Cone calculator
This cone calculator works from two measures: radius and height, radius and slant height, or height and slant height. With r = 3 and h = 4 you get s = 5, a volume of 37.70 and a surface area of 75.40, with the full steps.
Example: Known values: Radius r and Height h · Radius r 3 · Height h 4 → Result: Volume V = 37.69911 · Surface area S = 75.39822. Source: Wikipedia – Kegel (Geometrie). Updated: .
How it is calculated
A right circular cone is defined by its radius r and height h. The slant height s (the distance from the apex to the edge of the base) follows from the Pythagorean theorem: s = √(r² + h²). If you know s instead, the tool recovers the missing measure.
The formulas
- Base area: B = π · r²
- Lateral surface area: L = π · r · s
- Total surface area: S = B + L = π · r · (r + s)
- Volume: V = 1/3 · B · h = 1/3 · π · r² · h
- Apex angle: 2 · arctan(r ÷ h)
How to use it
Choose which two measures you know and enter the values. Example: r = 3 and h = 4 give s = 5, B = 28.27, L = 47.12, S = 75.40 and V = 37.70. A cone holds exactly one third of the cylinder with the same base and height. The unit is up to you; areas are in its square, the volume in its cube.
Frequently asked questions
How do you calculate the volume of a cone?
V = 1/3 · π · r² · h. For r = 3 and h = 4 that is 1/3 · π · 9 · 4 = 37.70, a third of the matching cylinder.
How do you calculate the lateral area of a cone?
L = π · r · s with the slant height s = √(r² + h²). For r = 3 and s = 5 it is 47.12.
How do you find the height from radius and slant height?
h = √(s² − r²). The tool uses it when you choose radius and slant height; the slant height must be longer than the radius.
What is the slant height of a cone?
The distance from the apex to a point on the edge of the base. It is the hypotenuse of the right triangle formed by radius and height.
How large is the apex angle?
It equals 2 · arctan(r ÷ h). With r = 3 and h = 4 that is about 73.74°.
Sources and legal basis
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