Rotational Linear Speed Calculator
Written by Thierno Sadou Diallo, formula verified per our methodology • Last checked on 9/9/2026
The linear speed at the edge of a rotating part is calculated with v = 2π × radius × rotational speed ÷ 60. For a 0.3 m radius at 1000 RPM, the linear speed is about 31.4 m/s, or about 113 km/h.
Explanation
A point located at the edge of a rotating part (wheel, pulley, disk, grinding wheel) moves at a linear speed that depends both on its distance from the center of rotation (the radius) and the part's rotational speed. The relationship comes from the angular velocity ω, expressed in radians per second: ω = 2π × N ÷ 60 for a rotational speed N in revolutions per minute (one full turn corresponds to 2π radians, covered in 60 seconds divided by N). Linear speed is then obtained by v = ω × radius. This calculator expresses the result both in m/s (consistent with the International System) and in km/h, more intuitive for an everyday sense of scale: at a given radius and rotational speed, doubling the radius doubles the linear speed, exactly like doubling the rotational speed. This principle explains why a bicycle wheel's rim moves much faster than its hub, or why the cutting speed at the edge of a grinding wheel depends directly on its diameter at a given rotational speed. To convert this same rotational speed into the torque available on the shaft, see our motor torque calculator; for a speed expressed directly in another unit than km/h, our speed conversion calculator.
Example: 0.3 m radius at 1000 RPM
Inputs
Radius: 0.3 m. Rotational speed: 1000 RPM.
Calculation
Linear speed = 2 × π × 0.3 × 1000 ÷ 60 ≈ 31.42 m/s. In km/h: 31.42 × 3.6 ≈ 113.1 km/h.
Result
A point located 0.3 m from the center moves at about 31.4 m/s, or about 113 km/h.
Frequently asked questions
Why don't two parts of different radii rotating at the same speed have the same linear speed?
Because linear speed is proportional to the radius, at a given rotational speed: v = ω × radius. A point further from the center travels a larger circumference in the same turn, and therefore in the same time — so it moves faster. This is why, on a wheel, the hub (near the center) rotates at the same angular speed as the rim, but moves much more slowly in linear terms.
Does this formula apply to a moving vehicle wheel?
Yes, with a specific interpretation: for a wheel rolling without slipping, the linear speed of its theoretical contact point with the ground corresponds to the vehicle's forward speed. This is in fact how a speedometer based on wheel rotational speed and radius works.
What is the difference between linear speed and angular speed?
Angular speed (ω, in radians per second, or in revolutions per minute) describes how fast an object rotates, independent of its size. Linear speed describes how fast a specific point on that object moves through space, which additionally depends on its distance from the center of rotation. Two points on the same rotating disk have the same angular speed, but different linear speeds depending on their radius.