Cone Calculator
Enter a radius and height below to instantly get volume, surface area, and slant height.
Cone Formulas
Volume = (1/3)πr²h. Slant height = √(r² + h²). Surface area = πr(r + slant height).
Worked example
A cone with radius 3 and height 4.
Slant height = √(3² + 4²) = √25 = 5
Volume = (1/3) × π × 9 × 4 = 12π ≈ 37.70
Surface area = π × 3 × (3 + 5) = 24π ≈ 75.40
A second example, with radius 5 and height 12.
Slant height = √(5² + 12²) = √169 = 13
Volume = (1/3) × π × 25 × 12 = 100π ≈ 314.16
Surface area = π × 5 × (5 + 13) = 90π ≈ 282.74
Keep going
- A cone holds exactly a third of the volume of a cylinder with the same base and height; the cylinder calculator gives that full comparison figure. Cylinder Calculator
Frequently Asked Questions
What is the formula for the volume of a cone?
Volume = (1/3) × π × r² × h — exactly one third the volume of a cylinder with the same radius and height.
What is slant height, and how is it different from height?
Height is the straight vertical distance from the base to the tip. Slant height is the distance along the cone's outer surface from the edge of the base to the tip, found with the Pythagorean theorem: slant height = √(r² + h²).
What is the formula for the surface area of a cone?
Surface area = πr(r + l), where l is the slant height — this adds the circular base (πr²) to the curved lateral surface (πrl).
Can you use slant height instead of height in the volume formula?
No — volume always uses the perpendicular height (h), not the slant height (l). Slant height is the hypotenuse of the right triangle formed by the radius and the height, so it's always the longer of the two. Swapping it in for h overstates the volume.
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