Math
Instant, private, and free
Ellipsoid Volume Calculator.
Calculate the volume of an ellipsoid from its three semi-axes.
Set your values
Results update as you type.
Results update automatically as you type.
Use Cases
Engineering and Design
Determine the volume of ellipsoidal tanks, pressure vessels, or components to estimate capacity or material requirements.
Example: Calculate the volume of an ellipsoidal tank with semi-axes 2m, 1.5m, and 1m.
Medical and Biological Applications
Estimate the volume of organs or lesions approximated as ellipsoids, such as in ultrasound or MRI measurements.
Example: Estimate the volume of a kidney with semi-axes 6cm, 3cm, and 2cm.
Frequently Asked Questions
- What is an ellipsoid and how is its volume calculated?
- An ellipsoid is a 3D shape where all cross-sections are ellipses. Its volume is calculated using the formula V = (4/3)πabc, where a, b, and c are the lengths of the three semi-axes. This calculator uses that formula to give you the volume instantly.
- What units should I use for the semi-axes?
- You can use any unit of length (e.g., meters, centimeters, inches) as long as all three semi-axes are in the same unit. The volume will be in cubic units of that same unit (e.g., cubic meters if you use meters).
- Can I use this calculator for a sphere?
- Yes, if all three semi-axes are equal, the ellipsoid becomes a sphere. The calculator will correctly compute the volume using the sphere formula V = (4/3)πr³, where r is the common semi-axis length.
Tips & Common Mistakes
Tips
- Ensure all three semi-axes are measured in the same unit to get the volume in cubic units of that unit.
- Double-check that you are entering semi-axes (half the full length) not full diameters. If you have diameters, divide each by 2 first.
- For a quick estimate, you can round the semi-axes to the nearest whole number, but for precise results, use exact measurements.
- Remember that the volume scales with the cube of the linear dimensions, so small measurement errors can lead to larger volume errors.
Common Mistakes to Avoid
- Entering diameters instead of semi-axes. The semi-axis is half the full length across the ellipsoid's center.
- Using different units for the three semi-axes, which leads to incorrect volume calculations. Always convert to the same unit first.
- Confusing the ellipsoid volume formula with that of an ellipse area. The volume formula includes the factor 4/3π, not π.
Last updated: August 13, 2026