Ellipsoid Volume Calculator
Find the volume of an ellipsoid.
Result
How it is calculated
An ellipsoid is a stretched sphere described by three semi-axes a, b and c, each the distance from the centre to the surface along one direction. Its volume is V = (4/3) π a b c. When all three are equal to r the formula becomes the sphere volume (4/3) π r³.
Enter the semi-axes, which are half of the full widths. The three lengths must be positive and in the same unit; the result is in that unit cubed and is shown with two decimals. The formula gives only volume; the surface area of a general ellipsoid has no simple closed form and is not calculated here.
Worked example
Semi-axes a = 3, b = 2, c = 1.5. Product a × b × c = 3 × 2 × 1.5 = 9. V = (4/3) × π × 9 = 12π ≈ 37.70. The tool shows 37.70 units³ (cubic units of whichever unit you used).
Common mistakes
- Entering full diameters instead of semi-axes; the volume then comes out 8 times too large.
- Mixing units, such as one axis in cm and another in m.
- Reading the result in square units; volume is cubed, so it is cm³ or m³ if you used cm or m.
- Using the formula for a rotated or egg-shaped body, which is not a true ellipsoid.
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.
Was this helpful?
You can pick up to 3 reactions.
Popular calculators
Loan Calculator
Monthly payment, total interest and full amortization schedule.
Percentage Calculator
Percent change, percent of, and ratio calculations.
Discount Calculator
Calculate final price, savings, and discount amount.
BMI Calculator
Body mass index from height and weight (metric or imperial).
Age Calculator
Compute your exact age in years, months and days from a birth date.
Compound Interest Calculator
Calculate the final amount and interest earned with compounding.
All Calculators
No calculators found
Comments (0)