so you can match the calculated capacitance to a physical part without converting prefixes by hand; values outside the 10 pF to 99 µF range print "—" because large electrolytic parts use direct µF markings.

When sizing a capacitor for AC filtering rather than energy storage, Capacitive Reactance Calculator takes the same capacitance and applies Xc = 1 / (2π f C) to find the impedance.

Enter the energy the capacitor must deliver and the voltage it will sit at, then read the capacitance and the 3-digit code.

1. 1 Estimate the start-up energy: Convert the motor, defibrillator, or DC-link energy budget into joules (1 mJ = 0.001 J, 1 µJ = 0.000001 J). For a current pulse, compute E = V * I * t first; for example, a small DC motor that draws 4 mA at 16 V for 1 ms needs E = 16 * 0.004 * 0.001 = 0.000064 J, which matches the 64 µJ default.
2. 2 Enter the operating voltage: Use the rated supply or motor operating voltage in volts, not the ripple peak. If the rail sags by 10 % during the pulse, use the sagged value to keep the answer conservative.
3. 3 Read the required capacitance: The primary output shows C in the most readable SI prefix. The unit appears next to the number and updates if you change the inputs.
4. 4 Note the 3-digit capacitor code: The second output prints the EIA 3-digit marking when the capacitance falls inside the 10 pF to 99 µF range the convention covers; values outside that range show "—" because large electrolytic capacitors use direct µF markings.
5. 5 Pick a part with margin: Choose a capacitor whose voltage rating is at least 1.5x the operating rail and whose tolerance fits the application. The calculator does not enforce those rules because they depend on the design.

A 12 V brushed motor that draws 2 A for 5 ms during start-up needs E = 12 * 2 * 0.005 = 0.12 J. The calculator reports C = 2 * 0.12 / 144 = 0.00167 F, or about 1.67 mF; the 3-digit code field shows "—" because 1.67 mF exceeds the 99 µF limit.

Once you have chosen the capacitance, Capacitor Charge Time Calculator tells you how long the same component takes to charge through a series resistor so you can confirm the start-up window.

Sizing a capacitor from energy and voltage collapses several design steps into one entry, which saves time on every motor-start and DC-link design.

• • Skip the algebra on every design: You avoid rewriting C = 2 E / V^2 from scratch each time, so you can compare energy budgets across multiple rails quickly.
• • Match the answer to a physical part: The auto-prefixed capacitance plus the EIA 3-digit code take you from joules and volts to a part number on a distributor page.
• • Quantify the energy cost of higher voltages: Doubling the operating rail quarters the capacitance, easy to see by re-entering the new V and watching the answer move.
• • Stay dimensionally correct: The farad, joule, and volt are SI units, so the result is dimensionally consistent with the input. You can sanity-check by multiplying C by V squared and dividing by two.
• • Support safety-critical applications: Defibrillator, welding, and pulsed-power designs all start from an energy target. Declaring the joules up front keeps safety margins visible during review.

If you would rather not enter joules, compute them from V * I * t for a known current pulse and plug the result into the same calculator.

If you would rather enter a known capacitance and a voltage to see the stored energy in joules, Capacitor Charge Calculator runs the math in the opposite direction.

Four factors influence how a real capacitor behaves compared with the calculator output: voltage tolerance, temperature, equivalent series resistance, and aging.

• • The calculator assumes a single ideal capacitor. Real circuits often combine parallel or series banks to hit a target while keeping voltage or ESR within limits.
• • It does not model leakage current, dielectric absorption, or frequency-dependent behavior. Use a separate tool or bench measurement if those effects dominate your design.
• • Auto-prefixing rounds the printed value to four significant figures, so the displayed capacitance is within 0.05 % of the underlying farad value but the part you buy may still sit on the wrong side of a tight tolerance band.

If your design sits on the edge of a safety margin, run the calculator with a slightly higher energy target to leave room for tolerance, temperature, and aging combined.

According to NIST Physical Measurement Laboratory, the farad is the SI derived unit of capacitance, defined as one coulomb per volt, which keeps the C = 2 E / V^2 relationship dimensionally consistent in joules, volts, and farads.

As published by Omni Calculator capacitor size reference, a 16 V motor with 64 µJ of start-up energy requires a 0.5 µF capacitor, matching C = 2 * 64e-6 / 16^2 = 5e-7 F.

When the printed capacitance needs to move between F, mF, uF, nF, and pF without losing precision, Capacitance Conversion Calculator handles the prefix conversion and the 3-digit code decode in one step.