Work out ellipsoid volume instantly with clear inputs, formula shown and shareable results.
An ellipsoid is a sphere scaled independently along three axes, so V = ⁴⁄₃πabc. Its surface area has no closed form; the Knud Thomsen approximation with p = 1.6075 is accurate to about 1%.
Volume
V = ⁴⁄₃π·a·b·c
Knud Thomsen surface
S ≈ 4π[((ab)^p + (ac)^p + (bc)^p)/3]^(1/p), p = 1.6075
The volume reduces to ⁴⁄₃πr³ and the surface approximation returns exactly 4πr².
The exact area requires elliptic integrals; no elementary closed form exists for a general triaxial ellipsoid.