Colatitude ($\theta =\pi /2-\lambda$)

Colatitude is the angle from the positive polar axis, usually denoted $\theta$ with $0\le \theta \le \pi$. On a sphere it complements latitude $\lambda$: $\theta =\pi /2-\lambda$. Thus the north pole, equator and south pole have colatitudes zero, $\pi /2$ and $\pi$.

With longitude $\varphi$, the standard spherical coordinates are $x=r\sin \theta \cos \varphi$, $y=r\sin \theta \sin \varphi$, $z=r\cos \theta$. The surface element is $r^2\sin \theta d\theta d\varphi$, which shows why an integral over the sphere must include the sine weight. Some disciplines exchange the names of $\theta$ and $\varphi$, so formulas should accompany symbol conventions.