Capacitor Voltage Formula: DC, AC, and RC Circuits

Capacitor voltage is calculated from charge and capacitance using V = Q/C, where V is voltage, Q is charge, and C is capacitance. For a capacitor charging or discharging through a resistor, use the time-dependent RC formula; this calculator finds that voltage from the supply voltage, resistance, capacitance, and elapsed time.

Formula

The calculator models a capacitor charging from an ideal constant-voltage source through a resistor, starting with no charge:

• Charging: V_C(t) = V_S[1 − e^−t/(RC)] = V_S(1 − e^−t/τ).
• Time constant: τ = RC.
• Charge relation: V_C = Q/C.

Here V_C is capacitor voltage in volts (V), V_S is the supply voltage in volts, t is elapsed time in seconds, R is resistance in ohms (Ω), C is capacitance in farads (F), and τ is the time constant in seconds. The calculator takes capacitance in microfarads, so it converts it to farads by multiplying by 0.000001. The exponential function e^x uses the mathematical constant e.

Worked Example

Using the calculator’s defaults: V_S = 5 V, R = 1,000 Ω, C = 100 μF, and t = 0.1 s.

1. Convert capacitance: 100 μF × 0.000001 = 0.0001 F.
2. Find the time constant: τ = RC = 1,000 × 0.0001 = 0.1 s.
3. Substitute into the charging equation: V_C = 5[1 − e^−0.1/0.1] = 5(1 − e⁻¹).
4. Evaluate and round to three decimal places: V_C ≈ 3.161 V.

So, after 0.1 seconds, the ideal capacitor has reached about 3.161 V, and the time constant is 0.100 s.

Which Formula Applies?

V = Q/C is the basic relationship for a capacitor: if you know its charge and capacitance, it gives the voltage across it. It is useful for static calculations and for understanding how much charge corresponds to a voltage. Since one farad is one coulomb per volt, charge in coulombs divided by capacitance in farads gives volts.

The RC equation describes voltage changing over time in a particular circuit. For discharge from an initial voltage V₀ through a resistor, use V_C(t) = V₀e^−t/(RC). For charging that begins at a nonzero voltage V₀, the more general equation is V_C(t) = V_S + (V₀ − V_S)e^−t/(RC). The calculator uses the special case V₀ = 0.

How to Read the Time Constant

The time constant τ = RC sets the pace of the response. After one time constant, an initially uncharged capacitor in this ideal charging circuit reaches about 63.2% of its final supply voltage. During discharge, it falls to about 36.8% of its starting voltage after one time constant. These percentages follow from 1 − e⁻¹ and e⁻¹, respectively.

As a practical guide, charging is about 95% complete after three time constants and about 99.3% complete after five. These are approximations, not a claim that the capacitor reaches the final voltage exactly at a finite time. The ideal exponential approaches its final value progressively.

Using the Calculator and Checking Results

Enter the supply voltage, series resistance, capacitance, and elapsed time. The first result is the modeled capacitor voltage; the second is the time constant. Use consistent SI units in the equation: the calculator accepts volts, ohms, microfarads, and seconds, and performs the capacitance conversion internally.

• If elapsed time is zero, the assumed initially uncharged capacitor reads 0 V.
• If elapsed time is much greater than τ, the result approaches the supply voltage.
• If resistance or capacitance increases, τ increases, so the capacitor charges more slowly.
• If the supply voltage increases, the final voltage increases proportionally, while the fraction reached at a fixed t/τ stays the same.

For example, using kilohms with farads without converting units would make the time constant wrong by a factor of 1,000. Likewise, μF is not F: 100 μF is 0.0001 F, not 100 F. Keep extra precision during intermediate steps and round only the displayed result. In US customary applications, resistance is still commonly expressed in ohms and capacitance in farads or submultiples; voltage remains in volts. The SI equation works the same regardless of the physical dimensions used to describe the circuit, provided values are converted consistently.

Assumptions and Common Misconceptions

The calculator assumes an ideal voltage source, a single resistor and capacitor in series, a fixed resistance and capacitance, and an initially uncharged capacitor. Real circuits may differ because of source resistance, leakage, capacitor tolerance, dielectric behavior, wiring, or additional circuit components. In those cases, the simple RC model may be an approximation rather than an exact prediction.

A capacitor does not have one universal voltage determined by capacitance alone. Capacitance tells how much charge is stored per volt; voltage also depends on the stored charge or the surrounding circuit. Nor does an RC charging equation give the voltage in every circuit: AC signals, switching networks, and circuits with multiple energy-storage components can require different analysis. For a sinusoidal AC circuit, capacitor current and voltage are related by the impedance magnitude X_C = 1/(2πfC), where f is frequency in hertz; this is not the same calculation as the transient charging formula.

Frequently Asked Questions

What is the basic formula for capacitor voltage?
For known charge and capacitance, use V = Q/C. Charge must be in coulombs and capacitance in farads to obtain volts.

How do I calculate capacitor voltage after a time?
For charging from zero through a resistor, use V_C = V_S(1 − e^−t/(RC)). For discharging from an initial voltage, use V_C = V₀e^−t/(RC).

How long does a capacitor take to charge?
There is no exact finite time to reach the supply voltage in the ideal exponential model. It reaches about 95% after 3RC and about 99.3% after 5RC.

Does a larger capacitor charge more slowly?
With the same resistor, yes. A larger capacitance increases the time constant τ = RC, so the voltage changes more slowly.

Can I use this formula for AC voltage?
Not as a general AC voltage calculator. The RC equation here describes a DC step response; sinusoidal AC behavior depends on frequency and circuit impedance.

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in vs | Supply voltage | V | 5 | 0
in r | Resistance | ohm | 1000 | 0
in c | Capacitance | uF | 100 | 0
in t | Elapsed time | s | 0.1 | 0
out v | Capacitor voltage, charging | V | vs * (1 - exp(-t / (r * c * 0.000001))) | 3
out tau | Time constant | s | r * c * 0.000001 | 3