Mathematics · Trigonometry

Angular and Linear Speed Calculator

Convert angular speed at a radius into tangential speed.

Runs locally
Your numbers

Inputs and results stay in this browser. Change one value at a time to explore the relationship.

Your inputCalculatedPassed forward in chains
Linear speed6
Revolutions per second0.477465

Calculation steps

  1. v=2×3=6.
  2. Report Linear speed=6, Revolutions per second=0.477464829275686.

Understand Angular to linear speed

One idea, three depths

Choose how deeply to explain Angular to linear speed

Angular to linear speed: Convert angular speed at a radius into tangential speed.

Age 5Explain it to a 5-year-oldStart with a picture

Imagine using Angular to linear speed to answer this question: convert angular speed at a radius into tangential speed? Enter Radius r and Angular speed ω; the calculator shows Linear speed. For example: At r=2 m and ω=3 rad/s, v=6 m/s. The answer tells you Linear speed.

Age 15Explain it to a 15-year-oldConnect it to the formula

A point farther from a rotation axis covers more distance for the same angular change. The rule is v=rω. Its input values are Radius r, Angular speed ω (rad/s), and the main result is Linear speed. For example: At r=2 m and ω=3 rad/s, v=6 m/s.

CollegeExplain it at college levelState the model precisely

This calculator evaluates the stated angular to linear speed relation over the valid real-number domain stated below. The implemented relation is v=rω, evaluated from Radius r, Angular speed ω (rad/s) to produce Linear speed. A point farther from a rotation axis covers more distance for the same angular change. Angular speed must be in radians per unit time.

Inputs and valid domain

  • Radius r must be a finite real number, at least 0.
  • Angular speed ω must be a finite real number in rad/s.

Important boundary: Angular speed must be in radians per unit time.

The formula

v=rω

How the calculator works through it

It substitutes Radius r, Angular speed ω into the formula and exposes every numerical step above. The main output is Linear speed, accompanied by Revolutions per second.

Read the result correctly

The Linear speed is the direct answer to “convert angular speed at a radius into tangential speed.” Read it with the units shown beside the inputs; a sign, angle, percentage or rate changes what the number means.

A worked check

At r=2 m and ω=3 rad/s, v=6 m/s.

Where this model stops being reliable

Angular speed must be in radians per unit time.

Learn it by changing one value

Begin with the worked example, then change one value while keeping the others fixed. Compare the new result and calculation steps to identify which part of the formula changed.

Dictionary terms behind this calculator

Before studying the codeWhat you should know firstUse the calculator immediately, or check the foundations before reading the implementation.

These foundations help you understand why Angular to linear speed works. They never block the calculator, and “optional” means useful context rather than a hidden requirement.

Hard requirements

  • Reading formulas and substituting values

    Angular to linear speed uses v=rω. You need to recognise what each side represents before substituting the stated inputs or rearranging the relationship.

    Review this foundation about 4 min

Strong support

Optional enrichment

Learn the missing foundationsI already know these — show the code

Mathematics → algorithm → program

Implement this calculation in code

These are direct reference implementations of the calculator's principal relationship and first output. They run locally and include a small known-answer check where the language supports it.

Algorithm

  1. Read Radius r, Angular speed ω.
  2. Evaluate the principal relationship: v=rω.
  3. Return Linear speed and check the domain conditions described above.
Python
            from math import *

def angular_linear_speed(a, b) -> float:
    return (a * b)

assert abs(angular_linear_speed(2, 3) - 6) < 1e-6 * max(1.0, abs(6))
          
Current calculator valuesUpdates when you change an input above.
              
            
C
            #include <assert.h>
#include <math.h>

double angular_linear_speed(double a, double b) {
    return (a * b);
}

int main(void) {
    const double expected = 6;
    const double actual = angular_linear_speed(2, 3);
    assert(fabs(actual - expected) < 1e-6 * fmax(1.0, fabs(expected)));
}
          
Current calculator valuesUpdates when you change an input above.
              
            
C++
            #include <cassert>
#include <cmath>
#include <numbers>

double angular_linear_speed(double a, double b) {
    return (a * b);
}

int main() {
    constexpr double expected = 6;
    const double actual = angular_linear_speed(2, 3);
    assert(std::fabs(actual - expected) < 1e-6 * std::fmax(1.0, std::fabs(expected)));
}
          
Current calculator valuesUpdates when you change an input above.
              
            
Linux x86-64 assembly

x86-64 NASM · System V ABI · Linux · SSE2 with libm where required

            ; double angular_linear_speed(double a, double b)
; Linux x86-64 NASM · System V ABI · first eight doubles in xmm0–xmm7
global angular_linear_speed
section .text

angular_linear_speed:
    push rbp
    mov rbp, rsp
    sub rsp, 32
    movsd [rbp-8], xmm0
    movsd [rbp-16], xmm1
    movsd xmm0, [rbp-8]
    mulsd xmm0, [rbp-16]
    movsd [rbp-24], xmm0
    movsd xmm0, [rbp-24]
    leave
    ret
          
Current calculator valuesUpdates when you change an input above.
              
            
MATLAB
            function result = angular_linear_speed(a, b)
    result = (a * b);
end
          
Current calculator valuesUpdates when you change an input above.
              
            
Wolfram Language
            ClearAll[mwCalculate];
mwCalculate[a_, b_] := (a * b);
          
Current calculator valuesUpdates when you change an input above.
              
            

Continue in mathematical software

The downloaded file includes your current inputs and first calculated result. It is created locally.

Floating-point answers can differ slightly by language, compiler and processor. Compare within a suitable tolerance rather than assuming every decimal representation will be identical.

Supporting sourcesAcademic referencesPrimary standards, textbooks and complete citations

Standards, reading and academic references

Use the calculator as the worked interaction, then consult the primary standards and academic textbooks listed below. MW SysArc links to the original sources; the explanation on this page is original and does not reproduce them.

Algebra and Trigonometry 2e

Read the related free OpenStax mathematics chapters
Cite this book
APA 7
Abramson, J. (2021). Algebra and trigonometry 2e. OpenStax. https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-introduction-to-prerequisites
MLA 9
Abramson, Jay. Algebra and Trigonometry 2e. OpenStax, 2021, https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-introduction-to-prerequisites.
Chicago author-date
Abramson, Jay. 2021. Algebra and Trigonometry 2e. Houston, TX: OpenStax. https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-introduction-to-prerequisites.

OpenStax entries are free to read online. Follow the licence shown on each linked source before redistributing or adapting its content.

Reuse the page responsiblyCite this pageAPA, MLA, Chicago, Harvard, BibTeX and RIS

These formats cite this calculator page itself. They are separate from the academic references above, which support the mathematical method and terminology.

APA 7

MW SysArc. (2026, July 21). Angular and Linear Speed Calculator. MW SysArc Tools. https://math.mwsysarc.com/trigonometry/angular-linear-speed

MLA 9

MW SysArc. “Angular and Linear Speed Calculator.” MW SysArc Tools, 21 July 2026, https://math.mwsysarc.com/trigonometry/angular-linear-speed. Accessed 31 Aug. 2026.

Chicago 17

MW SysArc. “Angular and Linear Speed Calculator.” MW SysArc Tools. Published July 21, 2026. Accessed August 31, 2026. https://math.mwsysarc.com/trigonometry/angular-linear-speed.

Harvard

MW SysArc (2026) ‘Angular and Linear Speed Calculator’, MW SysArc Tools. Published 21 July 2026. Available at: https://math.mwsysarc.com/trigonometry/angular-linear-speed (Accessed: 31 August 2026).

BibTeX and RIS records

BibTeX

@misc{mwsysarc_angular_linear_speed_2026,
  author = {{MW SysArc}},
  title = {Angular and Linear Speed Calculator},
  howpublished = {MW SysArc Tools},
  year = {2026},
  url = {https://math.mwsysarc.com/trigonometry/angular-linear-speed},
  note = {Published July 21, 2026; accessed August 31, 2026}
}

RIS

TY  - ELEC
AU  - MW SysArc
TI  - Angular and Linear Speed Calculator
T2  - MW SysArc Tools
PY  - 2026
DA  - 2026-07-21
Y2  - 2026-08-31
UR  - https://math.mwsysarc.com/trigonometry/angular-linear-speed
N1  - Published July 21, 2026
ER  -

Clear answers

Frequently asked questions

What does the Angular to linear speed do?

Convert angular speed at a radius into tangential speed.

How does the Angular to linear speed work?

The calculator applies v=rω. A point farther from a rotation axis covers more distance for the same angular change.

What can I learn from the Angular to linear speed?

It connects the mathematical rule to your chosen numbers and shows each calculation step. Change one input at a time to see how the result responds.

Does MW SysArc receive or store what I enter?

No. The calculation runs locally in your browser. MW SysArc does not receive or store your calculation inputs.

How should I use the result?

Use the steps to understand the method, then verify important school or professional work using the notation and rounding rules required in your setting.

Last reviewed . Calculations tested .

MW SysArc Certified