Free calculator
RL time constant calculator
Switch a coil on and its current doesn't jump: it rises, fast at first, then slower and slower. The time constant, τ = L ÷ R, sets the pace, and the voltage and resistance set where it ends up. Type the coil, the total resistance and the supply to see how fast it gets there.
500m = 0.5 H. m = milli, µ or u = micro.
The coil's own wire plus any resistor in series.
Time constant, τ = L ÷ R
- Final current, I = V ÷ R
- 30 mA
- Settled (5τ)
- 12.5 ms
- Heat in R once settled, I² × R
- 180 mW
| After | Time | Current | Of the final |
|---|---|---|---|
| 1τ | 2.5 ms | 19 mA | 63.2% |
| 2τ | 5 ms | 25.9 mA | 86.5% |
| 3τ | 7.5 ms | 28.5 mA | 95.0% |
| 4τ | 10 ms | 29.5 mA | 98.2% |
| 5τ | 12.5 ms | 29.8 mA | 99.3% |
As the current rises
Like a relay's pull-in current. 20m = 20 mA.
Time to get there, t = −τ × ln(1 − I ÷ I_final)
- That's
- 1.10 τ
The formulas
Rtotal includes the coil's own wire, and henries divided by ohms give seconds. In each τ the current closes about 63% of the gap to Ifinal, so it's there after about 5τ:
A worked example
A 6 V relay coil: 0.5 H with 200 Ω of wire.
It pulls in at 20 mA, two thirds of the way, which takes 2.5 ms × ln 3 ≈ 2.75 ms. To make it faster, raise the voltage and add series resistance together: 12 V across 380 Ω settles at 31.6 mA with τ ≈ 1.3 ms, about twice as fast.
Switching it off
A coil's current can't stop at once. Open the switch and the energy in its magnetic field makes a big voltage spike, enough to spark across the contacts or kill a transistor. Put a diode across a relay coil, pointing back towards the supply, to give the current a path while it dies away.
Free lesson
Now build it yourself
Each lesson comes in three short parts: see the idea, try it on a live board, then build it yourself, with quick checks as you go.
“RL circuits” is lesson 5 of 5 in Capacitor Caves, Electronics World 3. Free with an account. Lessons unlock in order, so you’ll do the 19 before it first.
Or start from the very first lesson, no account neededThe ideas behind it
Questions people ask
What is the time constant of an RL circuit?
τ = L ÷ R, in seconds when L is in henries and R in ohms. R is the total resistance, the coil's own wire included. After one τ the current has reached about 63% of its final value, and after 5τ it's over 99%.
Why does more resistance make an RL circuit faster?
Because R divides: τ = L ÷ R. Doubling R halves τ, but it also halves the final current, V ÷ R. That's why old stepper-motor drivers raised the voltage and added resistance together: the same current, reached sooner.
What is the final current in an RL circuit?
Once the current stops changing, the coil is just wire, so only resistance limits it: I = V ÷ R, with R the total. 24 V across 480 Ω in total settles at 50 mA, whatever the inductance.
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