RL Time Constant Calculator
By Santaji GadepatilinUpdated October 28, 2026
When voltage is applied to an inductor through a resistance, current rises exponentially with a time constant τ = L/R — and decays the same way when switched off. This RL time constant calculator gives τ and the current at any moment — see RC and RL time constants explained.
How to use the RL time constant calculator
Enter the inductance, the total resistance in the circuit (coil resistance plus any series resistor), the supply voltage and a time after switching. You get the time constant, the final current and the current at that time for both rising and decaying cases.
RL circuit formulas
τ = L ÷ R · i(t)rise = (V/R)(1 − e−t/τ) · i(t)decay = (V/R) e−t/τ
Current vs time constants
| Time | Rising (% of final) | Decaying (% of initial) |
|---|---|---|
| 0.5 τ | 39.3% | 60.7% |
| 1 τ | 63.2% | 36.8% |
| 2 τ | 86.5% | 13.5% |
| 3 τ | 95.0% | 5.0% |
| 4 τ | 98.2% | 1.8% |
| 5 τ | 99.3% | 0.7% |
Typical time constants
| Device | L | R | τ |
|---|---|---|---|
| 24 V DC relay coil | 0.5–2 H | 1–3 kΩ | about 0.5 ms |
| Solenoid valve coil | 0.1–1 H | 20–100 Ω | 5–20 ms |
| Contactor coil (DC) | 2–10 H | 100–500 Ω | 10–50 ms |
Inductive kick
Interrupting inductor current suddenly creates a voltage spike V = L × di/dt. See the inductor energy calculator for suppression methods.
Frequently asked questions
What is the RL time constant?
τ = L ÷ R. After one time constant, current reaches 63.2% of its final value when rising, or falls to 36.8% when decaying.
How long until the current is fully established?
About 5 time constants, when it reaches 99.3% of the final value.
Why do relays drop out slowly with a flyback diode?
The diode keeps current circulating through the coil's own low resistance, giving a long L/R decay. Adding a Zener or resistor in series speeds it up.
How is this different from an RC circuit?
In RC circuits voltage changes exponentially with τ = RC; in RL circuits current does, with τ = L/R.