ForHosting KIT · Developer Utilities

Group velocity calculator

Group velocity is the speed at which the envelope of a wave packet—and therefore the energy and information it carries—travels through a dispersive medium.

● BetaFree · in your browser

Run — free How it works & API

Use it from WebAPIEmailTelegramApp soon

For a continuous dispersion relation ω(k), the textbook definition is the derivative vg equals dω over dk evaluated near the carrier wave number. In lab notes, spectroscopy tables, and numerical simulations you rarely hold a closed-form ω(k); you hold two nearby points and need a trustworthy finite-difference estimate. This group velocity calculator accepts angular frequencies ω1 and ω2 together with wave numbers k1 and k2, forms Δω and Δk, and returns vg equals Δω over Δk with stable rounding, display equation, and step strings. Equal wave numbers are rejected because the denominator would vanish. The pure deterministic path powers both the free browser widget and the API at $0.002 per successful call, so homework checks, optics design notes, and CI fixtures never disagree on a simple two-point slope.

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/optics/group-velocity-finite-difference

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/optics/group-velocity-finite-difference \
  -H "Authorization: Bearer $KIT_KEY" \
  -H "Content-Type: application/json" \
  -d '{"omega1":1000000000000000,"k1":10000000,"omega2":1200000000000000,"k2":11000000}'

const res = await fetch("https://api.kit.forhosting.com/optics/group-velocity-finite-difference", {
  method: "POST",
  headers: {
    "Authorization": `Bearer ${process.env.KIT_KEY}`,
    "Content-Type": "application/json"
  },
  body: JSON.stringify({
    "omega1": 1000000000000000,
    "k1": 10000000,
    "omega2": 1200000000000000,
    "k2": 11000000
  })
});
const { task_id } = await res.json();

import os, requests

res = requests.post(
    "https://api.kit.forhosting.com/optics/group-velocity-finite-difference",
    headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
    json={
    "omega1": 1000000000000000,
    "k1": 10000000,
    "omega2": 1200000000000000,
    "k2": 11000000
},
)
task_id = res.json()["task_id"]

<?php
$res = file_get_contents("https://api.kit.forhosting.com/optics/group-velocity-finite-difference", false, stream_context_create([
  "http" => [
    "method"  => "POST",
    "header"  => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
    "content" => '{"omega1":1000000000000000,"k1":10000000,"omega2":1200000000000000,"k2":11000000}',
  ],
]));
$task = json_decode($res, true);

body := bytes.NewBufferString(`{"omega1":1000000000000000,"k1":10000000,"omega2":1200000000000000,"k2":11000000}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/optics/group-velocity-finite-difference", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)

Example request

{
  "omega1": 1000000000000000,
  "k1": 10000000,
  "omega2": 1200000000000000,
  "k2": 11000000
}

Example response

{
  "task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
  "type": "optics.group_velocity_finite_difference",
  "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.

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 →