Cone Layout Angle Calculator
Unrolled, the cone becomes a sector whose radius is the slant height and whose arc must equal the base circumference. Multiplying that ratio by 360° gives the angle to cut out.
Your numbers
Angle (°)
138.46°
Slant height
26cm
Lateral area
816.81cm²
Formula
Angle (°) = 360 × Radius ÷ √(Radius² + Height²)
Use it for party hats, funnels and conical roofs in paper or sheet metal. Add your own allowance for the glued or seamed overlap.
What to enter
| Input | Default | Accepted range |
|---|---|---|
| Radius (cm)Centre to edge — half the diameter. | 10 | 0 and up |
| Height (cm)The perpendicular height from the base — not the slanted side. | 24 | 0 and up |
Step by step
Quick reference table
Results when only Radius (cm) changes and everything else stays put.
| Radius (cm) | Angle (°) (°) | Slant height (cm) | Lateral area (cm²) |
|---|---|---|---|
| 5 | 73.42 | 24.515 | 385.09 |
| 7.5 | 107.38 | 25.145 | 592.46 |
| 10 | 138.46 | 26 | 816.81 |
| 15 | 190.8 | 28.302 | 1,333.7 |
| 20 | 230.47 | 31.241 | 1,962.93 |
What each result means
| Result | At default values |
|---|---|
| Angle (°) (°)An angle in degrees; a full turn is 360°. | 138.46 |
| Slant height (cm)The sloped length from apex to base edge — longer than the height. | 26 |
| Lateral area (cm²)The side surface only, without the bases — the size of a wraparound label. | 816.81 |
Common mistakes
Use it for party hats, funnels and conical roofs in paper or sheet metal. Add your own allowance for the glued or seamed overlap.
Glossary
- Radius
- Centre to edge — half the diameter.
- Height
- The perpendicular height from the base — not the slanted side.
- Angle (°)
- An angle in degrees; a full turn is 360°.
- 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 Cone Layout Angle Calculator calculated?
Angle (°) = 360 × Radius ÷ √(Radius² + Height²) — Unrolled, the cone becomes a sector whose radius is the slant height and whose arc must equal the base circumference. Multiplying that ratio by 360° gives the angle to cut out.
Q. Can you walk through an example?
With Radius 10cm, Height 24cm, the answer is Angle (°) 138.46°.
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) 5 → Angle (°) (°) 73.42 and Radius (cm) 20 → Angle (°) (°) 230.47. 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 party hats, funnels and conical roofs in paper or sheet metal. Add your own allowance for the glued or seamed overlap.
Related calculators
Keep your length units consistent across inputs — mixing centimetres and metres throws results far off.