Right Circular Cone Calculator — Volume & Surface Area
Enter the base radius and perpendicular height of a right circular cone to find its volume, slant height, lateral and total surface area, and base circumference instantly.
units
units
V = ⅓ × π × r² × h
- 1
Slant height l = √(r² + h²)
√(5² + 12²) = 13 - 2
Base area = π × r²
π × 5² = 78.539816 - 3
Volume = ⅓ × base area × h
⅓ × 78.539816 × 12 = 314.1593A cone's volume is exactly one third of the cylinder with the same base and height.
How does this calculator work?
For a right circular cone: slant height l = √(r²+h²), Volume = ⅓πr²h, Lateral SA = πrl, Total SA = πr(r+l). Enter base radius and height in any consistent length unit — volume comes out in that unit cubed, area in that unit squared.
Formula
How this is calculated
A right circular cone has a circular base and an apex located directly above the centre of that base. Two positive measurements fully define it: the base radius r and the perpendicular height h from the base centre to the apex.
The slant height l is the straight-line distance from the apex to any point on the base rim: l = √(r² + h²), by Pythagoras applied to the right triangle formed by r, h, and l. Volume is exactly one third of the volume of a cylinder with the same radius and height: V = ⅓πr²h. The factor of ⅓ arises from integration of circular cross-sections — or equivalently, three cones of the same base and height fill one cylinder. The lateral (curved) surface area is found by unrolling the cone into a flat sector of radius l and arc 2πr, giving area πrl. Adding the circular base πr² yields the total surface area πr(r+l).
All formulas assume a perfect right circular cone — the apex is exactly over the centre, the base is a flat circle, and every input is a positive real number. Volume is in the cube of the length unit and area is in the square of that unit. No approximations are used; π is taken to full machine precision.
Frequently asked questions
The slant height l is the distance from the apex to any point on the base rim, measured along the surface. Because the apex lies directly above the centre, the radius r, height h and slant height l form a right triangle, so l = √(r² + h²).
Three identical cones — same base radius and height — fit exactly inside one cylinder. This is proved formally by integrating the area of circular cross-sections along the height axis, giving V = ⅓πr²h.
Cutting the cone along a slant line and unrolling it produces a flat circular sector with radius l and arc length 2πr. The area of that sector is ½ × l × 2πr = πrl.
Also known as
TG we-Calculate Editorial Team. (2026). Right Circular Cone Calculator — Volume & Surface Area [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/right-circular-cone-calculator
TG we-Calculate Editorial Team. "Right Circular Cone Calculator — Volume & Surface Area." TG we-Calculate. 2026. https://we-calculate.com/calculator/right-circular-cone-calculator.
TG we-Calculate Editorial Team, "Right Circular Cone Calculator — Volume & Surface Area," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/right-circular-cone-calculator
@misc{wecalculate_right_circular_cone_calculator, title = {Right Circular Cone Calculator — Volume & Surface Area}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/right-circular-cone-calculator}}, year = {2026}, note = {TG we-Calculate} }
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