Frustum Surface Area Calculator
The side is π times the sum of the two radii times the slant height. The catch is the slant: it is not the vertical height but the hypotenuse built from the height and the difference of the radii.
Your numbers
Surface area
1,628.86cm²
Lateral area
975.41cm²
Slant height
15.524cm
Formula
Surface area = π × (Radius + Top radius) × Slant height + πRadius² + πTop radius²
Use it for plant pots, buckets and cups when working out paint, film or wrap quantities.
What to enter
| Input | Default | Accepted range |
|---|---|---|
| Radius (cm)Centre to edge — half the diameter. | 12 | 0 and up |
| Top radius (cm)The radius of the top circle; differing from the bottom makes a frustum. | 8 | 0 and up |
| Height (cm)The perpendicular height from the base — not the slanted side. | 15 | 0 and up |
Step by step
Quick reference table
Results when only Radius (cm) changes and everything else stays put.
| Radius (cm) | Surface area (cm²) | Lateral area (cm²) | Slant height (cm) |
|---|---|---|---|
| 6 | 979.73 | 665.57 | 15.133 |
| 9 | 1,258.42 | 802.88 | 15.033 |
| 12 | 1,628.86 | 975.41 | 15.524 |
| 18 | 2,691.47 | 1,472.53 | 18.028 |
| 24 | 4,215.44 | 2,204.82 | 21.932 |
What each result means
| Result | At default values |
|---|---|
| Surface area (cm²)The total area of a solid’s outer skin. | 1,628.86 |
| Lateral area (cm²)The side surface only, without the bases — the size of a wraparound label. | 975.41 |
| Slant height (cm)The sloped length from apex to base edge — longer than the height. | 15.524 |
Common mistakes
Use it for plant pots, buckets and cups when working out paint, film or wrap quantities.
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.
- Surface area
- The total area of a solid’s outer skin.
- Lateral area
- The side surface only, without the bases — the size of a wraparound label.
- Slant height
- The sloped length from apex to base edge — longer than the height.
Frequently asked questions
Q. How is Frustum Surface Area Calculator calculated?
Surface area = π × (Radius + Top radius) × Slant height + πRadius² + πTop radius² — The side is π times the sum of the two radii times the slant height. The catch is the slant: it is not the vertical height but the hypotenuse built from the height and the difference of the radii.
Q. Can you walk through an example?
With Radius 12cm, Top radius 8cm, Height 15cm, the answer is Surface area 1,628.86cm².
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) 6 → Surface area (cm²) 979.73 and Radius (cm) 24 → Surface area (cm²) 4,215.44. 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?
Use it for plant pots, buckets and cups when working out paint, film or wrap quantities.
Related calculators
Keep your length units consistent across inputs — mixing centimetres and metres throws results far off.