In the International System of Units (SI), most units measure things like length or weight. However, two special units called supplementary units exist to measure angles. These are the radian and the steradian.

What is a Radian?

A radian measures a plane angle, which is a flat angle drawn on a piece of paper. Imagine a circle. If you take a piece of string equal to the length of the circle's radius and lay it along the edge of the circle, the angle formed at the center is exactly one radian.

• The symbol for radian is rad.
• A full circle is equal to 2π radians.
• This unit is essential for calculating rotation and circular motion in physics.

What is a Steradian?

A steradian measures a solid angle. Think of this as a 3D version of an angle, like the shape of an ice cream cone. If you take a sphere and cut out a patch on its surface that has an area equal to the square of its radius, the angle this patch makes at the center of the sphere is one steradian.

• The symbol for steradian is sr.
• A full sphere subtends a total solid angle of 4π steradians.
• It is used in physics to measure how much light or radiation spreads out from a source in three dimensions.

Key Differences Between the Two

The main difference lies in the number of dimensions. A radian deals with a flat surface, while a steradian deals with a 3D space. Because they are ratios of lengths or areas, both radian and steradian are dimensionless units. This means they do not have a base unit like meters or kilograms in their final calculation, as the units cancel each other out during the measurement process.