Case 1
- Inductance L (mH)
- 100mH
- Total series resistance R (Ω)
- 10Ω
10.00ms
Open with these valuesRL Time Constant Calculator
Change any value to update the result.
10.00ms
Time constant τ: 10.00 msExamples
How the result moves
Total series resistance R (Ω) (Ω) → Time constant τ (ms)Your current valid inputs, with one value varied across the range.
How the result moves
Held fixed: Inductance L (mH) 100.000 mH.
| Total series resistance R (Ω) (Ω) | Time constant τ (ms) |
|---|---|
| 8.000 | 12.50 |
| 10.000Your value | 10.00 |
| 12.000 | 8.33 |
Millihenries divided by ohms give milliseconds directly: a 100 mH coil in series with 10 Ω has a time constant of 10 ms. After one time constant the current has reached about 63 % of its final value, after five about 99 %. Use the total series resistance, coil winding included.
Worked examples
Case 2
- Inductance L (mH)
- 47mH
- Total series resistance R (Ω)
- 100Ω
0.47ms
Open with these valuesCase 3
- Inductance L (mH)
- 220mH
- Total series resistance R (Ω)
- 4.7Ω
46.81ms
Open with these valuesHow it's calculated
τ = L ÷ R
- StepEnter the inductance in millihenries — a 1 H coil is 1000 mH.Inductance L (mH)=100mH
- StepEnter the total series resistance, the coil's own winding plus any resistor.Total series resistance R (Ω)=10Ω
- ResultRead the time constant in milliseconds; five times that is practically steady state.10.00ms
Reference table
| L (mH), R (Ω) | Steady state 5τ | τ in ms |
|---|---|---|
| 10, 2 | 25 ms | 5 |
| 47, 100 | 2.35 ms | 0.47 |
| 100, 10 | 50 ms | 10 |
| 220, 4.7 | 234.04 ms | 46.81 |
| 500, 1000 | 2.5 ms | 0.5 |
Questions
How do I calculate the time constant of an RL circuit?
Divide the inductance by the resistance. In millihenries over ohms the answer comes out in milliseconds, so 100 mH and 10 Ω give 10 ms. That is how long the current takes to reach about 63 % of its final value after switch-on.
What does the time constant tell me?
It sets how fast the current rises or falls. After 1τ the current is at about 63 % of its final value, after 2τ about 86 %, after 3τ about 95 % and after 5τ about 99 %. A larger inductance or a smaller resistance lengthens τ and slows the change.
Why is steady state taken as five time constants?
After five time constants the current is within about 1 % of its final value, which engineers treat as settled. It is a working convention, not a physical boundary — the curve never quite arrives. For 100 mH and 10 Ω that means roughly 50 ms.
Should I include the coil's own resistance?
Yes, use the total series resistance: the inductor's winding resistance plus any external resistor. Leaving the coil out makes R too small and the computed time constant too long. Measure the coil's DC resistance and add it.
Do I enter henries or millihenries?
Millihenries. A 1 H coil is 1000 mH and a 100 µH coil is 0.1 mH. Entering raw henries would give an answer a thousand times too large.