A cone holds exactly one third of the volume of a cylinder with the same base and height.
How to use the Cone Calculator
- Base radius
- Height
- Want to work backwards? Type a value into Volume and Height is calculated for you.
Results update as you type, and every field accepts the units shown in its menu.
How it works
Multiply the base area by the height and divide by three. Pythagoras gives the slant height.
Inputs explained
| Field | What to enter |
|---|---|
| Base radius | Units: m, cm, mm, km, in, ft … |
| Height | Units: m, cm, mm, km, in, ft … |
What each result means
- Volume = pi×[Base radius]^2×[Height]÷3
- Slant height = sqrt([Base radius]^2 + [Height]^2)
- Lateral area = pi×[Base radius]×[Slant height]
- Total surface area = pi×[Base radius]×([Base radius] + [Slant height])
Example values
How the main result changes when Height changes and everything else stays at the example values above:
| Height (m) | Volume (m³) |
|---|---|
| 2 | 18.85 |
| 3 | 28.27 |
| 4 | 37.7 |
| 5 | 47.12 |
| 6 | 56.55 |
| 8 | 75.4 |
Formula
V = ⅓ π r² hSlant height = √(r² + h²)Worked example
Inputs — Base radius: 3 m; Height: 4 m.
Results — Volume = 37.7 m³; Slant height = 5 m; Lateral area = 47.12 m²; Total surface area = 75.4 m².
Frequently asked questions
Is this for a party hat?
The lateral area tells you how much paper you need.
What about a truncated cone?
Use the frustum formula: V = ⅓πh(R² + Rr + r²).
What formula does the Cone Calculator use?
V = ⅓ π r² h.
Can I work backwards from the result?
Yes. Type the result you want into Volume and the calculator finds the matching height.