Rate constant from half-life calculator
A first-order half-life of 10 seconds gives a rate constant of 0.0693147181 per second, because k is ln 2 divided by the half-life. Enter the half-life in any time unit and k comes back in the reciprocal unit. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- First-order half-life t½
- 10
- Rate constant
- 0.0693147181
- K
- 0.0693147181
- Order
- first
- Precision
- 10
This rate constant from half-life calculator turns a first-order half-life into the corresponding first-order rate constant with the identity k equals the natural log of two divided by t½. Enter a positive half-life in any consistent time unit and the engine returns k in the reciprocal unit, rounded to your chosen precision, together with the half-life you supplied, the order tag first, a method tag, a short formula reminder, and a unit note. The arithmetic is fully deterministic: pure floating-point division with Math.LN2, no network calls, no sampling, and no date-dependent shortcuts. Classroom checks include a half-life of ten time units yielding k about zero point zero six nine three, and a half-life near ln two yielding a rate constant near one.
What first-order half-life and rate constant mean
First-order kinetics describe any process whose instantaneous rate is proportional to the amount of reactant still present, from unimolecular decomposition and many enzyme-limited steps under pseudo-first-order conditions to radioactive decay framed as a chemical rate law. The integrated rate law is concentration of A at time t equals initial concentration times e to the minus k t.
The half-life t½ is the time required for the reactant concentration to fall to half of its current value; substituting that condition into the integrated law gives one half equals e to the minus k t½, and taking natural logs rearranges to k equals ln two over t½. That single identity is what this calculator evaluates: you supply a positive half-life, and the engine returns the matching first-order rate constant without graphing concentration curves or fitting multi-point data.
Where the conversion fits in study, lab work, and software
Students meet k equals ln two over t½ when a textbook moves from half-life tables to integrated rate laws, when a kinetics lab measures a first-order half-life and asks for the rate constant, or when an exam gives t½ and demands k without a calculator under the desk. Teachers can pre-generate answer keys for modest positive half-lives without trusting opaque apps that silently switch units or drop scientific notation.
Pharmaceutical and environmental workflows often need a quick, offline conversion from tabulated half-lives of first-order processes to k before comparing clearance models or planning sampling intervals. Developers call the same contract from scripts to seed deterministic test vectors for kinetics simulators, to normalize user-entered half-lives before plotting concentration versus time curves, or to satisfy programming-challenge statements that demand k rather than a hand-waved sketch.
Product and education tools use the identity when a learner types a half-life in seconds, minutes, or hours and the UI must show the matching first-order rate constant with a clean formula reminder and an order tag. Pair it with first-order reaction-time or concentration tools when you are building a small lab of free, deterministic chemistry helpers, and keep a consistent time unit across half-life and k so the numbers stay physically meaningful for your experiment or homework set.
What you can do with it
Homework and kinetics checks
Convert textbook first-order half-lives into rate constants before graphing concentration curves or solving integrated rate-law problems.
Lab and teaching software
Normalize user-entered half-lives into k for lab notebooks, exam generators, and first-order reaction simulators.
FAQ
What does the rate constant from half-life calculator cost?
It is free in your browser on this page.
How is the first-order rate constant defined from half-life?
For first-order kinetics, k = ln(2)/t½. The half-life is the time for the reactant concentration to fall by half under the integrated rate law.
What happens if half-life is zero or negative?
Zero or negative half-life makes k = ln(2)/t½ undefined or non-physical for this model.
Does this tool handle zero-order or second-order half-lives?
No. It only converts a first-order half-life to k. Use a dedicated zero-order or second-order tool for those rate laws.
Does this tool compute remaining concentration after a given time?
No. It only returns k from t½. Use a first-order concentration or reaction-time calculator if you need [A](t) or elapsed time between two concentrations.
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/chem/rate-constant-from-half-life \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"half_life":10}'const res = await fetch("https://api.kit.forhosting.com/chem/rate-constant-from-half-life", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"half_life": 10
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/chem/rate-constant-from-half-life",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"half_life": 10
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/chem/rate-constant-from-half-life", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"half_life":10}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"half_life":10}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/chem/rate-constant-from-half-life", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"half_life": 10
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "chem.rate_constant_from_half_life",
"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.
Limits
max_abs_value | 1000000000000000 |
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
What first-order half-life and rate constant mean
The response includes half_life and rate_constant rounded to your precision, a mirrored k field for callers that prefer the short name, order set to first so downstream tools know which rate law was assumed, method first_order_half_life, a compact formula string, a unit_note that k is the reciprocal of the half-life time unit, and the precision used. There is no Monte Carlo sampling of reaction events and no database of tabulated rate constants: the engine either builds an exact floating-point conversion inside the supported magnitude range or rejects the input with invalid_input. Rejected cases include a missing half-life, non-finite values, magnitudes above the documented ceiling, and any zero or negative half-life, because division by zero or a non-physical negative t½ makes k undefined for this model.
How inputs are read and how results stay reproducible
The value must be a finite positive number: optional leading plus signs and scientific notation on numeric strings are allowed when they parse as finite decimals; embedded spaces, hex prefixes, and non-numeric tokens are rejected with a clear message so a bad cell does not become a wrong rate constant. Magnitude is capped at the documented limit so absurd half-lives that would produce non-finite k are refused rather than serialized as Infinity. The preferred field is half_life for t½, but aliases t_half, halfLife, t12, T_half, thalf, and t_half_life are accepted so spreadsheets, query strings, and typed forms can reuse the same contract without renaming columns. Zero and negative half-lives fail with invalid_input because k equals ln two over t½ is undefined or non-physical for first-order kinetics; the error message mentions that half_life must be positive so validation tooling and learners see the same rule. An optional precision field, with aliases decimals and dp, chooses how many decimal places to expose for half_life and rate_constant, defaulting to ten and capped at fifteen so JSON goldens stay stable across runs. Pair the free browser run on this page with the priced API when you need the identical mathematical result inside an automated pipeline without re-implementing first-order kinetics formulas yourself.
Where the conversion fits in study, lab work, and software
On this page the work runs entirely in your browser; through the API each successful lookup costs $0.002, failed validation is not charged, and nothing is stored after the response returns. That split — free interactive exploration and a priced, identical API — matches the rest of the KIT tier-A catalog and lets you move from a classroom demo to an automated pipeline without changing the mathematical result.
Integration use cases
Deterministic test fixtures
Generate reproducible half_life and rate_constant pairs for unit tests, property checks, and CI assertions on first-order kinetics helpers.