Capacitor Voltage: Calculate It for RC Circuits

This calculator finds the voltage across a capacitor while it charges or discharges through a resistor in a simple RC circuit. Enter the supply voltage, resistance, capacitance, elapsed time, and the capacitor’s starting voltage; the result is the capacitor voltage at that time.

Formula

For a capacitor moving toward a constant supply through a resistor, use:

VC(t) = VS + (V0 − VS)e−t/(RC)

• VC(t) is the capacitor voltage after elapsed time t, in volts (V).
• VS is the constant supply or final voltage, in volts.
• V0 is the capacitor’s voltage at the start of the interval, in volts.
• t is elapsed time, in seconds (s).
• R is the series resistance, in ohms (Ω).
• C is capacitance, in farads (F).

The product τ = RC is the time constant, measured in seconds. The calculator accepts capacitance in microfarads (µF), so it converts it to farads by multiplying by 0.000001. After one time constant, the voltage has completed about 63.2% of the difference between its initial value and the supply. This equation also covers discharging: set the final supply voltage to zero and enter the capacitor’s starting voltage.

Worked Example

Using the calculator’s default values: VS = 5 V, R = 10,000 Ω, C = 100 µF, t = 1 s, and V0 = 0 V.

1. Convert capacitance: 100 µF × 0.000001 = 0.0001 F.
2. Find the time constant: τ = RC = 10,000 × 0.0001 = 1 s.
3. Substitute into the voltage equation: VC = 5 + (0 − 5)e−1/1.
4. Evaluate: VC = 5(1 − e−1) ≈ 3.1606 V, or 3.161 V to three decimal places.

The time constant output is 1.000 s. The calculator rounds displayed results to three decimal places; intermediate values should not be rounded prematurely.

What You’ll Need

• The circuit’s supply or final voltage and the capacitor’s initial voltage.
• The resistance in the capacitor’s charge or discharge path.
• The capacitance, usually printed on the component or given in a circuit diagram.
• The elapsed time after the circuit changes, plus consistent units: volts, ohms, microfarads, and seconds for this calculator.
• For a physical measurement, a suitable voltmeter or multimeter and a safe way to connect it across the capacitor.

Step-by-Step

1. Identify the circuit behavior. This calculation applies to a first-order RC circuit: a capacitor connected through a resistance to a constant voltage. Identify whether it is charging toward a nonzero supply or discharging toward zero. A circuit with multiple changing sources or complex switching may need a different analysis.
2. Find the final voltage. Enter the steady voltage the capacitor is approaching as Supply voltage. For a discharge into a path with a zero-volt reference, enter 0 V. If it discharges toward another fixed voltage, enter that voltage instead.
3. Enter resistance and capacitance. Use the effective resistance seen by the capacitor in the relevant charge or discharge path. Enter resistance in ohms and capacitance in microfarads. Convert other units before entering them: 1 kΩ is 1,000 Ω, and 1 mF is 1,000 µF.
4. Set the initial voltage. Enter the capacitor voltage at the instant the elapsed-time measurement begins. A fully discharged capacitor starts at 0 V, but do not assume that if it may retain charge. If the circuit switches at a later time, use the voltage immediately before that switch as the starting value for the next interval.
5. Enter elapsed time. Use seconds measured from the start of the charging or discharging interval. If your timing is in milliseconds, convert it to seconds by dividing by 1,000.
6. Read the calculated voltage. The first output is the capacitor voltage at the entered time. The time constant is also shown to help you judge the progress: times much shorter than τ mean little change; after several time constants, the voltage is close to its final value.
7. Check the result against the circuit. At time zero, the formula returns the initial voltage. As time increases, the answer approaches the final voltage. It should not cross that final value in this ideal, single-step RC model.

Common Mistakes

• Mixing units: multiplying ohms by a capacitance number in microfarads without converting it gives a time constant one million times too large. Use farads in hand calculations, or enter µF in this calculator.
• Using the wrong initial voltage: a capacitor can retain charge after power is removed. The starting voltage is the voltage at the beginning of the interval, not automatically zero.
• Using the wrong resistance: the relevant value is the effective resistance in the path seen by the capacitor. A source’s output resistance or other connected components may affect it.
• Confusing elapsed time with time constant: elapsed time is the duration since the transition. The time constant is RC; they are equal only in some particular cases.
• Expecting an exact final value: an ideal RC response approaches its final voltage exponentially. It gets very close but does not reach it at a finite time in the equation.
• Rounding too early: keep extra digits through unit conversion and exponent calculations, then round the displayed voltage to the precision appropriate for your measurements.

Tips

• Remember the common landmarks: at 1τ, about 63.2% of the voltage change is complete; at 2τ, about 86.5%; at 3τ, about 95.0%; and at 5τ, about 99.3%.
• For a discharge toward zero, the equation simplifies to VC(t) = V0e−t/(RC). This makes it easy to check whether the result is decreasing as expected.
• For a physical reading, place the meter probes across the capacitor terminals, observing polarity for a polarized capacitor. A meter’s input resistance can affect some high-resistance circuits.
• Use the component’s actual or measured values when precision matters. Capacitance and resistance tolerances, leakage, and other circuit effects can make measured voltage differ from an ideal calculation.

Troubleshooting

The result is unchanged from the starting voltage: Check that elapsed time is greater than zero and that resistance and capacitance are entered in the intended units. A very large time constant compared with the elapsed time can also make the change too small to see at the displayed precision.

The result jumps toward the final voltage too quickly or too slowly: Recheck unit conversions, especially kΩ to Ω, mF to µF, and milliseconds to seconds. Confirm that the resistance is the effective resistance for the circuit state being analyzed.

The calculated voltage is outside the expected range: Verify the signs and values of the initial and final voltages. With a stable supply and positive resistance and capacitance, the result should lie between those two voltages. If it does not, the circuit may not fit this simple model, or an input may be wrong.

A meter reading differs from the estimate: Check probe placement, polarity, elapsed time, and whether the capacitor began at the assumed voltage. Consider component tolerances, leakage, load current, meter loading, and a supply that is not constant. Do not handle a capacitor or circuit while energized unless you are qualified to work safely; capacitors can retain hazardous charge after power is removed. Disconnect power and use an appropriate discharge method before working on a circuit.

Frequently Asked Questions

What is the basic formula for capacitor voltage?
For a capacitor approaching a constant final voltage, use VC}(t) = VS + (V0 − VS)e−t/(RC). For discharge to zero, it reduces to V0e−t/(RC).

How do I calculate the voltage across a capacitor while it charges?
Use the supply as the final voltage and the capacitor’s voltage at the start as its initial voltage. For a fully discharged capacitor, the result is VS(1 − e−t/(RC)).

How do I calculate capacitor voltage during discharge?
For discharge through a resistor to zero volts, multiply the starting voltage by e−t/(RC). If the discharge approaches a different constant voltage, use that as the final voltage in the general formula.

What does the RC time constant tell me?
It is the product of resistance and capacitance, in seconds. One time constant corresponds to about 63.2% of the total change toward the final voltage.

Can this formula describe every capacitor circuit?
No. It assumes a single effective resistance, constant capacitance, and a fixed final voltage during the interval. More complex networks, nonlinear components, or changing sources may require circuit analysis or simulation.

Can a capacitor still have voltage after power is off?
Yes. A capacitor can retain charge, and its voltage may decay slowly depending on its discharge path and leakage. Treat it as potentially charged until it has been safely checked and discharged.

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in v | Supply voltage | V | 5 | 0
in r | Resistance | ohm | 10000 | 0
in c | Capacitance | uF | 100 | 0
in t | Elapsed time | s | 1 | 0
in vi | Initial capacitor voltage | V | 0 | 0
out voltage | Capacitor voltage | V | v + (vi - v) * exp(-t / (r * c * 0.000001)) | 3
out tau | Time constant | s | r * c * 0.000001 | 3