Activation energy calculator
Rate constants of 0.0001 at 300 K and 0.0004 at 310 K give reciprocal temperatures of 0.003333333333 and 0.003225806452 and an activation energy of 107194.52158060214 J/mol. Enter two measured rates and their temperatures to read off the barrier. Free in your browser.
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Worked example
- K1
- 0.0001
- T1
- 300
- K2
- 0.0004
- T2
- 310
- Resistance (Ω)
- 8.314462618
- Gas constant
- 8.314462618
- Ln k2 over k1
- 1.3862943611
- Inv t1
- 0.0033333333
An activation energy calculator from two rate constants turns a kinetics pair into the barrier height that appears in the Arrhenius equation. Enter k1 at absolute temperature T1, k2 at T2, and optionally the gas constant R; the tool rearranges the two-point form so that the natural logarithm of k2 over k1 equals Ea over R times one over T1 minus one over T2, then returns Ea with reciprocal temperatures, the log rate ratio, a short message, and ordered substitution steps. Homework checks, lab reports that only list two measured rate constants, and coding kata expected values all need that same deterministic Ea without a spreadsheet or CAS.
What the two-point Arrhenius equation solves for Ea
The Arrhenius equation relates a first-order or pseudo-first-order style rate constant to absolute temperature through a pre-exponential factor A and an activation energy Ea: k equals A times e to the power of minus Ea over R T. Taking the natural log of two rate constants measured at two different temperatures cancels A when A is treated as constant, and yields the classic two-point identity: ln of k2 over k1 equals Ea over R times the difference of reciprocal temperatures one over T1 minus one over T2.
Solving for the unknown barrier gives Ea equals R times ln of k2 over k1, all divided by one over T1 minus one over T2. Absolute temperatures must be in kelvin; rate constants may use any consistent unit because only their ratio appears.
R and Ea must share energy units: with the default R of about eight point three one four joules per mole per kelvin, Ea is reported in joules per mole; if your table or report wants kilojoules per mole, either divide the result by one thousand offline or pass a matching R near zero point zero zero eight three. Equal temperatures are not allowed: the reciprocal difference vanishes, the formula is singular, and that failure mode is the documented error path for this capability.
Non-positive rate constants are also rejected because the logarithm of a non-positive ratio is undefined. The check path recomputes the same intermediate log and reciprocal temperatures with the same fixed rounding used for published fields, so a successful response always ships with steps you can assert in tests or worksheets.
Practical tips, units, limits, and related searches
Convert Celsius to kelvin before calling: add two hundred seventy-three point one five to °C; never pass bare Celsius into t1 or t2. Keep k1 and k2 in the same rate unit so the ratio is dimensionless for the log. Prefer R that matches the energy unit you want for Ea rather than mixing kJ and J without adjusting R.
Prefer this capability when you already have two measured rate constants and two absolute temperatures and only need Ea; if your source is a word problem in °C, convert first. Round-trip checks are easy: recompute ln of k2 over k1 by hand, form the reciprocal temperature difference, multiply by R, and confirm the result equals the published ea within the same twelve-decimal rounding.
What you can do with it
Homework checks for Arrhenius Ea
Students enter textbook k1, T1, k2, and T2 and compare hand-written Ea and substitution steps against a deterministic result before submitting.
Lab reports with two measured rates
Kinetics labs that record only two rate constants at two bath temperatures compute Ea without building a full ln-k versus 1/T spreadsheet.
FAQ
How is activation energy calculated from two rate constants?
Using the two-point Arrhenius form: Ea = R · ln(k2/k1) / (1/T1 − 1/T2), with absolute temperatures in kelvin and R consistent with the energy unit you want for Ea.
What happens when T1 equals T2?
The reciprocal-temperature difference is zero, so Ea is undefined.
What units does Ea use?
With the default R ≈ 8.314 J/(mol·K), Ea is in J/mol. Pass a matching R (for example ≈ 0.008314 kJ/(mol·K)) if you want kJ/mol.
Do I need the pre-exponential factor A?
No. The two-point ratio cancels A when A is assumed constant between T1 and T2. This calculator returns Ea only.
Is the activation energy calculator free?
The browser tool is free and runs locally.
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-activation-energy \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"k1":0.0001,"t1":300,"k2":0.0004,"t2":310}'const res = await fetch("https://api.kit.forhosting.com/chem/arrhenius-activation-energy", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"k1": 0.0001,
"t1": 300,
"k2": 0.0004,
"t2": 310
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/chem/arrhenius-activation-energy",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"k1": 0.0001,
"t1": 300,
"k2": 0.0004,
"t2": 310
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/chem/arrhenius-activation-energy", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"k1":0.0001,"t1":300,"k2":0.0004,"t2":310}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"k1":0.0001,"t1":300,"k2":0.0004,"t2":310}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/chem/arrhenius-activation-energy", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"k1": 0.0001,
"t1": 300,
"k2": 0.0004,
"t2": 310
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "chem.arrhenius_activation_energy",
"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 | 1000000000000 |
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
When the two temperatures are equal the denominator is zero, so the API returns a clear invalid_input error instead of infinity or NaN.
How to call the API and what comes back
Both rate constants and both temperatures must be strictly positive; temperatures that match within a tiny epsilon are treated as equal and rejected with a message that mentions equal temperatures and a zero denominator. Send a JSON body with four required finite numbers: k1 (aliases K1, rate1, rate_constant1, k_initial), t1 (aliases T1, temperature1, temp1, t_initial), k2 (aliases K2, rate2, rate_constant2, k_final), and t2 (aliases T2, temperature2, temp2, t_final). Optionally include r (aliases R, gas_constant, gasConstant); when omitted the solver uses eight point three one four four six two six one eight joules per mole per kelvin. Absolute values must stay within the published limit of one trillion so intermediate products remain finite on the Worker and in the browser. On success the response echoes rounded k1, t1, k2, t2, and r (also as gas_constant), sets ln_k2_over_k1, inv_t1, inv_t2, inv_t1_minus_inv_t2, ea and activation_energy to the same rounded Ea value, formula to the two-point rearrangement string, law to arrhenius, conditions noting constant Ea between the two temperatures, unit hints for rate, temperature, and Ea, message to a short English summary, and steps to an ordered array of substitution lines. Failed validation—missing fields, non-finite numbers, non-positive k or T, equal T1 and T2, zero R, or a non-finite Ea—returns invalid_input and is never charged. Pricing is a flat $0.002 per successful request with unit item and zero marginal unit price.
Practical tips, units, limits, and related searches
When teaching, pair examples: a four-fold rate increase from three hundred kelvin to three hundred ten kelvin, a colder pair that slows the reaction, and a deliberate equal-temperature case to demonstrate the hard invalid_input path. This landing targets people searching for an activation energy calculator from two rate constants, Arrhenius Ea from k1 and k2, or two-temperature kinetics barrier; it is not a multi-point linear regression of ln k versus one over T, not a full transition-state theory estimator, and not a half-life or integrated rate-law solver. Failed tasks that return invalid_input do not consume prepaid balance, which keeps exploratory scripts cheap when learners deliberately set T1 equal to T2.
Integration use cases
Unit tests for chemistry calculators
Generate known-good Ea cases plus deliberate equal-temperature rejections for coding kata and automated grading expected values.