RL Time Constant Calculator
From an inductor and a resistor, get the RL time constant that sets how fast the current rises and falls, plus the time to settle.
Two inputs, three answers
Enter the inductance (in millihenries) and the resistance and the calculator returns the time constant, the same value in milliseconds, and the time to reach steady state.
63 % at 1τ, 99 % at 5τ
After one time constant the current reaches about 63 % of its final value, and after five it is within about 1 % — which is why 5τ is treated as settled.
What is an RL time constant calculator?
An inductor and a resistor in, a settling time out
An RL time constant calculator turns two component values — an inductor L and a resistor R — into the time constant that governs how quickly current changes in the circuit. Unlike a resistor, an inductor resists sudden changes in current: when you apply a voltage, the current ramps up gradually rather than jumping, and the time constant τ = L / R sets the pace. It is the key number behind relay coils, motor windings, switching supplies, and any circuit where an inductor's current rise or fall matters. Enter L and R and the settling behaviour falls out of one short division.
Enter the inductance (in millihenries) and the resistance to get the time constant and the time to steady state instantly.
A short division, built from the inductance L (converted from millihenries to henries) and the resistance R.
τ = L / RThe time constant is τ = L / R, in seconds when L is in henries and R in ohms. Because you enter the inductance in millihenries, the calculator first multiplies by one-thousandth to get henries, then divides by R. The time in milliseconds is just the seconds value times 1000. The practical settling time is taken as five time constants, 5τ, because after five the current is within about 1 % of its final value — close enough to call steady.
Suppose you drive a relay coil with L = 100 mH and a total series resistance of R = 10 Ω.
Convert the inductance
100 mH × 0.001 = 0.1 H — the inductance in henries.
Time constant
0.1 / 10 = 0.01 s — one time constant, or 10 ms.
Time to steady state
5 × 0.01 = 0.05 s — after 50 ms the current is within about 1 % of its final value.
The time constant (0.01 s, or 10 ms, in the example) is how long the current takes to reach about 63 % of its final value after the voltage is switched on — and likewise to fall to about 37 % of its starting value when switched off. After two time constants it is at roughly 86 %, after three about 95 %, and after five about 99 %, which is why 5τ (here 50 ms) is treated as fully settled. A larger inductance stores more energy and slows the change, lengthening τ; a larger resistance speeds it up, shortening τ. So to make a coil respond faster, lower L or raise R; to make it ramp more gently, do the opposite. The same number tells you how fast a relay pulls in, how quickly a motor winding energises, or how long a switching node takes to settle.
The formula is the standard first-order result, but a couple of practical points are worth keeping in mind.
Series resistance, ideal coils, and switch-off spikes
The R in τ = L / R is the total series resistance, which includes the inductor's own winding resistance — leave it out and the computed time constant will be too long. The formula assumes an ideal inductor with constant inductance; real cores saturate at high current and change L, and stray capacitance matters at high frequencies. Tolerances on L and R (often ±10 % or more for inductors) shift the measured value. Note too that abruptly interrupting the current in an inductor produces a large voltage spike, so a practical RL circuit usually needs a flyback diode or snubber to protect the switching device.