Ellipsoid Volume Calculator

About this calculator

An ellipsoid is a 3D surface where every cross-section is an ellipse, defined by three semi-axes a, b, and c along the x, y, and z directions. Its volume is V = (4/3)·π·a·b·c — a direct generalization of the sphere's volume formula (4/3)πr³, which is the special case a = b = c = r.

Geometry and calculus students use it as a natural extension of sphere-volume problems, radiologists and medical researchers use ellipsoid volume as a standard approximation for estimating the volume of roughly oval organs, cysts, or tumors from MRI or CT scan measurements (the “ellipsoid formula” is a routine step in reporting tumor size), and agricultural scientists and food engineers use it to estimate the volume of eggs, fruits, or seeds from their measured dimensions. Engineers designing tanks, domes, or pressure vessels with an ellipsoidal shape also use it directly for capacity planning.