Diameter of a Cone Calculator
Enter the base radius and height of a right circular cone to find its diameter, slant height, volume, and both surface areas instantly.
d = 2r — diameter of the circular base
Cone
- 1
Square the radius
5 × 5 = 25 - 2
Square the height
12 × 12 = 144 - 3
Slant height = √(r² + h²)
√(25 + 144) = 13Hypotenuse of the right triangle formed by radius and perpendicular height. - 4
Diameter = 2 × r
2 × 5 = 10
How does this calculator work?
The base diameter of a cone is d = 2r (twice the base radius). From radius r and height h you also get slant height l = √(r²+h²), volume V = πr²h/3, lateral surface area πrl, and total surface area πr(r+l). Enter r and h to compute all of these at once.
Formula
How this is calculated
A right circular cone has a circular base of radius r and an apex directly above the centre at height h. The base diameter is simply d = 2r. The slant height l — the distance from the apex to any point on the circumference of the base — follows from the Pythagorean theorem: l = √(r² + h²), where r and h are the two legs of the right triangle formed by the radius, height, and slant.
The volume is one-third of the base area times the height: V = (1/3)πr²h. This equals exactly one-third the volume of the cylinder with the same base and height, a classical result first proved by Eudoxus. The lateral (curved) surface area is πrl, and adding the base circle (πr²) gives the total surface area πr(r + l).
All formulas assume a right circular cone — the apex is directly above the centre of the base. For an oblique cone, slant height varies around the circumference and these formulas no longer apply. Inputs must be positive real numbers; there are no approximations beyond floating-point arithmetic.
Frequently asked questions
Rearrange the volume formula V = (1/3)πr²h to get r = √(3V / (πh)), then d = 2r. Similarly, if you know the slant height l and the height h, you can use r = √(l² − h²) and d = 2r. These are algebraic inversions of the standard formulas.
The slant height l is the distance from the apex of the cone to any point on the edge of the circular base, measured along the surface. It equals √(r² + h²) — the hypotenuse of the right triangle formed by the radius and the perpendicular height.
This is a classical result from solid geometry: three identical cones fit inside one cylinder with the same base and height. It was proved rigorously by Eudoxus of Cnidus in the 4th century BC using the method of exhaustion (the ancient precursor to integration). The relationship V_cone = (1/3)V_cylinder holds for any right circular cone.
Also known as
TG we-Calculate Editorial Team. (2026). Diameter of a Cone Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/diameter-of-cone-calculator
TG we-Calculate Editorial Team. "Diameter of a Cone Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/diameter-of-cone-calculator.
TG we-Calculate Editorial Team, "Diameter of a Cone Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/diameter-of-cone-calculator
@misc{wecalculate_diameter_of_cone_calculator, title = {Diameter of a Cone Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/diameter-of-cone-calculator}}, year = {2026}, note = {TG we-Calculate} }
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