RC Time Constant Calculator — τ = R × C

τ (tau) = R × C exactly, with R in ohms and C in farads producing τ in seconds. If R is 10 kΩ and C is 10 µF, τ = 10 000 × 0.00001 = 0.1 seconds = 100 ms. The formula is clean dimensional analysis — ohms × farads = seconds by definition of the underlying SI units.

At t = 5τ the capacitor voltage has reached V = V₀ × (1 − e⁻⁵) = V₀ × 0.99326 — within 0.7% of the supply voltage V₀. That residual 0.7% is below the tolerance of almost every capacitor on the market, so industry practice rounds it to 'charged'. One more τ (6τ) gets you to 99.75%, and infinite τ would get you to exactly 100%.

They are inversely linked through the same R and C: fc = 1/(2πRC) = 1/(2πτ). The cutoff frequency marks the point where a high-pass or low-pass RC filter attenuates the input by −3 dB (half-power). A 10 kΩ × 10 µF pair gives τ = 100 ms and fc = 1.59 Hz — meaning frequencies below 1.59 Hz get severely attenuated by this RC network.

The formula τ = RC is exact for ideal capacitors and nearly exact for real ones above audio frequencies. At very high frequencies, parasitic inductance (ESL) starts to matter; at very low frequencies, leakage current and dielectric absorption matter. For any practical circuit from DC up to several MHz, τ = RC is the right answer.

Constant-current charging follows a different formula: t = C × V / I, where I is the current in amperes. This is much faster than resistor-limited charging — a 100 µF cap charging to 12V at 1A takes only 1.2 ms, compared with 120 ms through a 120 Ω resistor. If your supply is current-limited rather than voltage-limited, toggle to CC mode in the calculator.

RC circuits decay exponentially with τ = RC and no natural oscillation. LC circuits oscillate at ω = 1/√(LC) and decay with a time constant of L/R. If you build an RLC circuit with resistance in series with an LC pair, you get either an overdamped response (looks like RC), underdamped response (oscillations), or critically damped response (fastest non-oscillating step response).

Work backwards from τ to a product R × C that equals it, then split the product according to practical constraints. If you need τ = 100 ms (0.1s), you could pick R = 1 kΩ and C = 100 µF, or R = 10 kΩ and C = 10 µF, or R = 100 kΩ and C = 1 µF. The larger the RC product for the same τ, the more energy the capacitor stores — pick the pair that fits your voltage rating and power-handling budget.

Yes. For RC pairs in parallel, τ remains R × C (parallel capacitance values add together, so a 10 µF + 10 µF pair through a 10 kΩ resistor has τ = 10 kΩ × 20 µF = 200 ms). For series capacitors, the effective capacitance is smaller (1/C_series = Σ1/C_i), so τ is shorter — two 10 µF caps in series through 10 kΩ gives C_series = 5 µF and τ = 50 ms.