Zero-order half-life calculator
With k of 0.05 and a starting concentration of 1, the zero-order half-life is 10 time units. Enter the rate constant and the initial concentration to see how long it takes for half the reactant to disappear. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Zero-order rate constant k
- 0.05
- Initial concentration
- 1
- Half life
- 10
- Precision
- 10
This zero-order half-life calculator finds how long it takes for a reactant to fall to half of its starting amount when the reaction rate is constant and independent of concentration. The arithmetic is fully deterministic: one multiply and one divide on finite floating-point numbers, with no network calls, no sampling, and no date-dependent shortcuts. Classroom checks include k equals zero point zero five with [A]₀ equals one yielding t½ equals ten, and k equals two with [A]₀ equals eight yielding t½ equals two.
What the zero-order half-life tells you
Zero-order kinetics describe processes whose rate does not depend on the concentration of the reactant: the integrated rate law is simply [A] equals [A]₀ minus k t, so concentration falls in a straight line until the reactant is exhausted. The half-life is the time at which [A] has dropped to half of [A]₀. Substituting [A]₀ over two into the integrated law and solving for t gives t½ equals [A]₀ over two k.
Unlike first-order decay, where half-life is independent of starting amount, the zero-order half-life grows linearly with initial concentration: double [A]₀ and you double t½ for a fixed k.
Where zero-order half-life fits in study, lab work, and software
Students meet t½ equals [A]₀ over two k when a textbook contrasts reaction orders, when a kinetics lab measures a linear concentration-versus-time plot, or when a pharmacy problem models zero-order drug release or enzyme-saturated elimination. Teachers can pre-generate answer keys for modest positive k and [A]₀ pairs without trusting opaque apps that silently switch between first-order and zero-order formulas. Process chemists and formulation teams often need a quick, offline check that a proposed rate constant and fill concentration imply a half-life compatible with shelf-life or dosing windows.
Developers call the same contract from scripts to seed deterministic test vectors for kinetics simulators, to normalize user-entered k and [A]₀ before plotting [A] of t lines, or to satisfy programming-challenge statements that demand the zero-order half-life rather than a hand-waved sketch. Product and education tools use the identity when a learner types a rate and a starting concentration and the UI must show t½ with a clean formula reminder and unit note.
Pair it with reaction-order or concentration tools when you are building a small lab of free, deterministic chemistry helpers, and keep consistent concentration and time units so the numbers stay physically meaningful.
What you can do with it
Homework and kinetics checks
Compute textbook zero-order half-lives from k and [A]₀ before graphing linear [A](t) or comparing orders on a worksheet.
Formulation and lab software
Normalize user-entered rate constants and initial concentrations into t½ for release models, shelf-life demos, and teaching simulators.
FAQ
What does the zero-order half-life calculator cost?
It is free in your browser on this page.
How is the half-life defined for zero-order kinetics?
From [A] = [A]₀ − k t, the time to reach [A]₀/2 is t½ = [A]₀/(2k). Half-life increases with initial concentration for fixed k.
Does this tool compute first-order half-life?
No. First-order half-life is t½ = ln(2)/k and does not depend on [A]₀. Use a dedicated first-order or decay-constant tool for that model.
Why are results rounded to a precision?
Default precision is 10 decimal places; you can set precision from 0 to 15.
Why does the half-life get longer with a higher starting concentration?
Because in a zero-order reaction the reactant drops by the same amount in every unit of time, however much is left. Double the initial concentration with the same k and the half-life doubles too.
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/zero-order-half-life \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"rate_constant":0.05,"initial_concentration":1}'const res = await fetch("https://api.kit.forhosting.com/chem/zero-order-half-life", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"rate_constant": 0.05,
"initial_concentration": 1
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/chem/zero-order-half-life",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"rate_constant": 0.05,
"initial_concentration": 1
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/chem/zero-order-half-life", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"rate_constant":0.05,"initial_concentration":1}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"rate_constant":0.05,"initial_concentration":1}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/chem/zero-order-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
{
"rate_constant": 0.05,
"initial_concentration": 1
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "chem.zero_order_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
Enter a positive zero-order rate constant k and a positive initial concentration [A]₀, and the engine returns the half-life t½ equals [A]₀ divided by two k, together with the normalized inputs, the method tag zero_order_half_life, a short formula reminder, and a unit note so time and concentration units stay consistent.
What zero-order half-life means and what the response contains
This calculator returns the normalized rate_constant and initial_concentration, the computed half_life rounded to your chosen precision, the method tag zero_order_half_life, the precision used, a formula string that recalls t½ equals [A]₀ over two k from the integrated zero-order law, and a unit_note that half-life is in the time unit implied by k while concentration units must match between [A]₀ and the rate constant. There is no Monte Carlo sampling of reaction events and no lookup table of reaction orders: the engine either builds the exact floating-point half-life inside the supported magnitude range or rejects the input with invalid_input. Rejected cases include missing k or [A]₀, non-finite values, magnitudes above the documented ceiling, rate constant equal to zero (division by zero and an undefined or infinite half-life), non-positive k, and non-positive initial concentration.
How inputs are read and how results stay reproducible
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. The rate constant must be strictly positive: k equals zero is rejected explicitly because t½ equals [A]₀ over two k is undefined, and negative k is rejected because this tool models consumption under zero-order kinetics with a positive half-life. Initial concentration must likewise be strictly positive so the half-life is defined and positive. The preferred fields are rate_constant for k and initial_concentration for [A]₀, but aliases k, rateConstant, zero_order_k, and k0 for the rate constant, and A0, a0, concentration0, C0, c0, and initialConcentration for the starting concentration are accepted so spreadsheets, query strings, and typed forms can reuse the same contract. Both fields are required: if either is missing, empty, or not a finite decimal, the request fails with invalid_input so a bad cell does not become a wrong half-life. An optional precision field, with aliases decimals and dp, chooses how many decimal places to expose for rate_constant, initial_concentration, and half_life, defaulting to ten and capped at fifteen so JSON goldens stay stable. 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 the half-life formula yourself.
Where zero-order half-life 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 values for unit tests, property checks, and CI assertions on zero-order kinetics helpers.
Technical questions
What happens if the rate constant is zero?
The input is rejected with invalid_input. k = 0 makes t½ = [A]₀/(2k) undefined (division by zero / infinite half-life).