Angular Velocity Calculator
Calculate angular velocity from linear speed and radius using omega = v / r. Returns the result in radians per second. Use this for rotating machinery, circular motion, and converting between linear and rotational quantities.
How to use this tool
- Enter linear speed (v) and radius (r) in the fields above.
- Results update instantly as you type โ or click Calculate.
- Read your angular velocity and the full breakdown beneath it.
Formula
omega = v / r
How it works
Angular velocity ฯ describes how fast an object rotates in radians per second. It relates to linear speed v and radius r by ฯ = v / r.
Worked examples
Wheel hub
Circular orbit
Common mistakes to avoid
- Confusing angular velocity (rad/s) with linear speed (m/s) โ this calculator converts between them using the radius; entering the wrong quantity gives a meaningless result.
- Using the diameter of the circular path as the radius, halving the computed angular velocity.
- Assuming angular velocity in rpm is the same as rad/s โ multiply rpm by 2*pi/60 to convert before using physics formulas.
Key terms
Frequently asked questions
- What is the relationship between angular velocity and rotational speed in rpm?
- Angular velocity omega (rad/s) = rpm * 2*pi / 60. For example, 3000 rpm = 3000 * 2*pi / 60 = 314.2 rad/s.
- Can I use this calculator for rotating machinery?
- Yes, but you need the linear speed of a point on the rim and the radius. Alternatively, if you know rpm, convert directly to rad/s using omega = rpm * 2*pi/60 without needing the radius.
- Why are radians used instead of degrees for angular velocity?
- Radians are the natural unit for angular measure in calculus and physics because the arc length formula s = r * theta only holds when theta is in radians. Using degrees would require a conversion factor in every formula.