Solid Angle Calculator

Enter the surface area and the radius of a sphere into the calculator to determine the solid angle of the sphere.

Solid Angle Formula

The following equation can be used to calculate the solid angle of a sphere.

Ω =A / r^2

  • Where Ω is the solid angle (steradians)
  • A is the surface area of the projected area.
  • r is the radius

Solid Angle Definition

A solid angle is defined as the amount of field of view seen from a particular point that an object covers.

Is solid angle dimensionless?

A solid angle has dimensions or steradians, so in a sense it is dimensionless. Steradians are only a proportion of a circle, not a unit itself. If you look at the equation above you can see that the units would be units^2/units^2 which yields unitless.

Can solid angles be negative?

In general geometry solid angles cannot be negative. If they were, then either the radius or surface area would have to be negative. In complex physics or mathematics however, this may be possible.

How many solid angles are in a sphere?

Solid angles are measured in steradians, which by definition means there are 4*pi solid angles in a sphere. In other words, there are approximately 12.5663 solid angles total in a sphere.

Solid Angle Example

How to calculate a solid angle?

  1. First, determine the surface area.

    Calculate the surface area.

  2. Next, determine the radius.

    Measure the radius of the sphere.

  3. Finally, calculate the solid angle.

    Calculate the solid angle using the equation above.


What is a solid angle?

A solid angle is a ratio of the surface area of a field of view to it’s radius.

solid angle calculator
solid angle formula