RC Charging Voltage Calculator
When a capacitor charges through a resistor, the voltage across the capacitor rises exponentially, approaching but never quite reaching the supply voltage. The governing equation is V(t) = V0 * (1 - e^(-t/RC)), where V0 is the supply voltage, R is the resistance in ohms, C is the capacitance in farads, and t is the elapsed time in seconds. The product RC is the time constant (tau): after one tau, the voltage reaches 63.2% of supply; after five tau, it is effectively fully charged at 99.3%. This behavior underlies timing circuits, pulse shapers, integrators, and power supply filters throughout electronics.
RC charging formula
V(t) = V0 * (1 - e^(-t / RC))
Time constant: tau = R * C
At t = tau, V = 0.632 * V0. At t = 2*tau, V = 0.865 * V0. At t = 5*tau, V = 0.993 * V0 (considered fully charged). Enter R in ohms and C in farads (1 uF = 0.000001 F, 1 mF = 0.001 F).
Understanding RC circuits
- RC time constants determine the frequency response of low-pass and high-pass filters: f_cutoff = 1/(2 * pi * RC).
- In 555 timer circuits, resistors and capacitors set the timing period using the RC time constant.
- Power supply smoothing capacitors charge quickly through small source resistance, requiring large C for long discharge times.
- To convert: 1 kilohm = 1,000 ohms; 1 microfarad = 0.000001 farad; 1 millisecond = 0.001 second.
Frequently asked questions
What is the RC time constant?
The RC time constant (tau) equals R multiplied by C. After one time constant, the capacitor has charged to about 63.2% of the supply voltage. After 5 time constants, it is considered fully charged (99.3%).
What is the RC charging formula?
V(t) = V0 * (1 - e^(-t / RC)), where V0 is the supply voltage, R is resistance in ohms, C is capacitance in farads, and t is elapsed time in seconds.
How do I convert milliseconds to seconds for the formula?
Divide milliseconds by 1,000. For example, 500 ms = 0.5 s. Similarly, convert microfarads to farads by dividing by 1,000,000, and kilohms to ohms by multiplying by 1,000.
What percentage of supply voltage is reached after 2 time constants?
After 2 time constants (t = 2RC), the capacitor voltage is V0 * (1 - e^-2) = approximately 86.5% of the supply voltage.
Does the formula apply to RC discharging as well?
For discharging, the formula is V(t) = V0 * e^(-t / RC), where V0 is the initial voltage on the capacitor. This calculator covers charging from 0 V. A separate calculation is needed for discharge.
Official sources
- NIST: NIST SP 811, Guide for SI Units.
- OpenStax University Physics: RC Circuits, Vol. 2 Ch. 10.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.