Second year AC theory Free · works offline once loaded

RC / RL time constant calculator

Pick RC (a capacitor charging through a resistor) or RL (current building in a coil). Enter the parts and get τ, the full five-time-constant table, and — if you give a time — how far along it is.

Circuit

RC (condensateur) RL (bobine)

Résistance (Ω) Capacité Unité de capacité Temps après la commutation facultatif Unité de temps

Constante de temps—

Cinq constantes de temps—

Atteint au temps choisi—

Après	Atteint	Temps
1τ	63,2 %	—
2τ	86,5 %	—
3τ	95,0 %	—
4τ	98,2 %	—
5τ	99,3 %	—

Charge à partir de zéro vers la valeur finale. La décharge en est l’image miroir : après 1τ, il reste 36,8 %. Un condensateur qui semble déchargé peut encore donner un choc — mesurez-le.

Garder ces résultats

Nous envoyons ce seul courriel par notre fournisseur de courriel et ne gardons pas votre adresse.

How it works

τ = R × Cohms × farads = seconds
τ = L ÷ Rhenries ÷ ohms = seconds
1 − e^−t/τfraction reached at time t

A capacitor does not charge instantly: the resistor limits how fast current can fill it, and as it fills the push left to drive more current shrinks. The result is a curve that is steep at first and flattens out. A coil is the same shape turned round — its current climbs toward V ÷ R, fast at first and then slowly. The time constant τ is the yardstick for both: in each τ the circuit closes 63.2 % of the gap that is left.

Worked examples

RC: 10 kΩ and 100 µF

τ = 10,000 × 0.000 1 = 1 s.
Fully charged, for practical purposes, at 5τ = 5 s.
At 2 s: 1 − e⁻² = 1 − 0.135 = 86.5 % of the supply voltage.

RL: a 500 mH coil with 100 Ω of winding

τ = 0.5 ÷ 100 = 0.005 s = 5 ms.
On 24 V DC the current heads for 24 ÷ 100 = 0.24 A, and gets 63.2 % of the way (0.152 A) in 5 ms.
It is all but there at 5τ = 25 ms.

Questions fréquentes

Why 63.2 %?

Charging follows the curve 1 − e^−t/τ. At t = τ that is 1 − e⁻¹ = 0.632. Each further time constant closes 63.2 % of whatever gap is left, which is why the steps are 63.2, 86.5, 95.0, 98.2 and 99.3 %.

Is it really finished after five time constants?

Mathematically it never quite gets there; practically, at 5τ it is within 0.7 % of the final value, and that is the rule of thumb everyone uses for “fully charged” or “fully built up”. The same numbers apply to discharging: after 5τ less than 0.7 % is left — which is not the same as safe on a big capacitor. Measure before you touch.

What does the time constant mean for an RL circuit?

For a coil, τ = L ÷ R is how long the current takes to reach 63.2 % of its final value (V ÷ R) after the switch closes. A bigger inductance or a smaller resistance makes it slower.

Voir aussi

Capacitance — the lesson behind this tool.
Inductance — the lesson behind this tool.
Capacitive & inductive reactance — the same parts on AC.
Motor control: timers — where time delays show up on the job.
Feuilles de formules

Vous voyez une erreur sur cette page? Signalez-la

Merci — votre signalement a été envoyé.

L’envoi n’a pas fonctionné. Veuillez réessayer plus tard.