Education
Cone Volume Calculator
Last updated: May 31, 2026
Written by Blake Boege
A cone volume calculator is a geometry tool that computes the 3D space occupied by a cone. It uses the formula V = (1/3)πr²h, requiring the radius of the circular base and the perpendicular height. The resulting volume is expressed in cubic units such as cubic inches, cubic feet, or cubic centimeters, with conversions between them.
Compute the volume of a cone. Enter the base radius and height to find the three-dimensional space inside a cone in cubic units.
Quick Answer
Find the volume of a cone. Input the radius (or diameter) of the base and the vertical height to calculate volume in cubic units.
Shape
Measurement unit
Switch the shape to update the inputs. All dimensions use the same unit; results show the equivalent volume in cubic feet and cubic yards.
Volume
480 ft³
V = L × W × H
Volume of a rectangular prism with length 10 feet, width 8 feet, and height 6 feet is 480 ft³.
Examples
Radius = 3 ft, Height = 9 ft
Volume ≈ 84.82 cubic feet
Radius = 5 in, Height = 12 in
Volume ≈ 314.16 cubic inches
How it works
Volume of a Cone Formula
The volume of a cone is calculated using the base radius and vertical height:
V = (1/3) × π × r² × h
Where:
- r is the radius of the circular base (half of the diameter).
- h is the vertical height of the cone.
- π is Pi (approximately 3.14159).
To calculate the volume of other 3D shapes (such as spheres, cylinders, cubes, or pyramids), check out our comprehensive volume calculator or see our specialized pool volume calculator for swimming pool estimates.
Cone Volume Calculation Example
Suppose you want to find the volume of a cone with a base radius of 4 cm and a height of 9 cm:
- Square the radius: r² = 4 × 4 = 16 cm²
- Multiply by height: 16 × 9 = 144
- Multiply by π (pi): 144 × 3.14159 ≈ 452.39
- Divide by 3 (or multiply by 1/3): 452.39 ÷ 3 ≈ 150.80 cm³
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Frequently asked questions
The formula for the volume of a cone is: V = (1/3) × π × r² × h, where 'r' is the radius of the circular base, 'h' is the height of the cone (measured vertically from base to tip), and π (pi) is approximately 3.14159.
A cone has exactly one-third of the volume of a cylinder with the same base radius and height. If you were to fill a cone with water and pour it into a cylinder of equal dimensions, it would take exactly three full cones to fill the cylinder.
Vertical height (h) is the straight line distance from the center of the base to the top point (apex). Slant height (s) is the distance from any point on the base circle's edge to the apex. For volume calculations, always use the vertical height. If you only know the slant height and base radius, you can find the vertical height using the Pythagorean theorem: h = √(s² − r²).
Since the radius is half of the diameter (r = d ÷ 2), first divide the diameter by 2, then use the standard cone volume formula: V = (1/3) × π × (d/2)² × h.
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