RL Circuit Calculator (Inductor Current and Time Constant)
Current in a coil a given time after a voltage is switched on, the final current, the time constant L ÷ R and the energy stored in the magnetic field.
Results
The dashed line marks the value you entered.
What this tool does
An inductor opposes a sudden change of current, so when a voltage is applied across a coil and a resistor the current climbs along an exponential curve instead of jumping: it reaches 63 % of its final value V ÷ R after one time constant τ = L ÷ R and about 99 % after 4.6 τ. The energy kept in the field is ½·L·i². That energy has nowhere to go when the switch opens, which is why relay coils and motors need a flyback diode — otherwise the collapsing field makes a voltage spike many times the supply.
Formula
τ = L ÷ R · i(t) = (V ÷ R) × (1 − e^(−t ÷ τ)) · E = ½ L i²
Variables
| Symbol | Meaning | Unit |
|---|---|---|
v | Voltage | V |
r | Resistance | Ω |
l | Inductance of the coil | mH |
t | Time | ms |
IT | Current at that time | A |
IM | Final current (steady state) | A |
TA | Time constant | ms |
PC | Share of the final current reached | % |
EN | Energy stored in the coil at that time | mJ |
T9 | Time to reach 99 % of the final current | ms |
Worked example
- Voltage12 V
- Resistance10 Ω
- Inductance of the coil100 mH
- Time5 ms
- Current at that time0.472 A
- Final current (steady state)1.200 A
- Time constant10.00 ms
- Share of the final current reached39.3 %
- Energy stored in the coil at that time11.147 mJ
- Time to reach 99 % of the final current46.05 ms
Limitations
- Electrical installations are governed by national wiring rules. Cable sizing also depends on installation method, grouping, ambient temperature and protection devices, which this calculator does not evaluate.
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.