Arrhenius pre-exponential factor calculator
A rate constant of 0.001 with an activation energy of 50000 J/mol at 298.15 K gives a pre-exponential factor of 574938.003485542, in the same units as k. Enter k, Ea and the kelvin temperature to recover the frequency factor. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- K
- 0.001
- Ea
- 50,000
- Creativity
- 298.15
- Resistance (Ω)
- 8.314462618
- Exponent
- 20.1697727729
- Prefactor
- 574,938.003485542
- A
- 574,938.003485542
The Arrhenius equation links an observed chemical rate constant to temperature through an activation barrier and a pre-exponential frequency factor. When you already hold k at a known absolute temperature and a tabulated or fitted activation energy, rearranging the law gives A equals k times e to the power of Ea over R T, the collision-or-attempt frequency term used in textbooks, process models, and safety reviews.
What the Arrhenius prefactor is and how to choose inputs
Start from the classical Arrhenius form k equals A times e to the minus Ea over R T. Solving for the pre-exponential factor produces the working identity A equals k times e to the Ea over R T. Send three required numbers: k as a finite positive rate constant in whatever time or concentration units your mechanism uses, ea as the activation energy in energy per mole consistent with R, and temperature as absolute kelvin.
Optional field r defaults to eight point three one four four six two six one eight joules per mole kelvin, the CODATA molar gas constant; if your Ea is tabulated in kilojoules per mole, pass a matching R such as zero point zero zero eight three one four four six two six one eight so the exponent stays dimensionless.
Lab use and practical limits
Call the free in-browser Arrhenius pre-exponential factor calculator for lecture demos, homework checks, and quick process estimates without installing a kinetics package. Keep the exponent Ea over RT within ordinary floating-point ranges—classroom values such as fifty thousand joules per mole near room temperature land in a comfortable middle band, while mega-joule barriers at cryogenic kelvin may overflow and correctly fail. Authors shipping SDKs can map prefactor, exponent, and temperature into UI tables next to Arrhenius plots so students see the same identity written in physical chemistry textbooks.
This product does not estimate Ea from multi-temperature rate series, does not convert Celsius for you, and does not integrate concentration–time ODEs—those are different search intents served by other capabilities.
What you can do with it
Lab notebooks and process estimates
Process chemists paste an observed rate constant and tabulated activation energy at a known reactor temperature and store the derived A-factor beside batch metadata without reimplementing exp(Ea/RT) in each spreadsheet.
FAQ
Which gas constant R should I use?
Default R is 8.314462618 J/(mol·K). If Ea is in kJ/mol, pass r around 0.008314462618 so Ea/(R·T) is dimensionless and consistent.
Is the Arrhenius pre-exponential factor calculator free?
The browser tool runs free on your device.
What units does A have?
A has the same units as k when Ea, R, and T are dimensionally consistent. With default SI R, use Ea in J/mol and T in kelvin; k may be s⁻¹ or concentration-dependent units as appropriate.
Why can the calculation fail with a very large activation energy?
Because the exponent, Ea divided by R times T, can grow beyond what ordinary numbers hold, especially with huge barriers at very low temperatures. The calculation then fails on purpose instead of returning a meaningless value.
What does the exponent shown in the result tell me?
It is the activation energy divided by R times T, the plain number inside the exponential. In the example it is 20.169772772923, so you can check that step by hand before trusting the factor.
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/arrhenius-prefactor \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"k":0.001,"ea":50000,"temperature":298.15}'const res = await fetch("https://api.kit.forhosting.com/chem/arrhenius-prefactor", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"k": 0.001,
"ea": 50000,
"temperature": 298.15
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/chem/arrhenius-prefactor",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"k": 0.001,
"ea": 50000,
"temperature": 298.15
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/chem/arrhenius-prefactor", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"k":0.001,"ea":50000,"temperature":298.15}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"k":0.001,"ea":50000,"temperature":298.15}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/chem/arrhenius-prefactor", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"k": 0.001,
"ea": 50000,
"temperature": 298.15
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "chem.arrhenius_prefactor",
"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 that rearrangement deterministically with a CODATA default gas constant, accepts a custom R when energy units are not joules, rejects zero temperature with a clear invalid input error so division by zero never becomes a silent wrong answer, and returns structured JSON that lab notebooks, homework checkers, and kinetics pipelines can pin in automated tests.
What the Arrhenius prefactor is and how to choose inputs
Aliases rate_constant, rateConstant, constant, and k_obs map to k; activation_energy, Ea, E_a, and energy map to ea; T, t, temp, and kelvin map to temperature so pipelines can reuse field names from fits and tables. Temperature must be strictly positive: zero is invalid_input because the RT product in the denominator vanishes and the exponential is undefined, and negative kelvin values are also rejected as non-physical. Missing fields, non-finite numbers, and non-positive k fail with invalid_input and are not charged. Identical inputs always produce identical JSON because the path is pure arithmetic with no network, no random seed, and no wall clock.
Reading prefactor, exponent, and units in the response
The field exponent is Ea divided by R times T, the dimensionless argument of the exponential, so students and graders can check the intermediate without recomputing floating-point math. Use prefactor alone when a spreadsheet only needs the scalar; use exponent plus echoed inputs when grading software must prove that unit choices and R were not silently changed; use formula and method when audit logs need a human-readable identity. Extremely large Ea over RT can overflow floating-point range and is rejected as non-finite rather than returning infinity. The prefactor field and its alias A both equal k times e to the exponent—the quantity often called the frequency factor or Arrhenius A-factor. formula restates A equals k times exp of Ea over R T as a short string, and method is always arrhenius_prefactor so downstream code can branch without sniffing shapes. The units_note reminds integrators that A inherits the units of k when Ea, R, and T are dimensionally consistent; with default SI R you should send Ea in joules per mole and T in kelvin. Pair this endpoint with first-order half-life tools when the next step is converting k into a lifetime, or with rate-law calculators when you still need an effective k from concentrations and reaction orders.
API usage, pricing, lab pipelines, and practical limits
Send a JSON body with required positive finite k, finite ea, and strictly positive temperature, plus optional r when your energy unit is not joules. When you already hold k, Ea, and T and only need the frequency factor A, this endpoint is the direct, charge-transparent path.
Integration use cases
Homework and physical chemistry drills
Students rearrange Arrhenius from a published k, Ea, and T into A, check that larger barriers raise the prefactor for fixed k, and get invalid_input when they submit T equals zero by mistake.
Teaching platforms and CI fixtures
Tutoring apps and automated graders call a stable prepaid endpoint so worked Arrhenius examples and unit tests share one deterministic contract for the pre-exponential factor.
Technical questions
How do I compute the Arrhenius pre-exponential factor A?
Send JSON with k (positive rate constant), ea (activation energy), and temperature in kelvin. The response returns prefactor (and alias A) equal to k·exp(Ea/(R·T)).
What happens if temperature is zero?
The request fails with invalid_input. At T=0 the product R·T vanishes and A = k·exp(Ea/(R·T)) is undefined; zero kelvin is rejected and not charged.