# [RL Time Constant Calculator](https://blog.hirnschall.net/tools/rl-time-constant/)

author: [Sebastian Hirnschall](https://blog.hirnschall.net/about/)

meta description: Calculate the RL time constant τ = L/R. Solve for time constant, inductance, or resistance. Optionally compute energizing or de-energizing current at a given time.

meta title: RL Time Constant Calculator — Solve for τ, L, or R

date published: 11.05.2026 (DD.MM.YYYY format)
date last modified: 11.05.2026 (DD.MM.YYYY format)

---

Calculator
----------

Provide any two of \( R \), \( L \), \( \tau \) — the third is solved. Optionally provide a time \( t \) and a supply voltage or initial current to calculate the energizing or de-energizing current at that time.

* Resistance (R):
* Ω
  kΩ
  MΩ

* Inductance (L):
* H
  mH
  µH
  nH

* Time constant (τ):
* s
  ms
  µs
  min

---

* Time (t) — optional:
* s
  ms
  µs
  min

* Supply voltage Vs (energizing) — optional:
* V
  mV
  kV

* Initial current I0 (de-energizing) — optional:
* A
  mA

Provide any two of R, L, τ to calculate.

Calculate



RL Time Constant — Explanation
------------------------------

The RL time constant \( \tau \) characterises how quickly the current in an RL circuit rises or falls in response to a voltage step:
\[
\tau = \frac{L}{R}
\]
Where \( L \) is in Henrys and \( R \) is in Ohms, giving \( \tau \) in seconds. A larger inductance stores more energy and takes longer to change its current; a larger resistance dissipates energy faster and shortens the transition. The time constant is the single number that governs every transient in the circuit.

The unit check is worth doing once: \( [L/R] = [\text{H}/\Omega] = [\text{H} \cdot \text{A} / \text{V}] = [\text{Wb} / \text{V}] = [\text{V} \cdot \text{s} / \text{V}] = [\text{s}] \). This is the RL counterpart of the RC time constant \( \tau = RC \); see the [RC time constant calculator](https://blog.hirnschall.net/tools/rc-time-constant/) for the capacitive version.

Energizing
----------

When a voltage \( V\_s \) is applied to a series RL circuit with zero initial current, the current rises exponentially toward its steady-state value \( I\_{\max} = V\_s / R \):
\[
I(t) = \frac{V\_s}{R} \left(1 - e^{-t/\tau}\right)
\]
At \( t = 0 \) the inductor looks like an open circuit — it carries no current yet and all of \( V\_s \) appears across it. As current builds up, the back-EMF of the inductor falls and the resistor takes an increasing share of the voltage. After five time constants the current is within 1% of \( I\_{\max} \) and the inductor looks like a plain wire carrying DC:
\[
\begin{align}
t = 1\tau &\Rightarrow I = 63.2\%\ I\_{\max} \\
t = 2\tau &\Rightarrow I = 86.5\%\ I\_{\max} \\
t = 3\tau &\Rightarrow I = 95.0\%\ I\_{\max} \\
t = 4\tau &\Rightarrow I = 98.2\%\ I\_{\max} \\
t = 5\tau &\Rightarrow I = 99.3\%\ I\_{\max}
\end{align}
\]

De-energizing
-------------

When the supply is removed from an inductor carrying an initial current \( I\_0 \), the current decays exponentially through the discharge path (typically a freewheeling diode or the source resistance):
\[
I(t) = I\_0 \cdot e^{-t/\tau}
\]
After one time constant the current has fallen to \( 1/e \approx 36.8\% \) of \( I\_0 \). The inductor resists the drop and will develop whatever voltage across itself is needed to keep current flowing — this is the source of the inductive voltage spike that appears when an inductive load is switched off without a suppression path. The energy stored at \( I\_0 \) is \( E = \frac{1}{2}LI\_0^2 \); see the [inductor energy calculator](https://blog.hirnschall.net/tools/inductor-stored-energy/) to quantify it.

Purpose of the Calculator
-------------------------

Given any two of \( R \), \( L \), \( \tau \), the calculator solves for the third:

* To solve for \( \tau \): \[ \tau = \frac{L}{R} \]
* To solve for \( R \): \[ R = \frac{L}{\tau} \]
* To solve for \( L \): \[ L = \tau \cdot R \]

Optionally, providing \( t \) and \( V\_s \) calculates the energizing current at that time, and providing \( t \) and \( I\_0 \) calculates the de-energizing current. Both can be provided together to compare the two in the same circuit. If L is a combination of inductors, compute the equivalent value first with the [inductors in series](https://blog.hirnschall.net/tools/inductors-in-series/) or [inductors in parallel](https://blog.hirnschall.net/tools/inductors-in-parallel/) calculator.

Related Tools
-------------

* [RC Time Constant Calculator](https://blog.hirnschall.net/tools/rc-time-constant/) — the capacitive equivalent: \( \tau = RC \), voltage across capacitor as the state variable.
* [Inductor Impedance Calculator](https://blog.hirnschall.net/tools/inductor-impedance/) — frequency-domain view of the same RL circuit.
* [Inductor Energy Calculator](https://blog.hirnschall.net/tools/inductor-stored-energy/) — quantify the energy stored at a given current.
* [Inductors in Series](https://blog.hirnschall.net/tools/inductors-in-series/) / [Inductors in Parallel](https://blog.hirnschall.net/tools/inductors-in-parallel/) — compute the equivalent inductance of a network before using it here.

More calculators: [blog.hirnschall.net/tools/](https://blog.hirnschall.net/tools/).