Cone Surface Area & Slant
The slant height runs from apex to base edge and is the hypotenuse of radius and height. The lateral area is πrl; add the base circle for the total. This is what you need to cut a paper cone.
Your numbers
Surface area
282.74cm²
Slant height
13cm
Lateral area
204.2cm²
Volume
314.16cm³
Formula
Slant height = √(Radius ² + Height ²), Surface area = π × Radius × (Radius + Slant height)
Confusing height with slant height throws the lateral area badly off. The slant is always longer.
What to enter
| Input | Default | Accepted range |
|---|---|---|
| Radius (cm)Centre to edge — half the diameter. | 5 | 0 and up |
| Height (cm)The perpendicular height from the base — not the slanted side. | 12 | 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) | Slant height (cm) | Lateral area (cm²) |
|---|---|---|---|
| 2.5 | 115.91 | 12.258 | 96.27 |
| 3.75 | 192.29 | 12.572 | 148.11 |
| 5 | 282.74 | 13 | 204.2 |
| 7.5 | 510.14 | 14.151 | 333.42 |
| 10 | 804.89 | 15.62 | 490.73 |
What each result means
| Result | At default values |
|---|---|
| Surface area (cm²)The total area of a solid’s outer skin. | 282.74 |
| Slant height (cm)The sloped length from apex to base edge — longer than the height. | 13 |
| Lateral area (cm²)The side surface only, without the bases — the size of a wraparound label. | 204.2 |
| Volume (cm³)The space a solid holds — length cubed. | 314.16 |
Common mistakes
Confusing height with slant height throws the lateral area badly off. The slant is always longer.
Glossary
- Radius
- Centre to edge — half the diameter.
- Height
- The perpendicular height from the base — not the slanted side.
- Surface area
- The total area of a solid’s outer skin.
- 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.
- Volume
- The space a solid holds — length cubed.
Frequently asked questions
Q. How is Cone Surface Area & Slant calculated?
Slant height = √(Radius ² + Height ²), Surface area = π × Radius × (Radius + Slant height) — The slant height runs from apex to base edge and is the hypotenuse of radius and height. The lateral area is πrl; add the base circle for the total. This is what you need to cut a paper cone.
Q. Can you walk through an example?
With Radius 5cm, Height 12cm, the answer is Surface area 282.74cm².
Q. What do I need to enter?
Enter 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) 2.5 → Surface area (cm²) 115.91 and Radius (cm) 10 → Surface area (cm²) 804.89. 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?
Confusing height with slant height throws the lateral area badly off. The slant is always longer.
Related calculators
Keep your length units consistent across inputs — mixing centimetres and metres throws results far off.