Rate constant at new temperature calculator
A rate constant of 0.0001 at 300 K with an activation energy of 50000 J/mol becomes 0.000190908785 at 310 K, almost double after a 10-degree rise. Enter k1, both kelvin temperatures and Ea to get k2 with each step. Free in your browser.
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Worked example
- K1
- 0.0001
- T1
- 300
- Ea
- 50,000
- T2
- 310
- Activation energy
- 50,000
- Resistance (Ω)
- 8.314462618
- Gas constant
- 8.314462618
- Inv t1
- 0.0033333333
A rate constant at new temperature calculator turns one measured kinetic rate, its bath temperature, and a known activation energy into the rate constant you would observe at a second absolute temperature. Enter k1 at T1, Ea, and the target T2 (optionally R); the tool applies the two-point Arrhenius identity so that the natural log of k2 over k1 equals Ea over R times one over T1 minus one over T2, then returns k2 with reciprocal temperatures, the exponent, a short message, and ordered substitution steps. Homework checks, process-safety estimates that only list one rate and Ea, and coding kata expected values all need that same deterministic k2 without a spreadsheet or CAS.
What the Arrhenius form solves for k2 at a new temperature
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 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 rate at the second temperature gives k2 equals k1 times the exponential of Ea over R times one over T1 minus one over T2. Absolute temperatures must be in kelvin; the known rate constant may use any consistent unit, and k2 is returned in that same unit.
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 expected in joules per mole; if your table lists kilojoules per mole, either convert Ea offline or pass a matching R near zero point zero zero eight three. Zero temperatures are not allowed: one over T diverges, the formula is singular, and that failure mode is the documented error path for this capability.
Non-positive known rate constants are also rejected because a physical k2 cannot be built from a non-positive base. The check path recomputes the same reciprocal temperatures and exponent 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 Ea and R in matching energy units so the ratio Ea over R is correct. Prefer R that matches the energy unit of Ea rather than mixing kJ and J without adjusting R.
Prefer this capability when you already have one measured rate constant, its absolute temperature, and Ea, and only need k2; if your source is a word problem in °C, convert first. Round-trip checks are easy: recompute one over T1 and one over T2 by hand, form the exponent with Ea over R, multiply the exponential by k1, and confirm the result equals the published k2 within the same twelve-decimal rounding.
What you can do with it
Homework checks for Arrhenius k2
Students enter textbook k1, T1, Ea, and T2 and compare hand-written k2 and substitution steps against a deterministic result before submitting.
Process estimates with one measured rate
Labs or plants that know one rate constant and Ea estimate the rate at a new bath temperature without rebuilding a full ln-k versus 1/T fit.
FAQ
How is the rate constant at a new temperature calculated?
Using the two-point Arrhenius form: k2 = k1 · exp((Ea/R)·(1/T1 − 1/T2)), with absolute temperatures in kelvin and R consistent with the energy unit of Ea.
What happens when a temperature is zero?
The reciprocal 1/T is undefined, so k2 cannot be computed.
What units does k2 use?
The same unit as k1. Only the ratio and the exponential factor appear; no unit conversion is performed on the rate constant itself.
Do I need the pre-exponential factor A?
No. The two-point form cancels A when A is assumed constant between T1 and T2. This calculator returns k2 from k1, Ea, and the two temperatures.
Is the rate constant at new temperature 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/rate-constant-new-temperature \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"k1":0.0001,"t1":300,"ea":50000,"t2":310}'const res = await fetch("https://api.kit.forhosting.com/chem/rate-constant-new-temperature", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"k1": 0.0001,
"t1": 300,
"ea": 50000,
"t2": 310
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/chem/rate-constant-new-temperature",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"k1": 0.0001,
"t1": 300,
"ea": 50000,
"t2": 310
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/chem/rate-constant-new-temperature", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"k1":0.0001,"t1":300,"ea":50000,"t2":310}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"k1":0.0001,"t1":300,"ea":50000,"t2":310}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/chem/rate-constant-new-temperature", 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,
"ea": 50000,
"t2": 310
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "chem.rate_constant_new_temperature",
"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 either temperature is zero the reciprocal is undefined, so the API returns a clear invalid_input error instead of infinity or NaN.
How to call the API and what comes back
The known rate constant and both temperatures must be strictly positive; a temperature of zero is treated as invalid and rejected with a message that mentions temperature zero and the Arrhenius equation. Send a JSON body with four required finite numbers: k1 (aliases K1, rate1, rate_constant1, k_initial), t1 (aliases T1, temperature1, temp1, t_initial), ea (aliases Ea, activation_energy, E_a, activationEnergy), 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, ea (also as activation_energy), t2, and r (also as gas_constant), sets inv_t1, inv_t2, inv_t1_minus_inv_t2, ea_over_r, exponent, ln_k2_over_k1, k2 and rate_constant2 to the same rounded k2 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 k1, zero or non-positive T, zero R, or a non-finite k2—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 fifty kilojoule per mole barrier from three hundred kelvin to three hundred ten kelvin that speeds the reaction, a colder target that slows the rate, and a deliberate zero-temperature case to demonstrate the hard invalid_input path. This landing targets people searching for a rate constant at new temperature calculator, Arrhenius k2 from k1 and Ea, or temperature-adjusted kinetics; it is not a multi-point linear regression of ln k versus one over T, not an activation-energy estimator from two rates, 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 a temperature to zero.
Integration use cases
Unit tests for chemistry calculators
Generate known-good k2 cases plus deliberate zero-temperature rejections for coding kata and automated grading expected values.