ForHosting KIT · Math

Power of a point calculator

Enter the distance from a point to the center of a circle and the radius, and get the power of the point, d² − R²: at a distance of 5 from a circle of radius 3 it is 16, so the point is outside. Free in your browser.

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Run — free How it works & API

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Worked example

If you enter

D: 5
R: 3
Decimal places: 6

You get

Power: 16
Position: exterior

Search intent: power of a point calculator. No network calls or random seeds are required. Failed jobs are not billed.

What the power of a point measures

The power of a point is a single number that relates a point to a circle. You take the distance from the point to the center, square it, and subtract the square of the radius. The result is positive when the point lies outside the circle, zero when it sits exactly on the circle and negative when it is inside. Despite the name, it has nothing to do with raising numbers to exponents: here power is a term from geometry. For a point outside, the power is also the square of the tangent length, which is why a point 5 units from the center of a circle of radius 3 has a power of 16 and a tangent of 4.

Common mistakes when you work it out

The distance must be measured to the center of the circle, not to its edge, and the second length is the radius, not the diameter. A negative result is not an error: it simply says the point is inside. Both lengths have to use the same unit, and the power comes out in that unit squared. If you ask for decimals, the result is rounded only once, at the end, so the intermediate steps keep their full precision.

What you can do with it

Teaching

Pinned goldens.

FAQ

What does the sign of the power of a point mean?

It tells you where the point is. A positive power means the point is outside the circle, zero means it sits exactly on the circle, and a negative power means it is inside, closer to the center than the radius.

How is the power of a point calculated?

Square the distance from the point to the center and subtract the square of the radius. For a point 5 units from the center of a circle of radius 3, that is 5 squared minus 3 squared, which gives 16.

How is the power of a point related to a tangent line?

When the point is outside, its power equals the square of the tangent length from the point to the circle. With a distance of 5 and a radius of 3, the tangent measures 4, and 4 squared is the power, 16.

Can I round the power of a point to a set number of decimals?

Yes. Choose how many decimals you want and the power is rounded once, at the very end, with halves rounded up. If you do not ask for decimals, you see the result without rounding.

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

POSThttps://api.kit.forhosting.com/math/power-of-a-point

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/math/power-of-a-point \
  -H "Authorization: Bearer $KIT_KEY" \
  -H "Content-Type: application/json" \
  -d '{"d":5,"R":3}'

const res = await fetch("https://api.kit.forhosting.com/math/power-of-a-point", {
  method: "POST",
  headers: {
    "Authorization": `Bearer ${process.env.KIT_KEY}`,
    "Content-Type": "application/json"
  },
  body: JSON.stringify({
    "d": 5,
    "R": 3
  })
});
const { task_id } = await res.json();

import os, requests

res = requests.post(
    "https://api.kit.forhosting.com/math/power-of-a-point",
    headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
    json={
    "d": 5,
    "R": 3
},
)
task_id = res.json()["task_id"]

<?php
$res = file_get_contents("https://api.kit.forhosting.com/math/power-of-a-point", false, stream_context_create([
  "http" => [
    "method"  => "POST",
    "header"  => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
    "content" => '{"d":5,"R":3}',
  ],
]));
$task = json_decode($res, true);

body := bytes.NewBufferString(`{"d":5,"R":3}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/math/power-of-a-point", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)

Example request

{
  "d": 5,
  "R": 3
}

Example response

{
  "task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
  "type": "math.power_of_a_point",
  "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.

Technical notes

Power Π=d²−R² and interior/exterior/on-circle. The calculator is free in the browser, deterministic, and identical on the API path. Inputs are validated before arithmetic so invalid payloads fail with invalid_input. Half-up rounding is applied once from raw IEEE values when decimals are requested. Use the same JSON from spreadsheets, CMS, automation, or teaching demos.

How it works

No network calls or random seeds are required. Failed jobs are not billed. No network calls or random seeds are required. Failed jobs are not billed. Power Π=d²−R² and interior/exterior/on-circle. Π=d²−R². The calculator is free in the browser, deterministic, and identical on the API path. Inputs are validated before arithmetic so invalid payloads fail with invalid_input. Half-up rounding is applied once from raw IEEE values when decimals are requested. Use the same JSON from spreadsheets, CMS, automation, or teaching demos. The calculator is free in the browser, deterministic, and identical on the API path. Inputs are validated before arithmetic so invalid payloads fail with invalid_input. Half-up rounding is applied once from raw IEEE values when decimals are requested. Use the same JSON from spreadsheets, CMS, automation, or teaching demos.

Inputs, limits and rounding

Optional decimals use half-up once. Outputs echo inputs. No network calls or random seeds are required. Failed jobs are not billed. No network calls or random seeds are required. Failed jobs are not billed. Provide required JSON fields. Invalid types raise invalid_input. The calculator is free in the browser, deterministic, and identical on the API path. Inputs are validated before arithmetic so invalid payloads fail with invalid_input. Half-up rounding is applied once from raw IEEE values when decimals are requested. Use the same JSON from spreadsheets, CMS, automation, or teaching demos. The calculator is free in the browser, deterministic, and identical on the API path. Inputs are validated before arithmetic so invalid payloads fail with invalid_input. Half-up rounding is applied once from raw IEEE values when decimals are requested. Use the same JSON from spreadsheets, CMS, automation, or teaching demos.

When to use it

Use when search intent matches. No network calls or random seeds are required. Failed jobs are not billed. No network calls or random seeds are required. Failed jobs are not billed. Power Π=d²−R² and interior/exterior/on-circle. The calculator is free in the browser, deterministic, and identical on the API path. Inputs are validated before arithmetic so invalid payloads fail with invalid_input. Half-up rounding is applied once from raw IEEE values when decimals are requested. Use the same JSON from spreadsheets, CMS, automation, or teaching demos. The calculator is free in the browser, deterministic, and identical on the API path. Inputs are validated before arithmetic so invalid payloads fail with invalid_input. Half-up rounding is applied once from raw IEEE values when decimals are requested. Use the same JSON from spreadsheets, CMS, automation, or teaching demos.

Integration use cases

Quick check

Free widget.

Automation

Same JSON via API.

Technical questions

Free?

Yes tier A.

Network?

No.

Bad input?

invalid_input.

API?

Yes.

Locales?

EN-only; Nitro hydrates.

Read the full KIT documentation →

Run — free