RL Time Constant Calculator

Calculator

Calculation mode

All modes use the same τ = L / R core relationship.

Inductance (L)

Tip: Common inductors are in µH or mH.

Resistance (R)

Include series resistance for real coils.

Supply voltage (V)

V

Used to compute I∞ = V / R.

Initial current (I0)

A

Used in I(t)=I0·e^−t/τ.

Evaluate at time (optional)

Enter t to compute I(t) and voltages.

Inductance L	Resistance R	Time constant τ = L/R	Corner frequency fc = R/(2πL)
10 mH	5 Ω	2 ms	79.6 Hz
220 µH	22 Ω	10 µs	15.9 kHz
1 H	1 kΩ	1 ms	159 Hz

The RL time constant is the characteristic time that sets how fast current changes in a series resistor–inductor circuit. It is defined as:

τ = L / R

For a step voltage applied to a series RL circuit, the current rises as: I(t) = I∞(1 − e^(−t/τ)), where I∞ = V/R. If the source is removed and current decays through R, then: I(t) = I0 e^(−t/τ).

The corner frequency used in filter and bandwidth thinking is fc = R/(2πL), with ωc = R/L.

Enter inductance L and choose its unit.
Enter resistance R and include any series coil resistance.
Select a mode: time constant only, rise, or decay.
For rise mode, enter a positive supply voltage V.
For decay mode, enter the initial current I0.
Optionally enter time t to evaluate I(t) and voltages.
Press Calculate to see results above the form.
Use Download CSV or PDF for saving results.

At 1τ the rise reaches about 63.2% of the final current.
At 3τ the rise reaches about 95%.
At 5τ the rise reaches about 99.3%.
A larger inductance slows changes, increasing τ.
A larger resistance speeds changes, decreasing τ.

RL Time Constant Guide

1) What the time constant represents

The RL time constant τ describes how quickly current changes after a switching event. It is the time required for current to reach about 63.2% of its final value during a step response, or to fall to 36.8% of its initial value during decay. A small τ means fast current transitions.

2) Core relationship and units

For a series resistor–inductor circuit, τ equals inductance divided by resistance: τ = L/R. When L is in henries and R is in ohms, τ is in seconds. This calculator converts common sub-units (mH, µH, ns, and more) to keep calculations consistent and comparable.

3) Typical component ranges in practice

Power inductors often fall between 1 µH and 10 mH, while signal inductors may be in the nH range. Series resistance can range from under 0.1 Ω in power stages to kilo-ohms in sensing networks. A 10 mH inductor with 5 Ω yields τ = 2 ms, which is easy to observe on an oscilloscope.

4) Step response data you can predict

In rise mode, the steady current is I∞ = V/R. The time to reach 90% is about 2.3τ, 95% is about 3τ, and 99% is about 4.6τ. These landmarks help estimate settling time for relays, solenoids, and current-controlled converters.

5) Decay behavior after source removal

In decay mode, current follows I(t)=I0·e^(−t/τ). After one τ, current is about 36.8% of I0. After five τ, only about 0.67% remains. This is useful for estimating discharge time in inductive loads and damping networks.

6) Corner frequency and bandwidth insight

The RL corner frequency links time-domain behavior to frequency response. The angular corner frequency is ωc = R/L, and fc = R/(2πL). Increasing R raises fc (wider bandwidth), while increasing L lowers fc (stronger smoothing and slower current changes).

7) Including real coil resistance

Real inductors include copper resistance and sometimes core losses represented as additional series resistance. If you ignore these, τ can be overestimated and predicted current rise can look slower than measured. Use the effective series resistance seen by the inductor in the operating condition.

8) Using results for design decisions

Engineers use τ to pick sampling times, choose switching delays, and estimate transient stress. For example, if your controller needs current to settle within 1%, plan for roughly 5τ before sampling. The CSV and PDF exports help document calculations for reviews and lab notes.

FAQs

1) Why is 63.2% associated with one time constant?

Because the exponential term e^−t/τ equals e⁻¹ at t=τ. That leaves 1−e⁻¹ ≈ 0.632 of the final value for a rising current response.

2) What does 5τ mean in switching and control?

Five time constants is a common settling guideline. A rising current reaches about 99.3% of its final value by 5τ, which is often “close enough” for stable sampling, timing, or measurement.

3) Should I use DC resistance or impedance for R?

Use the effective series resistance that sets the time-domain current change. For simple DC step tests, DC resistance is appropriate. For more complex networks, use the equivalent resistance seen by the inductor in that configuration.

4) Why does higher resistance make the response faster?

Because τ = L/R decreases when R increases. A smaller τ reduces the exponential time scale, so the current approaches its target value more quickly, even though the final current magnitude may be lower for the same voltage.

5) Can this calculator handle very small inductances?

Yes. Enter values in µH or nH and the calculator converts them to henries internally. The output will show τ in seconds and can be interpreted in ms or µs by multiplying accordingly.

6) What voltage appears across the inductor during rise?

Right after a step, current is near zero, so most voltage appears across the inductor. Over time, resistor drop increases and inductor voltage falls. The calculator reports VR(t) and VL(t) when you provide a time value.

7) Is corner frequency the same as resonance?

No. The RL corner frequency is a first-order cutoff where magnitude changes by −3 dB in a simple RL filter model. Resonance involves energy exchange between L and C and requires a capacitor.