ellipsoid volume calculator
Calculate the volume of an ellipsoid (an egg or dome shape) in cubic feet, cubic yards, gallons, and liters from its three diameters.
Some shapes aren’t a simple cylinder or box — a domed tank lid, an egg-shaped cistern, or a rounded stockpile all bulge unevenly in three directions. This calculator handles that case: enter the three diameters and get the volume in cubic feet, cubic yards, gallons, and liters.
How this calculator works
An ellipsoid is a sphere stretched by three different amounts along three perpendicular axes. Its volume comes from the same constant used for a sphere, applied to all three radii instead of one.
Formula: Cubic feet = (4/3) × π × (A ÷ 2) × (B ÷ 2) × (C ÷ 2), where A, B, and C are the three diameters in feet.
Worked example
A dome-shaped shape with diameters of 4 ft, 3 ft, and 2 ft:
- Radii: 4 ÷ 2 = 2 ft, 3 ÷ 2 = 1.5 ft, 2 ÷ 2 = 1 ft
- Cubic feet: (4/3) × π × 2 × 1.5 × 1 ≈ 12.57 ft³
- Cubic yards: 12.57 ÷ 27 ≈ 0.465 yd³
- Gallons: 12.57 × 7.48 ≈ 94.0 gal
- Liters: 94.0 × 3.785 ≈ 355.8 L
Reference
| Diameters (A × B × C) | Cubic feet |
|---|---|
| 2 × 2 × 2 ft | 4.19 ft³ |
| 4 × 3 × 2 ft | 12.57 ft³ |
| 6 × 4 × 3 ft | 37.70 ft³ |
How to measure
Measure the widest point of the shape along three roughly perpendicular directions — width, depth, and height — and enter those as the three diameters. For an upright cylindrical tank instead of a dome shape, the Tank Volume Calculator uses a simpler two-measurement formula.
Frequently asked questions
What shapes count as an ellipsoid?
Any dome, egg, or stretched-sphere shape — a domed septic tank lid, an egg-shaped water tank, a rounded mound of stockpiled material, or a decorative pond basin. If it has three different widths along three perpendicular directions, it's an ellipsoid rather than a true sphere.
What if two of the diameters are equal?
That's a spheroid — a sphere stretched along one axis, like a rugby ball or a squashed dome. The same formula still applies; you're just entering the same number twice.
What if all three diameters are equal?
Then it's a true sphere, and this formula reduces to the standard sphere volume formula. You could use either calculator and get the same answer.
How do I measure diameter A, B, and C on a real object?
Measure the widest point along three directions that are roughly perpendicular to each other: side-to-side, front-to-back, and top-to-bottom. Order doesn't matter — the formula multiplies all three the same way.
Is this exact for an irregular dome or mound?
It's exact for a true mathematical ellipsoid. A real dirt pile or rough dome is an approximation of that shape, so treat the result as a close estimate and round up slightly for ordering material.
Estimates only. Verify quantities with your supplier before purchasing.