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RL Circuit Time Constant Calculator

Find a resistor-inductor circuit's time constant (τ = L ÷ R) and the percent of final current reached (or remaining) at a given moment.

Time constant (τ = L ÷ R)
0.002 s
Percent of final current reached at t
63.212%
Time to ~99.3% (5 time constants)
0.01 s

How it works

An inductor resists any change in the current flowing through it, so a resistor and inductor in series don't jump to a new current instantly — they approach it exponentially, with the time constant τ = L ÷ R setting the pace (L in henries, R in ohms). This is the inductive counterpart to an RC circuit's τ = R × C, this site's RC Circuit Time Constant calculator.

When a voltage source starts driving current through the circuit ('energizing'), the current climbs as i(t) = I_max(1 − e^(−t/τ)), reaching about 63.2% of its final value after one time constant. When the source is instead removed and the inductor's stored magnetic energy drives the current back down through the resistor ('de-energizing'), the current decays as i(t) = I_initial × e^(−t/τ), falling to about 36.8% of its starting value after one τ — mirroring an RC circuit's discharge curve, just governed by L/R instead of R×C.

As with any first-order exponential response, the transient is conventionally treated as finished after five time constants (about 99.3% of the way there), which this calculator reports alongside the percentage at your specified elapsed time.

FAQ

Why doesn't this calculator ask for a source voltage?

Because the percentage of the way to the final (or initial) current only depends on elapsed time relative to τ = L/R, not on the actual current or voltage values — the same reason this site's RC Circuit Time Constant calculator only needs R, C, and time. If you know your circuit's final steady-state current (V ÷ R for a simple loop), multiply it by the percentage shown to get the actual current at that moment.

What happens physically at the instant a switch opens in an RL circuit?

The inductor's stored energy has to go somewhere — it can't allow current to change instantaneously, so it forces current to keep flowing through whatever path is available (often generating a brief high-voltage spike, which is why real RL circuits like relay coils are usually built with a flyback diode or snubber to give that current somewhere safe to go).

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