RC Circuit Time Constant Calculator

The time constant τ (tau) of an RC circuit equals the resistance multiplied by the capacitance, τ = R × C. It has units of seconds and measures how quickly the capacitor charges or discharges through the resistor. After one time constant, a charging capacitor has reached about 63.2% of the supply voltage; after five time constants, it is considered fully charged (≈ 99.3%).

For a resistor-inductor circuit the time constant is τ = L / R, not R × C. Instead of describing how voltage builds on a capacitor, it describes how current builds (or decays) through an inductor. The same exponential form applies: i(t) = I_max × (1 − e^(−t/τ)) when energising, and i(t) = I_0 × e^(−t/τ) when de-energising.

The charging equation V(t) = Vs × (1 − e^(−t/τ)) becomes V(τ) = Vs × (1 − 1/e). The value 1 − 1/e ≈ 0.6321, so after one τ the capacitor has reached about 63.2% of the supply voltage. The number is intrinsic to the exponential decay of the curve, not to any particular component.

Mathematically, a capacitor never fully reaches the supply voltage — the exponential curve only approaches it. Engineers use the convention that the capacitor is fully charged after about 5τ, by which point the voltage is about 99.3% of Vs. Beyond 5τ the remaining error is typically below circuit tolerance.

Component values can span twelve orders of magnitude: capacitors in picofarads (10⁻¹²) up to farads, resistors from milliohms to megaohms. The product R × C lands anywhere from nanoseconds to hours, so converting every value to SI base units (ohms and farads) before multiplying is the only way to get a correct result, especially when the inputs are in different scales like kΩ and µF.