Definition:Solid Angle Subtended/Also presented as

Definition

Let $S$ be a surface oriented in space.

Let $P$ be a point in that space.

The solid angle subtended by $S$ at $P$ can also be presented as:

$\ds \Omega = \iint_S \frac {\mathbf {\hat r} \cdot \mathbf {\hat n} \rd S} {r^2}$

where:

$\mathbf {\hat r} = \dfrac {\mathbf r} r$ is the unit vector corresponding to the position vector $\mathbf r$ of the infinitesimal surface $\d S$ with respect to $P$

$r$ is the magnitude of $\mathbf r$

$\mathbf {\hat n}$ represents the unit normal to $\d S$.

Sources

• Weisstein, Eric W. "Solid Angle." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SolidAngle.html