Cone Volume Formula Calculator
Enter a radius or diameter and the perpendicular height.
Use the perpendicular height, not the slanted side.
Exact:
Use the cone volume formula with radius or diameter
The standard formula is V = πr²h/3. Square the base radius, multiply by the perpendicular height and π, then divide by 3. If the problem gives a diameter, divide it by 2 first—or select Diameter above and let the calculator show that step. Using the diameter as if it were the radius makes the answer four times too large.
Example: radius 5 cm and height 8 cm
Substitute the values: V = π × 5² × 8 ÷ 3 = 200π/3 cm³, which is approximately 209.4395102 cm³. The exact π form and decimal name the same volume; the decimal is rounded for display.
Perpendicular height, not slant height
The height h meets the circular base at a right angle. A slanted measurement along the cone's side is a different length and cannot be placed directly into the volume formula. This first version intentionally asks for perpendicular height rather than silently deriving it from other measurements.
Why the answer uses cubic units
Radius and height are lengths, but volume occupies three-dimensional space. A cone measured in centimeters therefore has an answer in cubic centimeters (cm³), not cm or cm². This calculator uses one shared length unit for both measurements so it never combines, for example, an inch radius with a centimeter height without warning.
Exact π and decimal limits
Plain positive decimals with up to six decimal places are converted to fractions before the π coefficient is simplified. The exact result does not replace π with 3.14. The approximate result uses JavaScript floating-point arithmetic and is rounded only when displayed; very small or large answers may use scientific notation. This page calculates right circular cone volume only, not surface area or a truncated cone.
Frequently asked questions
What is the cone volume formula?
For a cone with base radius r and perpendicular height h, V = πr²h/3. The result uses cubic units. If you know the diameter d instead, use V = πd²h/12 because the radius is d/2.
Can I enter the diameter instead of the radius?
Yes. Select Diameter and enter it directly. The result steps first divide the diameter by 2, then use that radius in the cone volume formula.
Is cone height the same as slant height?
No. Volume uses the perpendicular height from the center of the circular base to the tip. The slant height runs along the side and cannot replace h in this formula.
Why is the cone volume one third of a cylinder?
A cone and cylinder with the same circular base and perpendicular height have volumes πr²h/3 and πr²h. The matching cone therefore holds one third of the cylinder's volume.
Why does the answer include both π and a decimal?
The π form keeps the result exact for supported decimal inputs. The decimal multiplies that exact coefficient by the browser's value of π and is an approximation rounded only for display.
Which units can I use?
Choose millimeters, centimeters, meters, inches, feet, or yards. Radius or diameter and height must use the same selected length unit, and the answer is labeled in the matching cubic unit.