Radian and Degree Measure

When a cyclist pedals, the rotation of the wheel sweeps out angles, which are commonly measured in degrees or radians.

One full rotation equals 360 degrees or 2π radians, both describing complete circular movement.

Degrees divide a circle into 360 equal parts and are widely used in navigation, design, and geometry.

A radian is defined as the angle formed when an arc’s length equals the radius of a circle.

Since the full circumference of a circle is 2π times its radius, it spans 2π radians. Counterclockwise angles are positive, while clockwise ones are negative. With each additional rotation, the angle keeps changing, ranging from negative infinity to positive infinity.

To convert degrees to radians, multiply degrees by π over 180 degrees, and to convert radians to degrees, multiply by 180 degrees over π.

For instance, 45 degrees equals π over 4 radians and vice versa. Similarly, 5π over 4 radians will be equal to 225 degrees.

On a bike, any angular displacement θ in radians results in a linear distance along the wheel’s path.

The total distance equals the wheel’s radius times the angle in radians.