Frustum Volume (Cup Shape)
Takeaway cups, plant pots and buckets are all frustums. Add the squares of both radii and their product, then multiply by height and π and divide by three. Equal radii collapse it to the cylinder formula.
Your numbers
Volume
1,114.22cm³
Litres
1.114L
Slant height
14.142cm
Lateral area
444.29cm²
Formula
Volume = π × Height ÷ 3 × (Radius ² + Radius × Top radius + Top radius ²)
A cup’s stated capacity is not filled to the rim. Usable volume normally stops 1–2 cm below it.
What to enter
| Input | Default | Accepted range |
|---|---|---|
| Radius (cm)Centre to edge — half the diameter. | 4 | 0 and up |
| Top radius (cm)The radius of the top circle; differing from the bottom makes a frustum. | 6 | 0 and up |
| Height (cm)The perpendicular height from the base — not the slanted side. | 14 | 0 and up |
Step by step
Quick reference table
Results when only Radius (cm) changes and everything else stays put.
| Radius (cm) | Volume (cm³) | Litres (L) | Slant height (cm) |
|---|---|---|---|
| 2 | 762.36 | 0.762 | 14.56 |
| 3 | 923.63 | 0.924 | 14.318 |
| 4 | 1,114.22 | 1.114 | 14.142 |
| 6 | 1,583.36 | 1.583 | 14 |
| 8 | 2,169.79 | 2.17 | 14.142 |
What each result means
| Result | At default values |
|---|---|
| Volume (cm³)The space a solid holds — length cubed. | 1,114.22 |
| Litres (L)Capacity in litres; one litre is 1,000 cm³. | 1.114 |
| Slant height (cm)The sloped length from apex to base edge — longer than the height. | 14.142 |
| Lateral area (cm²)The side surface only, without the bases — the size of a wraparound label. | 444.29 |
Common mistakes
A cup’s stated capacity is not filled to the rim. Usable volume normally stops 1–2 cm below it.
Glossary
- Radius
- Centre to edge — half the diameter.
- Top radius
- The radius of the top circle; differing from the bottom makes a frustum.
- Height
- The perpendicular height from the base — not the slanted side.
- Volume
- The space a solid holds — length cubed.
- Litres
- Capacity in litres; one litre is 1,000 cm³.
- Slant height
- The sloped length from apex to base edge — longer than the height.
- Lateral area
- The side surface only, without the bases — the size of a wraparound label.
Frequently asked questions
Q. How is Frustum Volume (Cup Shape) calculated?
Volume = π × Height ÷ 3 × (Radius ² + Radius × Top radius + Top radius ²) — Takeaway cups, plant pots and buckets are all frustums. Add the squares of both radii and their product, then multiply by height and π and divide by three. Equal radii collapse it to the cylinder formula.
Q. Can you walk through an example?
With Radius 4cm, Top radius 6cm, Height 14cm, the answer is Volume 1,114.22cm³.
Q. What do I need to enter?
Enter Radius, Top radius, 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) 2 → Volume (cm³) 762.36 and Radius (cm) 8 → Volume (cm³) 2,169.79. 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?
A cup’s stated capacity is not filled to the rim. Usable volume normally stops 1–2 cm below it.
Related calculators
Keep your length units consistent across inputs — mixing centimetres and metres throws results far off.