Capacitor charge & ripple calculator
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Charge / discharge
Time constant (τ)
τ = R × C
Time to 63.2 %
1τ = 63.2 % of the supply
Time to 95.0 %
3τ = 95.0 % of the supply
Time to 99.3 %
5τ = 99.3 % of the supply
Stored energy
E = ½ × C × V²
Rectifier output ripple
Ripple voltage (Vr)
Full-wave — I ÷ (2 × 50 × C)
Ripple as % of output
Vr ÷ V × 100
Required C for target ripple
C = I ÷ (2 × 50 × Vr)
About the model
Charging a capacitor through a resistor follows the exponential V(t) = V·(1 − e^(−t/τ)) with τ = R·C: after one time constant the capacitor is at 63.2 %, after 3τ at 95 %, and after 5τ it is effectively full at 99.3 %. The stored energy E = ½·C·V² is the same expression used for the inrush peak when the capacitor first connects to the supply.
On a rectified rail the capacitor recharges at the ripple peaks and supplies the load between them, so the peak-to-peak ripple is Vr = I / (2·f·C) for a full-wave rectifier (charging twice per cycle) and I / (f·C) for half-wave. Halving the ripple needs double the capacitance — or double the ripple frequency, which is why full-wave and higher-mains designs use smaller bulk capacitors. The model ignores capacitor ESR and the real conduction angle, which add a few tens of percent on top.
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