Work out capacitor charge time instantly with clear inputs, formula shown and shareable results.
An RC circuit charges exponentially: V(t) = Vs x (1 - e^(-t/RC)). One time constant reaches 63.2%, three reach 95% and five reach over 99%. Rearranging gives the time to any target voltage as -RC x ln(1 - Vt/Vs).
RC charging
V(t) = Vs (1 - e^(-t/tau)), tau = R x C; t = -tau x ln(1 - Vt/Vs)
Electrical results are planning estimates only. Verify against the applicable wiring rules (IEC 60364, BS 7671, NEC or local code) and have all installation work designed and checked by a qualified electrician.
The charging current is proportional to the remaining voltage difference, so it decays asymptotically. Five time constants is treated as complete in practice.
Use a constant-current source rather than a resistor: dV/dt = I/C gives a straight line instead of an exponential.