What the RL Time Constant Calculator does
This calculator gives the time constant of an inductive load, how its current rises and decays against time, the energy stored in the magnetic field and an order-of-magnitude estimate of the voltage spike an abrupt switch-off produces. It is the tool for relay coils, solenoids, valves, motors and any other winding you have to switch.
An inductor opposes a change in current, so tau = L / R - note the division, not the multiplication an RC uses. The consequence that bites is at switch-off: interrupt the current quickly and the coil produces whatever voltage it takes to keep it flowing, which is usually enough to destroy the switch.
How to use it
- Enter the inductance of the winding and the total circuit resistance, which is the coil's own DC resistance plus anything in series with it.
- Enter the supply voltage to get the final current and the stored energy.
- Enter how fast the current is interrupted. A mechanical contact opens in microseconds; a MOSFET can do it in tens of nanoseconds, which makes the spike far worse.
- Read the stored energy. That is the quantity your clamp has to absorb, every single switch-off.
- Compare the decay time through a plain freewheel diode with what your application can tolerate - a relay that releases slowly can weld its own contacts.
Reading the results
The time constant tells you how long the coil takes to pull in. A relay with a 10 ms time constant is not fully energised for 50 ms, which is often longer than the datasheet's operate time because the armature moves before the current has settled.
The kickback voltage shown is an order of magnitude, not a prediction. The real peak is limited by the winding's own stray capacitance, by the avalanche rating of whatever is switching, and by any clamp you fit - but the message is the same: without a clamp it is far above the supply voltage.
Stored energy, not voltage, is what sizes the protection. A clamp diode has to carry the full coil current at switch-off and dissipate 0.5 L I^2 each time; at any repetition rate that becomes an average power.
Worked example: a 12 V relay coil with 100 mH and 10 ohms
tau = L / R = 0.1 / 10 = 10 ms, and the final current is 12 / 10 = 1.2 A. The coil reaches 63.2% of that in 10 ms and is effectively fully energised at 50 ms. Steady-state dissipation is 1.2^2 x 10 = 14.4 W, which is why relay coils get warm.
The stored energy is 0.5 x 0.1 x 1.2^2 = 72 mJ. Interrupt that 1.2 A in 1 microsecond and V = L di/dt gives 0.1 x 1.2 / 1e-6 = 120,000 V - obviously not what actually happens, but a clear statement that the circuit will arc, and that whatever is switching will not survive it.
Fit a freewheel diode and the coil is clamped at about 0.7 V, so the current decays in roughly L x I / V = 171 ms. The relay is protected, but it releases slowly. A 24 V zener in series with the diode clamps at 24 V instead, dropping the decay to about 5 ms at the cost of putting 24 V across the switch.
Formulas and scoring rules
- Time constant
tau = L / RHenries divided by ohms gives seconds. Note the division - an RC multiplies.- Current rise
i(t) = (V/R) x (1 - e^(-t/tau))- Current decay
i(t) = I0 x e^(-t/tau)With the same R still in the loop. A clamp changes R and therefore the decay.- Stored energy
E = 0.5 x L x I^2In joules. This is what the clamp must absorb at every switch-off.- Switch-off voltage
V = L x di/dtAn order of magnitude only: stray capacitance and the clamp set the real peak.- Decay through a clamp
t = L x I / VclampA higher clamp voltage means a faster release.
Choosing the clamp
A plain freewheel diode across the coil is the cheapest and gentlest option: it holds the coil at a diode drop, protects everything, and lets the current decay slowly. The slow decay is its weakness - a relay's contacts stay closed longer, and in a DC load-break application that extra time is when the arc happens.
Adding a zener in series with the diode, or using a transient-voltage-suppression diode, raises the clamp voltage and shortens the decay in direct proportion. An RC snubber does the same job for AC loads and where you want to limit dV/dt rather than clamp a peak. Whatever you choose has to carry the full coil current the instant the switch opens, and dissipate the stored energy at your repetition rate.
Why the L/R time constant is often the wrong number
A relay's inductance is not constant. It changes by a factor of two or more as the armature moves and the magnetic circuit closes, so a single L is an approximation - useful for the order of magnitude, not for a precise operate time. The manufacturer's stated operate and release times are measured, and they are what you should design against.
The same applies to any iron-cored part near saturation: the inductance falls as the current rises, so the current climbs faster than the exponential predicts. A ferrite-cored switching inductor past its saturation current does this dramatically, which is why a converter that starts fine can fail on a load step.
Limitations: what the result does not prove
- Inductance is treated as constant. Real coils, relays and motors change inductance with current and with position, and a saturated core behaves very differently from this model.
- The switch-off voltage is an order-of-magnitude estimate, not a prediction. Measuring it needs a scope and a probe that can survive it.
- A motor is not a simple RL: it also generates a back-EMF proportional to speed, which this calculation does not include.
- The result is indicative and must be checked by a qualified engineer against the component data sheets and the applicable standard before anything is built. Inductive switching at mains voltage is a safety matter.
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Standards and sources
- Texas Instruments - Op amps for everyone design reference - checked 19 Sep 2026
- Vishay - Freewheeling and clamping diode selection application note
- TE Connectivity - Relay coil suppression and its effect on release time
Frequently asked questions
What is the time constant of an RL circuit?
tau = L / R, in seconds when L is in henries and R in ohms. The current reaches 63.2% of its final value in one time constant and is treated as settled after five. Note that a larger resistance makes an RL circuit faster, the opposite of an RC.
Why do I get a voltage spike when I switch off a relay?
An inductor opposes a change in current, so when the path is broken it produces whatever voltage it must to keep current flowing - far more than the supply. The calculator's V = L di/dt figure shows the scale of the problem; a freewheel diode, a TVS or a snubber is the answer.
Which way round does a freewheel diode go?
Reverse biased across the coil: cathode to the positive supply end, anode to the switched end. In normal operation it does nothing; at switch-off it conducts and gives the collapsing current a path, clamping the coil at about one diode drop.
Does a freewheel diode slow the relay down?
Yes. Clamping at 0.7 V makes the current decay slowly, so the armature releases later - often several times later than without a clamp. Where release time matters, put a zener in series with the diode: the higher clamp voltage shortens the decay in proportion.
How much energy does an inductor store?
E = 0.5 x L x I^2 joules. For a 100 mH coil at 1.2 A that is 72 mJ. Every switch-off dumps that energy into whatever is clamping the coil, so at a high switching rate it becomes an average power the clamp must dissipate.
How long does an inductor take to reach full current?
About five time constants, in the same way as a capacitor. With 100 mH and 10 ohms that is 50 ms. If the supply cannot hold its voltage during that time, the rise is slower still.
Why does a larger resistance make an RL circuit faster?
Because tau = L / R. More resistance means less final current and a quicker approach to it - the circuit is more damped. This is also why adding a series resistor is a crude way to speed up a solenoid, at the cost of dissipating extra power continuously.
Can I use this for a motor?
Only for the winding itself, at standstill. A running motor also produces a back-EMF proportional to speed, which dominates its behaviour and is not modelled here. Motor drive design needs the machine's full electrical and mechanical model.
Last reviewed by the A2Z.Tools team against the sources listed above.
