RL time constant calculator
A 0.1 H coil in series with 50 Ω has a time constant of 2 ms, the time its current needs to cover about sixty-three percent of a step. Handy for sizing coils, relay drivers and series resistors. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Inductance L in henries
- 0.1
- Resistance R in ohms
- 50
- Tau
- 0.002
The RL time constant tau equals inductance L divided by resistance R and sets the natural speed of current change in a series resistor-inductor circuit. After one tau, a step-driven RL loop has risen to about sixty-three percent of its steady current or fallen to about thirty-seven percent of its starting current, so designers, students, and lab teams reach for tau whenever they size coils, pick series resistors, or check how fast a relay driver or snubber path settles.
What the RL time constant tells you
When the voltage across a resistor and an inductor in series steps on or off, the current cannot jump at once, because the inductor opposes any sudden change. Instead it glides towards its new value along an exponential curve, and the time constant sets the pace of that curve. After one time constant, a current that is switching on has reached about sixty-three percent of its final value, and one that is switching off has dropped to about thirty-seven percent of where it started. Designers use it to size coils, pick series resistors and check how quickly a relay driver or a snubber path settles.
Working it out without unit mistakes
The time constant is the inductance divided by the resistance, and the answer comes out in seconds only when the inductance is in henries and the resistance in ohms. The calculator does no unit conversion, so turn millihenries into henries and kilohms into ohms before you enter them. A coil of 0.1 H with 50 Ω gives 2 ms, the kind of millisecond value you can read off an oscilloscope on a step response. A resistance of zero is rejected, since the division would make no sense. Negative values are accepted for sign conventions, but real passive parts are normally positive.
What the RL time constant means and how to choose L and R
Model a series RL branch as an ideal inductor L in henries and a resistance R in ohms sharing the same current. When voltage steps on or off, current cannot jump instantly because of the inductor; instead it approaches its new value with exponential time scale tau equals L over R, measured in seconds. Larger inductance stores more magnetic energy for a given current and therefore lengthens tau; larger resistance dissipates energy faster and shortens tau.
Use SI base units end to end: convert millihenries to henries and kilohms to ohms before calling, because this product does not perform unit conversion. Classroom examples often use tenths of a henry and tens of ohms, which yield millisecond-scale tau values that match oscilloscope cursors on first-order step responses. Magnitude bounds keep pathological inputs from overflowing isolate arithmetic while still covering relay coils, choke filters, and motor armature estimates.
What you can do with it
Lab notebooks and curriculum tools
Lesson builders and lab apps produce deterministic tau checks for oscilloscope labs, auto-graded drills, and SI-unit worksheets without embedding a full circuit simulator.
FAQ
How do I calculate the RL time constant τ = L/R?
The response includes tau in seconds, formula tau=L/R, and SI unit labels.
What units should I use?
Use SI base units: inductance in henries (H), resistance in ohms (Ω), and read tau in seconds (s). Convert mH, µH, kΩ, etc. before calling; this calculator does not convert units.
Is the RL time constant calculator free?
The browser tool runs free on your device.
Does this compute the full i(t) waveform?
No. This capability returns only the first-order time constant tau = L/R. Full exponential current versus time, mutual inductance, and multi-element nets need a dedicated circuit solver.
Why does a bigger resistor make an RL circuit faster?
Because the time constant is inductance divided by resistance. More inductance stores more magnetic energy and stretches the transient, while more resistance dissipates that energy faster, so a larger resistor shortens the time constant.
Related tools
For developers — API access
Everything on this page is available programmatically. This section is for teams who want to wire it into their own systems; everyone else can just use the tool above.
API endpoint
Prefer to automate it? One authenticated POST creates the task; the result comes back by webhook or a signed link. The same capability also runs here on the web, by email and from Telegram — and soon from our app too.
Call it from your stack
curl -X POST https://api.kit.forhosting.com/elec/rl-time-constant \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"inductance":0.1,"resistance":50}'const res = await fetch("https://api.kit.forhosting.com/elec/rl-time-constant", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"inductance": 0.1,
"resistance": 50
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/elec/rl-time-constant",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"inductance": 0.1,
"resistance": 50
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/elec/rl-time-constant", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"inductance":0.1,"resistance":50}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"inductance":0.1,"resistance":50}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/elec/rl-time-constant", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"inductance": 0.1,
"resistance": 50
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "elec.rl_time_constant",
"status": "queued",
"_links": {
"result": "/tasks/tsk_…/result"
}
}The API is asynchronous: the call returns a task_id immediately and the result arrives by webhook. Polling is capped at 1 req/s per task.
Pricing
Published price — no tokens, no invented credits. A failed task is never charged.
Errors
| HTTP | Code | Meaning |
|---|---|---|
401 | unauthorized | Missing or invalid API key. |
402 | insufficient_balance | Your balance doesn't cover the task price. |
404 | unknown_type | That task type doesn't exist. |
429 | rate_limited | Too many requests. Use the webhook instead of polling. |
Technical notes
This capability evaluates tau equals L over R deterministically from a JSON body, returns seconds with SI unit labels, and rejects zero resistance so division by zero never becomes infinity or NaN. The algorithm is pure floating-point arithmetic with stable rounding—no network, no random seed, no wall clock—so identical inputs always yield identical JSON.
What the RL time constant means and how to choose L and R
Send required fields inductance and resistance as finite JSON numbers or numeric strings; aliases L, L_H, and henries for inductance and R, R_ohm, and ohms for resistance are accepted so homework forms and lab notebooks map without renaming columns. Identical inputs always produce identical JSON because the path is pure division with fixed rounding—no model, no filesystem, and no external circuit simulator.
Reading tau, formula, units, and zero-resistance errors
Negative L or R are accepted as finite signed quantities for modeling polarity conventions or reflected parameters; interpret signs according to your reference frame, remembering that physical passive elements are usually positive. On success the response echoes inductance and resistance after stable rounding, then reports tau as the signed seconds value of L divided by R, formula as the string tau equals L over R, and method as rl_time_constant so downstream code can branch without sniffing shapes. The units object labels inductance in H, resistance in ohm, and tau in s so UI tables and SDK demos stay SI-consistent. Use tau alone when you only need the settling scale for a display or grader; use formula and method when reports must cite the identity; use the echoed L and R when you need to prove the request was interpreted correctly after string-to-number parsing. Zero resistance is never allowed: an ideal short leaves tau undefined because division by R would diverge, so the engine raises invalid_input with a message that names resistance and the tau equals L over R identity. Missing inductance or resistance, non-finite numbers, and out-of-range magnitudes also fail with invalid_input and are not charged after the engine rejects the request.
API usage, pricing, lab workflows, and practical limits
Call the free in-browser RL time constant calculator for homework checks, lecture demos, and quick verification of hand calculations without installing SPICE or a spreadsheet template. Authors shipping SDKs can map tau, formula, and units directly into tables students recognize from textbook RL step-response problems, including clear errors when someone accidentally submits zero ohms. Send a JSON body with required numeric fields inductance and resistance (or their aliases). Use the prepaid API when a tutoring platform, power-electronics curriculum generator, lab notebook, relay sizing tool, or filter design pipeline needs a stable contract under KIT balance at $0.002 per successful item; validation failures never consume balance after the engine rejects the request. Pair this endpoint with RC tools when the next exercise contrasts capacitive and inductive first-order dynamics, or with watts-volts-amps calculators when you already know coil resistance from a DC ohm measurement and want both power and tau. This product does not integrate the full current waveform, Laplace transforms, or mutual inductance; for multi-element nets use a dedicated circuit solver.
Integration use cases
Homework and exam verification
Students enter L and R for a series RL branch, compare tau in seconds with hand work, and get a clear invalid_input when resistance is zero by mistake.
Relay, choke, and filter design checks
Firmware and hardware pipelines call a stable prepaid endpoint to size series RL time scales before SPICE or board-level layout.
Technical questions
What happens if resistance is zero?
The request fails with invalid_input. Zero resistance would make tau = L/R undefined (division by zero), so the engine rejects the input and does not charge the call.