Capacitor Discharge Voltage Calculator and Formula

A capacitor discharge voltage calculator estimates the voltage remaining after a capacitor discharges for a specified time through a resistance. Enter the initial voltage, resistance, capacitance, and elapsed time; the result is the predicted capacitor voltage, along with the time constant and discharged charge.

Formula

For an ideal capacitor discharging through a resistor, voltage falls exponentially:

V(t) = V₀ × e^−t/(RC)

• V(t) is the voltage remaining after elapsed time t, in volts (V).
• V₀ is the capacitor’s voltage at the start of the discharge, in volts.
• t is elapsed time, in seconds (s).
• R is the discharge resistance, in ohms (Ω).
• C is capacitance, in farads (F). The calculator accepts microfarads (µF) and converts them to farads by multiplying by 0.000001.

The time constant is τ = RC, measured in seconds. After one time constant, the voltage is about 36.8% of its starting value. Remaining charge is Q = CV, in coulombs (C), with capacitance converted to farads. These equations assume a fixed resistor and capacitance and a simple discharge path.

Worked Example

Using the calculator’s default inputs: V₀ = 12 V, R = 10,000 Ω, C = 100 µF, and t = 1 s.

1. Convert capacitance: 100 µF × 0.000001 = 0.0001 F.
2. Find the time constant: τ = 10,000 Ω × 0.0001 F = 1 s.
3. Calculate voltage: V(1) = 12 × e^−1/1 = 12 × 0.367879… = 4.415 V, rounded to three decimal places.
4. Calculate remaining charge: Q = 0.0001 F × 4.415 V = 0.0004415 C, or 0.0004415 C at the calculator’s nine-decimal display precision.

The main result is approximately 4.415 V remaining after one second. The time constant is 1 s. The charge output uses the rounded voltage result, so its displayed value is 0.0004415 C.

How to Use the Calculator

Enter the voltage measured or specified at the beginning of the discharge, the resistance actually connected across the capacitor, the capacitance, and the time since discharge began. The calculator returns the estimated voltage. Resistance is entered in ohms, capacitance in microfarads, and time in seconds; do not enter kilo-ohms or milliseconds without converting them first.

• Convert kilo-ohms to ohms by multiplying by 1,000. For example, 4.7 kΩ is 4,700 Ω.
• Convert milliseconds to seconds by dividing by 1,000; 250 ms is 0.250 s.
• Convert nanofarads to microfarads by dividing by 1,000; 100 nF is 0.1 µF.
• For a resistance given in megohms, multiply by 1,000,000 to enter ohms.

The calculator permits zero as an input limit, but the discharge equation is undefined if resistance or capacitance is zero. Use positive, nonzero values for both, and use a nonnegative elapsed time. A zero starting voltage simply gives zero volts throughout the idealized calculation.

Interpreting the Result

A larger resistance or capacitance makes the time constant longer, so the capacitor voltage falls more slowly. A smaller resistance provides a faster discharge in this model. Voltage does not drop by a fixed number of volts per second: it loses the same fraction over each successive time interval equal to one time constant.

For instance, after two time constants, the remaining voltage is about 13.5% of the initial voltage; after five, it is about 0.67%. These are percentages of the starting voltage, not fixed voltage thresholds. A calculator result is a mathematical estimate, not a measurement of a particular circuit.

Assumptions and Common Errors

The formula describes a capacitor connected to a constant resistance, with no continuing power source and no significant additional discharge paths. Real circuits can depart from this model: capacitor tolerance, resistor tolerance, leakage, wiring, measurement equipment, and temperature can change the observed decay. Some circuits also have a load or active component that changes the effective resistance as voltage falls.

• Confusing capacitance and resistance units: using 100 instead of 0.1 for 100 µF when entering farads changes the result substantially. This calculator specifically takes µF.
• Using the wrong resistance: when several resistive paths are connected, the effective resistance seen by the capacitor may differ from one resistor’s printed value.
• Starting the clock at the wrong point: elapsed time should begin when the capacitor starts discharging through the modeled path, not necessarily when a switch is first moved if the circuit has delay.
• Over-interpreting decimal places: the displayed precision is rounding, not a statement of component accuracy. A result such as 4.415 V should not be treated as guaranteed to the nearest millivolt.

For an ideal RC circuit, the resistor’s energy dissipation and a capacitor’s stored energy can also be described by circuit equations, but this calculator does not determine component ratings, safe discharge procedures, or whether a specific device has reached a safe voltage. A charged capacitor can retain hazardous energy; follow the equipment manufacturer’s instructions and have qualified personnel handle high-energy or high-voltage circuits. Never assume a capacitor is discharged merely because a calculated time has passed—verify using an appropriate method.

When This Estimate Is Useful

The calculation is useful for understanding an RC timing circuit, estimating how quickly voltage decays in a simple test setup, or comparing how changing R or C affects discharge time. It can also help estimate when a measurement should be taken, provided the circuit matches the model. For a target voltage, rearrange the equation to find the ideal elapsed time: t = RC ln(V₀/V), where V is the desired remaining voltage and must be positive and no greater than V₀. This calculator reports voltage for a time you provide; it does not solve that inverse question directly.

When you need a more reliable circuit prediction, account for component tolerances and all connected paths, or use a circuit simulator or measurement. If the capacitor is part of a complex powered device, its behavior may not follow a single-resistor discharge curve.

Frequently Asked Questions

How long does it take a capacitor to discharge?
There is no single discharge time; it depends on resistance and capacitance. One time constant leaves about 36.8% of the initial voltage, while five time constants leave about 0.67% in the ideal RC model.

What is the capacitor discharge voltage formula?
For a capacitor discharging through a resistor, V(t) = V₀e^−t/(RC). Use volts, ohms, farads, and seconds, or convert other units consistently.

Does a capacitor discharge linearly?
No. In an ideal resistor-capacitor circuit it decays exponentially: the voltage falls quickly at first and then more slowly.

How do I calculate the time constant?
Multiply resistance in ohms by capacitance in farads: τ = RC. The result is in seconds. For example, 10 kΩ and 100 µF give a 1-second time constant.

Can I use this calculator to confirm a capacitor is safe?
No. It is an idealized estimate, not a safety test. Actual voltage can differ, and capacitors may retain dangerous energy. Follow device instructions and verify with suitable equipment and expertise.

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in v0 | Initial voltage | V | 12 | 0
in r | Resistance | ohm | 10000 | 0
in c | Capacitance | uF | 100 | 0
in t | Elapsed time | s | 1 | 0
out v | Voltage remaining | V | v0 * exp(-t / (r * c * 0.000001)) | 3
out tau | Time constant | s | r * c * 0.000001 | 6
out q | Remaining charge | C | c * 0.000001 * v | 9