Ellipsoid Volume Calculator
Calculate the volume and surface area of an ellipsoid using its three semi-axes
Calculate Ellipsoid Properties
Length of first semi-axis
Length of second semi-axis
Length of third semi-axis
Ellipsoid Properties
Volume formula: V = (4/3) × π × a × b × c
Input values: a = 0, b = 0, c = 0 cm
Surface area: Approximated using Knud Thomsen's formula
Ellipsoid Type
Example Calculation
Medical Application Example
Organ: Prostate volume estimation
Semi-axis A: 3 cm (anteroposterior)
Semi-axis B: 6 cm (transverse)
Semi-axis C: 8 cm (craniocaudal)
Calculation
V = (4/3) × π × 3 × 6 × 8
V = (4/3) × π × 144
V = 192π cm³
V ≈ 603.19 cm³
Types of Ellipsoids
Sphere
a = b = c
Perfect symmetry
Oblate Spheroid
a = b > c
Flattened sphere
Prolate Spheroid
a = b < c
Elongated sphere
Triaxial
a ≠ b ≠ c
All axes different
Real-World Applications
Medical organ volume estimation
Earth's shape modeling
Fresnel zone calculations
Architectural design
Molecular modeling
Understanding Ellipsoids
What is an Ellipsoid?
An ellipsoid is a three-dimensional surface that can be described as a "stretched" or "compressed" sphere. It's defined by three semi-axes (a, b, c) that extend from the center to the surface along three perpendicular directions.
Key Properties
- •All cross-sections through the center are ellipses
- •Semi-axes meet at right angles (90°)
- •Volume depends on all three semi-axes
- •Surface area requires complex calculations
Mathematical Formula
V = (4/3) × π × a × b × c
Standard Form: x²/a² + y²/b² + z²/c² = 1
- V: Volume of the ellipsoid
- a, b, c: Lengths of the three semi-axes
- π: Pi (approximately 3.14159)
Note: When a = b = c, the ellipsoid becomes a sphere with volume V = (4/3)πr³