A cone volume calculator determines the space inside a cone — a shape with a circular base tapering to a point (apex). Enter the base radius and height for instant results.
A cone is a 3D shape with a circular base that narrows smoothly to a single point called the apex or vertex. The straight line from the apex to the center of the base is the height (h). The slant height is the distance along the surface from the apex to the base edge.
A cone's volume is exactly one-third of a cylinder with the same base radius and height. This relationship was proven by Archimedes.
Cone volume = (1/3) × π × radius² × height (V = (1/3)πr²h).
Example: A cone with radius 4 cm and height 9 cm:
V = (1/3) × π × 16 × 9 = 48π = 150.8 cm³ = 0.151 L = 5.1 fl oz.
Radius 2.5 cm, height 12 cm: V = (1/3)π×6.25×12 = 78.54 cm³ = 0.079 L.
Base radius 14 cm, height 72 cm: V = (1/3)π×196×72 = 14,779 cm³ = 14.78 L.
Radius 8 cm, height 20 cm: V = (1/3)π×64×20 = 1,340.4 cm³ = 1.34 L.
Base radius 2 m, height 1.5 m: V = (1/3)π×4×1.5 = 6.28 m³ of sand.
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Answers to common questions about the cone volume calculator.
V = (1/3)πr²h where r = base radius and h = perpendicular height. The 1/3 factor means a cone is exactly one-third the volume of a cylinder with the same base and height.
Divide the diameter by 2 to get radius, then use V = (1/3)πr²h. A cone with diameter 10 cm and height 15 cm: r = 5, V = (1/3)π×25×15 = 392.7 cm³.
s = √(r² + h²) using the Pythagorean theorem. For r=3, h=4: s = √(9+16) = 5. Slant height is used for lateral surface area = πrs.
A cone and cylinder with the same base and height: cone volume = ⅓ × cylinder volume. You can fit exactly 3 cones of water into the equivalent cylinder.
Use the frustum formula: V = (πh/3)(r₁² + r₂² + r₁r₂) where r₁ and r₂ are the top and bottom radii. This accounts for the removed tip.