RPM to linear speed calculator
A wheel of 0.25 m radius turning at 60 rpm makes one turn per second, so its rim covers a full circumference every second. Enter rpm and radius to get the rim speed, plus angular velocity, frequency and period. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Rpm
- 60
- Radius
- 0.25
- Velocity
- 1.5707963268 m/s
- Angular velocity
- 6.2831853072
- Frequency hz
- 1
- Period
- 1
This RPM to linear speed calculator converts rotational speed in revolutions per minute and a path radius into the linear speed at the rim, also called tangential speed. The identity is fully closed form: frequency in hertz equals rpm divided by sixty, angular velocity omega equals two pi times that frequency, and linear speed v equals omega times radius, which expands to v equals two pi r times rpm over sixty. When radius is in metres and rpm is revolutions per minute, the result is metres per second; any consistent length unit works the same way for the speed unit you care about. Zero rpm yields zero linear speed; zero radius yields zero rim speed at any finite spin rate. Negative radius is rejected because a geometric path radius cannot be negative. The engine is deterministic arithmetic only: no network calls, no sampling, and no date-dependent shortcuts.
What rim speed means and what you get
In rigid-body rotation about a fixed axis, every point at radial distance r from the axis moves on a circle of circumference two pi r. If the body turns at n revolutions per minute, it completes n over sixty revolutions each second, so the time for one revolution is sixty over n seconds when n is not zero. Distance per unit time along the circle is therefore circumference times revolutions per second: v equals two pi r times rpm over sixty.
That quantity is the linear or tangential speed at the rim (or at any chosen radius). Angular velocity omega in radians per second is two pi times revolutions per second; equivalently v equals omega r.
Where rpm-to-linear conversion fits in study, design, and software
Students meet rim speed when a textbook introduces uniform circular motion, when a lab measures wheel radius and motor rpm, or when a contest problem asks for belt or grinding-wheel surface speed without calculus. Machine designers convert spindle rpm and tool radius into surface feet or metres per minute (after a unit scale) before checking cutting-speed charts. Teachers can pre-generate answer keys for modest rpm and r values without trusting opaque calculator apps that silently switch between period-based and rpm-based formulas.
Developers call the same contract from scripts to seed deterministic test vectors for conveyor demos, to normalize user-entered motor nameplates before a visualization, or to satisfy programming-challenge statements that demand v rather than a hand-waved sketch. Vehicle and robotics first-order checks use v equals omega r when only wheel radius and rotational rate are known, before slip or tire deflection are modeled.
What you can do with it
Homework and lab checks
Convert measured motor rpm and wheel or disk radius into rim linear speed before grading worksheets or comparing to tachometer data.
Machine and cutting-speed prep
Turn spindle rpm and tool or workpiece radius into surface speed for first-order process checks and design notes.
FAQ
What does the RPM to linear speed calculator cost?
It is free in your browser on this page.
What formula is used for linear rim speed?
Equivalently v = ωr with ω = 2π · (rpm/60).
What happens if radius is negative?
A geometric path radius cannot be negative; use a non-negative radius (zero is allowed and yields zero rim speed).
Can rpm be zero or negative?
Yes. Zero rpm yields zero linear speed and a null period. A negative rpm is treated as a signed rotation rate and produces a signed linear velocity.
How is this different from a period-based circular velocity calculator?
This tool takes revolutions per minute and radius. Same physics, different common input forms and search intent.
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/mech/rpm-to-linear \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"rpm":60,"radius":0.25}'const res = await fetch("https://api.kit.forhosting.com/mech/rpm-to-linear", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"rpm": 60,
"radius": 0.25
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/mech/rpm-to-linear",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"rpm": 60,
"radius": 0.25
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/mech/rpm-to-linear", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"rpm":60,"radius":0.25}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"rpm":60,"radius":0.25}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/mech/rpm-to-linear", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"rpm": 60,
"radius": 0.25
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "mech.rpm_to_linear",
"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_rpm | 1000000000000000 |
max_abs_radius | 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. |
Technical notes
What rim linear speed means and what the response contains
This calculator returns the normalized inputs rpm and radius, the computed linear velocity, angular velocity, frequency in hertz, period in seconds when rpm is non-zero (null when rpm is zero), circumference, the precision used, a method tag rpm_to_linear, a short formula reminder, and a unit hint m/s for SI length inputs. There is no numerical ODE integration and no Monte Carlo sampling of trajectories: the engine either evaluates the closed forms inside the supported numeric range or rejects the input with invalid_input. Rejected cases include a missing rpm or radius, non-finite values, magnitudes above the documented ceilings, and any radius that is strictly negative, because a circular path radius cannot be negative.
How rpm and radius are read and how v stays reproducible
Rpm may be zero or negative: zero means no motion, and a negative value is a signed sense of rotation that yields a signed linear velocity along the chosen convention. Only non-finite values and magnitudes above the documented ceiling are rejected for rpm. Optional leading plus signs and scientific notation on numeric strings are allowed when they parse as finite decimals; embedded spaces and non-numeric tokens are rejected. The preferred field for rotational speed is rpm, but aliases n, N, revolutions_per_minute, and rev_per_min are accepted so spreadsheets, query strings, and typed forms can reuse the same contract. The preferred field for radius is radius, with aliases r, R, and path_radius. Radius must be finite and non-negative: a strictly negative value fails with invalid_input and a message that names the field and explains that a path radius cannot be negative, so a bad cell does not become a silent nonsense speed. An optional precision field, with aliases decimals and dp, chooses how many decimal places to expose for the numeric outputs, defaulting to ten and capped at fifteen so JSON goldens stay stable. Pair the free browser run on this page with the priced API when you need the identical mathematical result inside an automated pipeline without re-implementing the rpm-to-linear formula yourself.
Where rpm-to-linear conversion fits in study, design, and software
Product and education tools use the endpoint when a learner types rpm and radius and the UI must show metres per second at the rim. On this page the work runs entirely in your browser; through the API each successful lookup costs $0.002, failed validation is not charged, and nothing is stored after the response returns. That split — free interactive exploration and a priced, identical API — matches the rest of the KIT tier-A catalog and lets you move from a classroom demo to an automated pipeline without changing the mathematical result. Pair it with circular-velocity helpers that take period T when your data is timed rather than rpm-based, and with other mechanics endpoints when you are building a small lab of free, deterministic physics calculators.
Integration use cases
Deterministic test fixtures
Generate reproducible velocity and omega values for unit tests, robotics demos, and CI assertions on v = 2πr·(rpm/60).