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Calculator Answers

Cone Calculator

Blake Boege
Written by Blake Boege · Founder, Calculator Answers

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.

See also: Cone Volume Calculator and Volume Calculator – Rectangular Prism, Cylinder, Sphere & Cone.

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 Solved Dimensions

Cone Volume (V)

37.6991

Slant Height (l)5
Height (h)4
Radius (r)3
Total Surface Area (SA)75.3982
Lateral Area (L)47.1239
Base Area (B)28.2743
Step-by-Step Solutions1. Solve dimensions using Pythagorean Theorem (r² + h² = l²): Radius (r) = 3 Height (h) = 4 Slant Height (l) = 5 2. Calculate Base Area (B): B = π × r² = π × 3² ≈ 28.2743 3. Calculate Lateral Surface Area (L): L = π × r × l = π × 3 × 5 ≈ 47.1239 4. Calculate Total Surface Area (SA): SA = B + L ≈ 75.3982 5. Calculate Volume (V): V = 1/3 × π × r² × h = 1/3 × π × 3² × 4 ≈ 37.6991

This calculator solves standard right circular cones, where the apex aligns vertically above the center of the base.

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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:

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More tools from Education

Cone Volume CalculatorCalculate the volume of a cone using the formula V = (1/3)πr²h with radius and height inputs.Volume Calculator – Rectangular Prism, Cylinder, Sphere & ConeCalculate the volume of common 3D shapes including rectangular prism volume, cylinder volume, sphere, cone, and pyramid. Round shapes accept a radius or a diameter. Includes formulas and cubic unit conversions.

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.