Rate constant from rate law calculator
A rate of 0.002 with A at 0.1 (first order) and B at 0.2 (second order) gives a rate constant k of 0.5 and an overall order of 3. Enter the measured rate and each reactant's concentration and order. Free in your browser.
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In chemical kinetics the empirical rate law writes the instantaneous reaction rate as the product of a rate constant k and reactant concentrations each raised to a reaction order. Laboratory work often measures the rate at known concentrations and needs k instead of predicting rate from a published constant. This capability inverts that product deterministically: you send a finite measured rate and a list of species with positive concentration and order, and you receive the numerical rate constant, overall order, per-species concentration powers, the concentration product, and a readable expression string ready for homework checkers, tutoring apps, and lightweight process scripts. Zero concentration is rejected with a clear invalid input error because the product that divides the rate would vanish or become undefined, so k cannot be recovered honestly.
What the inverse rate law computes and how to prepare inputs
Start from the familiar power-law form rate equals k times the product over i of open bracket A sub i close bracket to the power n sub i. Solving for the constant gives k equals rate divided by that same concentration product. For a second-order reaction in a single species the form is k equals rate over concentration squared; for a reaction that is first order in A and second order in B it is k equals rate over A times B squared.
Concentrations must be finite and strictly positive: a zero concentration is invalid input because division by a vanishing product is undefined, and a negative concentration is also rejected as non-physical in this calculator. Orders may be zero, positive, or fractional as in many textbook empirical laws; keep units consistent yourself so that the implied units of k match concentration and time.
What you can do with it
Homework and exam verification
Students plug a measured rate and concentrations with orders into the inverse rate law, compare the returned k and overall order, and get a clear error when a zero concentration is submitted by mistake.
Lab notebook and initial-rate analysis
Teaching labs recover k from an initial-rate measurement at known positive concentrations before comparing trials or building Arrhenius plots.
FAQ
How is this different from the rate law calculator?
The rate law calculator predicts rate from a known k and concentrations. This capability does the inverse: it recovers k from a measured rate and the same concentration and order inputs.
Is the rate constant from rate law calculator free?
The browser tool runs free on your device.
Can reaction orders be fractional or zero?
Yes. Reaction orders may be zero, integer, or fractional as in empirical rate laws. Concentrations must still be strictly positive so the product that divides the rate stays defined.
What is the overall reaction order?
It is the sum of the individual orders. A reaction that is first order in A and second order in B is third order overall, and the calculator shows that total next to k.
Can I use it for initial-rate experiments?
Yes. Teaching labs recover k from an initial-rate measurement at known positive concentrations, then compare trials or build Arrhenius plots from the values they collect.
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-rate \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"rate":0.002,"reactants":[{"concentration":0.1,"order":1,"name":"A"},{"concentration":0.2,"order":2,"name":"B"}]}'const res = await fetch("https://api.kit.forhosting.com/chem/rate-constant-from-rate", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"rate": 0.002,
"reactants": [
{
"concentration": 0.1,
"order": 1,
"name": "A"
},
{
"concentration": 0.2,
"order": 2,
"name": "B"
}
]
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/chem/rate-constant-from-rate",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"rate": 0.002,
"reactants": [
{
"concentration": 0.1,
"order": 1,
"name": "A"
},
{
"concentration": 0.2,
"order": 2,
"name": "B"
}
]
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/chem/rate-constant-from-rate", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"rate":0.002,"reactants":[{"concentration":0.1,"order":1,"name":"A"},{"concentration":0.2,"order":2,"name":"B"}]}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"rate":0.002,"reactants":[{"concentration":0.1,"order":1,"name":"A"},{"concentration":0.2,"order":2,"name":"B"}]}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/chem/rate-constant-from-rate", 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": 0.002,
"reactants": [
{
"concentration": 0.1,
"order": 1,
"name": "A"
},
{
"concentration": 0.2,
"order": 2,
"name": "B"
}
]
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "chem.rate_constant_from_rate",
"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
What the inverse rate law computes and how to prepare inputs
Send the required field rate as a JSON number or numeric string; aliases reaction_rate, reactionRate, r, and v are accepted. Send reactants as a non-empty array of objects; each object needs concentration (aliases conc, c, molarity, M) and order (aliases reaction_order, power, exponent, n), and may include an optional name or species label for display. The engine caps the list at thirty-two species for Worker isolate safety while still covering multi-reactant classroom exercises and simple industrial examples. Identical inputs always produce identical JSON because the path is pure arithmetic with no network, no random seed, and no wall clock.
Reading k, overall order, factors, and the expression string
The reactants array is the structured heart of the contract: each entry includes the optional name, the concentration, the order, and the factor equal to concentration raised to that order. The expression field builds a human-readable recovery line such as k equals rate over open bracket A close bracket times open bracket B close bracket squared equals zero point five for quick display in UIs and worksheets. On success the response echoes the measured rate rounded for stable display, reactant_count, and overall_order equal to the sum of the individual reaction orders. The concentration_product field multiplies those factors into the denominator that divides rate, and both k and rate_constant hold the recovered constant—the same scalar in two keys so callers can pick the name that fits their schema. The method label is always rate_constant_from_rate so downstream code can branch without sniffing shapes. Use k alone when a sensor pipeline only needs the scalar; use reactants and factors when grading software must check each power separately; use overall_order when classifying elementary versus non-elementary schemes in teaching materials. Missing rate, missing reactants, empty arrays, non-finite numbers, negative concentrations, and any zero concentration all fail with invalid_input and are not charged. Keep units consistent yourself: this endpoint multiplies and divides numbers and does not convert molarity to millimolar or minutes to seconds.
API usage, pricing, classroom workflows, and practical limits
Call the free in-browser rate constant from rate law calculator for homework checks, lecture demos, and quick lab sanity checks without installing a spreadsheet template or a local kinetics package. Floating-point powers can overflow for extreme concentration and order combinations, so keep classroom-scale inputs for grading oracles and prefer moderate magnitudes in continuous integration. Authors shipping SDKs can map the reactants array directly into UI tables that show concentration, order, and factor columns—the same breakdown students write when they rearrange a multi-reactant rate law by hand to solve for k. Send a JSON body with the required measured rate and the reactants array of concentration and order objects. Use the prepaid API when a tutoring platform, coding-assessment sandbox, curriculum generator, or process-control script 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 the forward rate law calculator when students must check that the recovered k reproduces the original rate, or with half-life tools when the next question is remaining amount after first-order decay.
Integration use cases
Tutoring and curriculum generators
Lesson builders produce worked multi-reactant inverse rate-law examples with structured JSON for drills and auto-graded kinetics problems without embedding a full CAS.
Technical questions
How do I compute the rate constant k from a measured rate?
Send JSON with rate set to the measured reaction rate and reactants as an array of objects each with concentration and order (for example rate: 0.002 and two species). The response includes k, rate_constant, overall_order, factors, and an expression string.
What happens if a concentration is zero?
The request fails with invalid_input. Zero concentration makes the concentration product zero or undefined, so the rate constant cannot be recovered; the error is returned without charging the request.