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.
| After | Reached | Time |
|---|---|---|
| 1τ | 63.2 % | — |
| 2τ | 86.5 % | — |
| 3τ | 95.0 % | — |
| 4τ | 98.2 % | — |
| 5τ | 99.3 % | — |
Charging from zero toward the final value. Discharging is the mirror image: after 1τ, 36.8 % is left. A discharged-looking capacitor can still bite — measure it.
Keep these results
We send this one email through our mail provider and don't keep your address unless you tick the box.
We send this one email through our mail provider and don't keep your address.
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 people ask
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.
Related
- 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.
- Formula sheets
Spot something wrong on this page? Report it
Thanks — your report was sent.
That didn’t send. Please try again later.
A heads-up on tools that fit — by email, optional
Leave your email and tick the box for a short heads-up, at most every two weeks, about tools, drills and diagrams that fit what you've been working through — here and on bentright.com and fieldcalc.net. One list across the three, one click to leave, and nothing is sent until you confirm from your inbox.