ForHosting KIT · Developer Utilities

Instantaneous rate from tangent calculator

This instantaneous rate from tangent calculator turns two nearby concentration and time readings into a local reaction-rate estimate.

● BetaFree · in your browser

Run — free How it works & API

Use it from WebAPIEmailTelegramApp soon

Enter concentration c1 at time t1 and concentration c2 at a nearby time t2, and the engine returns the secant slope of concentration versus time together with the magnitude used as the instantaneous rate: the absolute value of c2 minus c1 divided by the absolute value of t2 minus t1. You also get the raw points, Δc and Δt, absolute deltas, a method tag, a short formula reminder, and a unit note so concentration and time units stay consistent. The arithmetic is fully deterministic: finite floating-point subtraction and division only, with no network calls, no sampling, and no date-dependent shortcuts. Classroom checks include c1 equals zero point eight five at t1 equals ten and c2 equals zero point eight zero at t2 equals twelve yielding rate zero point zero two five, and c1 equals one at t equals zero with c2 equals zero point nine two at t equals five yielding rate zero point zero one six. Use it free in the browser for kinetics homework, graphing labs, and worksheet keys, or call the API at $0.002 per successful request when you need reproducible tangent-rate fixtures in CI, tutoring software, or teaching demos.

How to use it

Enter your values in the form above. The tool checks them before calculating and shows the result on the same page.

Check your inputs

Use the labels and units shown next to each field. If something is missing or outside the allowed range, the page points to the field to fix.

Use it again or automate it

Use the browser tool for individual checks and the API when you need the same capability in an automated workflow.

What you can do with it

Get an answer now

Enter one set of values and see the result without building a spreadsheet or script.

Compare scenarios

Change one value at a time and rerun the calculation to understand what affects the result.

Automate repeated work

Use the API when the same calculation needs to run inside your product or workflow.

FAQ

How do I use this capability?

Complete the fields above and run it on this page. The form highlights anything that needs attention.

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

POSThttps://api.kit.forhosting.com/chem/instantaneous-rate

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/instantaneous-rate \
  -H "Authorization: Bearer $KIT_KEY" \
  -H "Content-Type: application/json" \
  -d '{"c1":0.85,"t1":10,"c2":0.8,"t2":12}'

const res = await fetch("https://api.kit.forhosting.com/chem/instantaneous-rate", {
  method: "POST",
  headers: {
    "Authorization": `Bearer ${process.env.KIT_KEY}`,
    "Content-Type": "application/json"
  },
  body: JSON.stringify({
    "c1": 0.85,
    "t1": 10,
    "c2": 0.8,
    "t2": 12
  })
});
const { task_id } = await res.json();

import os, requests

res = requests.post(
    "https://api.kit.forhosting.com/chem/instantaneous-rate",
    headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
    json={
    "c1": 0.85,
    "t1": 10,
    "c2": 0.8,
    "t2": 12
},
)
task_id = res.json()["task_id"]

<?php
$res = file_get_contents("https://api.kit.forhosting.com/chem/instantaneous-rate", false, stream_context_create([
  "http" => [
    "method"  => "POST",
    "header"  => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
    "content" => '{"c1":0.85,"t1":10,"c2":0.8,"t2":12}',
  ],
]));
$task = json_decode($res, true);

body := bytes.NewBufferString(`{"c1":0.85,"t1":10,"c2":0.8,"t2":12}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/chem/instantaneous-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

{
  "c1": 0.85,
  "t1": 10,
  "c2": 0.8,
  "t2": 12
}

Example response

{
  "task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
  "type": "chem.instantaneous_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

Per request$0.002

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.

Read the full KIT documentation →

Run — free