# RL Time Constant Calculator

> Calculate the time constant τ = L ÷ R of a resistor–inductor circuit, the inductor current at any time as it rises or decays, and the RL cut-off frequency.

Category: Science & engineering · Applies to: Worldwide · Last updated: 2026-10-29
Interactive calculator: https://calculators.geekmidst.com/calculators/rl-time-constant-calculator

Current through an inductor cannot change instantly: it rises towards V ÷ R with time constant τ = L ÷ R, reaching about 63% after one τ.

Also called: L/R time constant calculator.

## Inputs
- Inductance (default 100)
- Inductance unit (options: µH, mH, H; default mH)
- Total series resistance (default 10)
- Resistance unit (options: Ω, kΩ, MΩ; default ohm)
- Current is (options: Rising, Decaying; default rise)
- Supply voltage (unit V; default 12; optional)
- Time after switching (default 10; optional)
- Time unit (options: ns, µs, ms, s; default ms)

## Results
- Time constant τ
- τ in seconds
- 5τ (≈ 99.3% settled)
- Steady-state current V ÷ R
- Current at that time
- Share of the steady-state current
- Cut-off frequency R/(2πL)

## Formula

```
τ = L ÷ R;  I = V ÷ R;  rising: i(t) = I × (1 − e^(−t/τ));  decaying: i(t) = I × e^(−t/τ);  f_c = R ÷ (2πL)
```

Where:
- L: inductance in henries
- R: total series resistance in ohms
- V: supply voltage
- I: steady-state current
- t: time since the switch

## Worked example
1. τ = 0.1 H ÷ 10 Ω = 0.01 s = 10 ms.
2. Steady-state current I = 12 ÷ 10 = 1.2 A.
3. After 10 ms = 1τ: i = 1.2 × (1 − e⁻¹) ≈ 0.7585 A.

**Result:** A 100 mH coil with 10 Ω in series has τ = 10 ms; 10 ms after switching on 12 V the current is about 0.76 A of its final 1.2 A.

## What the result means

Use τ to estimate how quickly a relay, solenoid or motor winding reaches full current, and how long the current takes to die away when switched off (which is why inductive loads need a flyback path).

## Assumptions and limits
- Ideal inductor (no core saturation) in series with the resistance entered, switched by a step from a stiff voltage source.
- Decaying current starts from V ÷ R and flows through the same resistance.
- Iron-cored inductors saturate, so L falls at high current and the real rise is faster than calculated.

## Questions

### Why does the decay need a path?

Interrupting inductor current abruptly produces a large voltage spike (V = L di/dt). A diode or snubber lets the current decay with the time constant instead.

### Is the coil resistance included?

Only if you add it. Enter the total of the external resistor and the winding resistance.

## Related calculators
- [RC Time Constant Calculator](https://calculators.geekmidst.com/calculators/rc-time-constant-calculator)
- [Ohm’s Law Calculator](https://calculators.geekmidst.com/calculators/ohms-law-calculator)
- [Resistor Calculator](https://calculators.geekmidst.com/calculators/resistor-calculator)

Source: GM¹X CalcVerse — https://calculators.geekmidst.com/calculators/rl-time-constant-calculator