Spherical Cap (Partly Filled Sphere)
This is the chunk left when you slice a sphere with a plane. Multiply the depth squared by (3R − depth), then by π over three. It converts a level reading in a spherical tank into a volume.
Your numbers
Filled volume
11,762.1cm³
Litres
11.762L
Fill share
10.4%
Volume
113,097.3cm³
What it means
Filled to 12 in a sphere of radius 30 is 10.4% of the total. Half the height is exactly 50%, but below that it fills far less than it looks.
Formula
Filled volume = π × Fill height ² ÷ 3 × (3 × Radius − Fill height)
At half depth the volume is exactly half, but below that it drops away much faster than the level suggests, because the bottom is narrow.
What to enter
| Input | Default | Accepted range |
|---|---|---|
| Radius (cm)Centre to edge — half the diameter. | 30 | 0.01 and up |
| Fill height (cm)How deep the sphere is filled, measured from the bottom. | 12 | 0 and up |
Step by step
Quick reference table
Results when only Radius (cm) changes and everything else stays put.
| Radius (cm) | Filled volume (cm³) | Litres (L) | Fill share (%) |
|---|---|---|---|
| 15 | 4,976.3 | 4.976 | 35.2 |
| 22.5 | 8,369.2 | 8.369 | 17.54 |
| 30 | 11,762.1 | 11.762 | 10.4 |
| 45 | 18,548 | 18.548 | 4.86 |
| 60 | 25,333.8 | 25.334 | 2.8 |
What each result means
| Result | At default values |
|---|---|
| Filled volume (cm³)The volume held up to that depth. | 11,762.1 |
| Litres (L)Capacity in litres; one litre is 1,000 cm³. | 11.762 |
| Fill share (%)The filled share of the total volume. | 10.4 |
| Volume (cm³)The space a solid holds — length cubed. | 113,097.3 |
Common mistakes
At half depth the volume is exactly half, but below that it drops away much faster than the level suggests, because the bottom is narrow.
Glossary
- Radius
- Centre to edge — half the diameter.
- Fill height
- How deep the sphere is filled, measured from the bottom.
- Filled volume
- The volume held up to that depth.
- Litres
- Capacity in litres; one litre is 1,000 cm³.
- Fill share
- The filled share of the total volume.
- Volume
- The space a solid holds — length cubed.
Frequently asked questions
Q. How is Spherical Cap (Partly Filled Sphere) calculated?
Filled volume = π × Fill height ² ÷ 3 × (3 × Radius − Fill height) — This is the chunk left when you slice a sphere with a plane. Multiply the depth squared by (3R − depth), then by π over three. It converts a level reading in a spherical tank into a volume.
Q. Can you walk through an example?
With Radius 30cm, Fill height 12cm, the answer is Filled volume 11,762.1cm³.
Q. What do I need to enter?
Enter Radius, Fill height. The result recalculates as you type, and an empty box counts as zero.
Q. How much does the answer move if I change a number?
Changing only Radius (cm) moves the answer to Radius (cm) 15 → Filled volume (cm³) 4,976.3 and Radius (cm) 60 → Filled volume (cm³) 25,333.8. The table below lays out five steps.
Q. How are the numbers rounded?
Money is shown to the nearest whole unit, percentages to one decimal place and everything else to two. What you see is rounded; the calculation itself carries the unrounded value forward.
Q. Anything to watch out for?
At half depth the volume is exactly half, but below that it drops away much faster than the level suggests, because the bottom is narrow.
Related calculators
Keep your length units consistent across inputs — mixing centimetres and metres throws results far off.