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Cone Calculator
Last updated: May 31, 2026
Written by Blake Boege
A cone calculator is a 3D geometry tool that computes all spatial measurements of a right circular cone given any two dimensions. By combining the Pythagorean relationship between radius, height, and slant height with geometric constants, it solves for missing dimensions. It calculates base area, lateral surface area, total surface area, and internal volume.
Solve for a cone's height, slant height, base area, lateral area, total surface area, and volume from any two inputs.
Quick Answer
Solve right circular cone dimensions and volumes. Input any two parameters (radius, height, slant height) to calculate volume and surface area.
Given Information
e.g. 3
e.g. 4
Cone Volume (V)
37.6991
This calculator solves standard right circular cones, where the apex aligns vertically above the center of the base.
Examples
Radius = 3m, Height = 4m
Slant = 5m, Volume ≈ 37.70 m³, Surface Area ≈ 75.40 m²
Radius = 5m, Slant = 13m
Height = 12m, Volume ≈ 314.16 m³, Surface Area ≈ 282.74 m²
How it works
Enter any two of radius, height, or slant height. The calculator solves the third dimension using the Pythagorean theorem, then computes volumes and surface areas.
Pythagorean link · r² + h² = l²
Volume · V = 1/3 × π × r² × h
Right circular cone formulas
Right circular cones can be fully solved using the relationships between the radius (r), perpendicular height (h), and slant height (l):
- Slant Height (l): l = √(r² + h²)
- Volume (V): V = 1/3 × π × r² × h
- Lateral Surface Area (L): L = π × r × l
- Base Surface Area (B): B = π × r²
- Total Surface Area (SA): SA = B + L = π × r × (r + l)
Related 3D geometry tools
Check out other spatial solid calculation tools:
- Cone Volume Calculator — specialized tool for cone capacity.
- Volume Calculator — calculate volume of cylinders, spheres, boxes, and pyramids.
- Surface Area Calculator — calculate the total surface area of standard geometric solids.
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Frequently asked questions
A cone is a three-dimensional geometric shape that tapers smoothly from a flat circular base to a single point called the apex or vertex.
The volume formula is: V = 1/3 × π × r² × h, where r is the base radius and h is the perpendicular height. It is exactly one-third of the volume of a cylinder with the same radius and height.
The radius, height, and slant height of a right cone form a right-angled triangle. By the Pythagorean theorem, the slant height is: l = √(r² + h²).
Lateral surface area is the area of the curved slanted side only (L = π × r × l). Total surface area is the lateral area plus the area of the circular base (SA = πrl + πr²).
Yes. If you know the radius (r) and slant height (l), you can find the height using the Pythagorean theorem: h = √(l² − r²), and then calculate the volume and areas.
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