ellipsoid volume calculator
An ellipsoid volume calculator uses V = 4/3 × π × a × b × c with half of each diameter; diameters of 4, 3 and 2 ft give 12.57 cubic feet, or 94.0 gallons.
Ellipsoid volume calculator: 4/3 × π × a × b × c
This ellipsoid volume calculator finds the space inside an egg-like or stretched-ball shape from its three diameters. The formula is V = (4/3) × π × (A ÷ 2) × (B ÷ 2) × (C ÷ 2), where A, B, and C are the full widths in feet. The result is shown in cubic feet and cubic yards, plus gallons (× 7.48052) and liters (× 3.78541 per gallon).
The formula in plain words
A sphere’s volume is 4/3 × π × r × r × r. An ellipsoid is a sphere that has been pulled to different lengths in three directions, so each “r” is replaced by its own half-width. Halve each diameter to get the three semi-axes, multiply them together, then multiply by 4/3 and by π (about 3.1416). Together, 4/3 × π is about 4.19.
A quick check: an ellipsoid fills about 52% of the box that would fit around it, because π ÷ 6 = 0.524. A 4 × 3 × 2 ft box holds 24 cu ft, and the ellipsoid inside it holds about 12.6.
Worked examples
- Default: diameters 4 × 3 × 2 ft
- Half-widths: 2, 1.5, and 1 ft
- Volume: 4.18879 × 2 × 1.5 × 1 = 12.57 ft³
- Cubic yards: 12.566 ÷ 27 = 0.465 yd³
- Gallons: 12.566 × 7.48052 = 94.0 gal
- Liters: 94.0 × 3.78541 = 355.8 L
- Egg-shaped water tank: 8 × 8 × 4 ft
- Half-widths: 4, 4, and 2 ft
- Volume: 4.18879 × 4 × 4 × 2 = 134.04 ft³
- Gallons: 1,002.7 gal, or 3,795.6 L
A tank never fills to the brim, so its usable volume is somewhat less than this. Water weighs about 8.34 lb per gallon, so a full 1,002.7 gallon tank holds roughly 8,360 lb of water, which matters when you plan its base.
Ellipsoid volume reference
| Diameters (A × B × C) | Cubic feet | Cubic yards | Gallons |
|---|---|---|---|
| 2 × 2 × 2 ft | 4.19 | 0.155 | 31.3 |
| 4 × 3 × 2 ft | 12.57 | 0.465 | 94.0 |
| 6 × 4 × 3 ft | 37.70 | 1.396 | 282.0 |
| 8 × 8 × 4 ft | 134.04 | 4.964 | 1,002.7 |
| 10 × 6 × 6 ft | 188.50 | 6.981 | 1,410.0 |
How to measure an ellipsoid
- Use calipers or two boards. Hold a straight board against each side of the object and measure between them. That gives the true widest point.
- Measure at right angles. Length, width, and height should be perpendicular to one another.
- Convert inches to feet. The fields take feet. 30 inches is 2.5 ft.
- For a tank, measure inside if you can. Outside dimensions include wall thickness and overstate capacity.
- Take each width twice. Measure again a quarter turn away and average the two readings if they differ.
Where ellipsoid volume comes up
Egg-shaped and oval tanks show up in water storage, septic, and hot tubs. Ponds and basins dug with sloping sides are often close to half an ellipsoid. Rounded boulders, decorative concrete domes, and planters also fit the shape well enough for estimating.
The calculator gives cubic feet and gallons together. Cubic feet tell you how much concrete or soil fills the shape. Gallons tell you how much water it holds and how much treatment chemical to add. Liters are there for labels with metric doses.
Common mistakes
- Entering radii instead of diameters. The calculator halves your numbers. Entering 2 instead of 4 gives one-eighth of the volume if all three are halved.
- Using the ellipsoid for a cylinder with rounded ends. That is a capsule. Use the capsule volume calculator.
- Treating a dirt mound as a full ellipsoid. A pile sits on the ground like half a shape. Use the half-ellipsoid method in the FAQ, or the stockpile volume calculator.
- Mixing feet and inches between fields. All three diameters must be in feet. One field in inches makes the answer 12 times too large.
- Forgetting that small errors cube. A 10% error on all three diameters changes the volume by about 33%.
Related calculators
For a round ball, the sphere volume calculator needs only one diameter. For a dome with a round base, use the hemisphere volume calculator.
Frequently asked questions
What shapes count as an ellipsoid?
Any smooth, closed shape that looks like a stretched or squashed ball: an egg-shaped tank, a rugby ball, a rounded boulder, or a lens-shaped basin. If its widest measurements in three perpendicular directions differ, it is an ellipsoid rather than a sphere.
What if two of the diameters are equal?
Then it is a spheroid. Enter the same number twice. A spheroid 4 ft long and 2 ft across in both other directions holds 4/3 × π × 2 × 1 × 1 = 8.38 cu ft.
What if all three diameters are equal?
It is a sphere, and the formula becomes 4/3 × π × r³. Diameters of 2, 2, and 2 ft give 4.19 cu ft, the same answer as the sphere volume calculator.
How do I measure diameter A, B, and C on a real object?
Measure the full width at the widest point in three directions at right angles to each other: side to side, front to back, and top to bottom. The order does not matter, because the formula multiplies all three.
How do I get the volume of half an ellipsoid, like a dome?
Enter the dome's width and depth as diameters A and B, then enter twice its height as diameter C. That describes the full ellipsoid; divide the result by 2. A dome 6 ft wide, 4 ft deep, and 1.5 ft tall uses 6, 4, and 3, giving 37.70 ÷ 2 = 18.85 cu ft.
Estimates only. Verify quantities with your supplier before purchasing.