Tangential Speed Calculator: v = omega x r

How fast a point on a rotating object moves.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

Choose which quantity you want to find.

Enter the other values in the units shown.

The calculator gives the answer with the formula, the substituted numbers, and the answer in other units.

Formulas used

  • v = \omega\,r
  • \omega = \frac{v}{r}
  • r = \frac{v}{\omega}

Worked example

With the default numbers in the calculator above:

  1. The formula, arranged to find the tangential speed: tangential speed = angular speed x radius
  2. Put the values in (every value in its SI unit): tangential speed = 10 x 0.5
  3. The answer: tangential speed: 5 m/s
  4. The same answer in other units: 18 km/h; 11.1847 mph

Change the numbers in the calculator to see the full working, every step, for your own case.

Common questions

What is the formula for the speed of a point on a wheel?

The angular speed in radians per second times the radius. At 10 rad/s and 0.5 m the rim moves at 5 m/s.

How do I convert rpm to rad/s?

Multiply by 0.10472.

Do all points on a wheel have the same speed?

They have the same angular speed, but points further out move faster.

Related calculators

Got a question about this? Ask an engineering question and get a plain-language answer with references.

Further reading: Any school physics text (circular motion).

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