Every circuit that combines a resistor and a capacitor — from a camera flash to a simple LED timer to a low-pass audio filter — follows the same exponential charging and discharging curve, and that curve's pace is set by a single number: the RC time constant. This calculator computes τ = R × C and shows the resulting voltage over time for both charging and discharging.

How the RC Time Constant Calculator works

The calculator multiplies resistance (converted to ohms) by capacitance (converted to farads) to get τ in seconds: τ = R × C. On the Charging and Discharging tabs, it plugs that τ into the standard first-order RC differential equation solutions — V(t) = V₀(1 − e^(−t/τ)) for charging and V(t) = V₀·e^(−t/τ) for discharging — both derived from Kirchhoff's voltage law applied to a series RC circuit. These are the same equations used in introductory electronics and physics courses (e.g. Sedra & Smith's Microelectronic Circuits, Halliday & Resnick's Fundamentals of Physics).

Inputs and what they mean

Resistance (R) and capacitance (C) set the time constant — pick whichever unit (Ω/kΩ/MΩ for resistance, µF/nF/pF for capacitance) matches your component's datasheet; the calculator converts everything internally. Supply or starting voltage (V₀) is the voltage the capacitor is charging toward or discharging from. Elapsed time (t) is how long the circuit has been charging or discharging, in µs, ms, or s. The time constant τ itself has an outsized effect: doubling either R or C doubles τ and doubles how long every stage of the curve takes.

Limits and edge cases

This calculator models an ideal series RC circuit with a single resistor and capacitor — it does not account for parallel/series combinations of multiple resistors or capacitors (combine them into equivalent R and C first), source impedance, capacitor leakage current, or non-ideal component tolerances (real resistors and capacitors typically vary ±5-20% from their labeled value). For circuits with an inductor (RLC) the behavior is oscillatory rather than a simple exponential, and this tool does not apply. Treat the checkpoint milestones (63.2%, 86.5%, 95.0%, 98.2%, 99.3%) as textbook approximations — real circuits settle exactly to those percentages only under ideal conditions.