Cone Volume Calculator
Enter a radius and height to calculate cone volume instantly.
How to use this cone volume calculator
- Enter the radius
Type the cone's base radius into the Radius field.
- Enter the height
Type the perpendicular height of the cone into the Height field using the same unit.
- Read the volume
The calculator returns the cone volume in cubic units.
- Check the slant height
Review the Slant height if you need the length along the cone's outer surface.
- Note the surface area
Use the Surface area output for material or coverage estimates.
How this cone volume calculator works
This calculator finds cone volume by taking the cylinder-style base area and scaling it by one-third of the height. It also returns the slant height and total surface area because those are the next most common values needed in geometry, manufacturing, and fabrication work.
volume = (πr²h) ÷ 3 If the radius is 4 and the height is 9, the volume is (π × 16 × 9) ÷ 3 = 150.80.
If the radius is 6 and the height is 12, the volume is (π × 36 × 12) ÷ 3 = 452.39.
If the radius is 3 and the height is 5, the volume is (π × 9 × 5) ÷ 3 = 47.12.
- ✓ The cone has a circular base.
- ✓ Height is measured perpendicular to the base.
- ✓ Radius and height are entered in the same unit.
- Slant height is not the same as vertical height.
- Surface area includes the circular base plus the curved side area.
- Cones show up in funnels, hoppers, piles, and packaging shapes.
- Solid geometry formulas for cones
What is cone volume?
Cone volume measures the space enclosed by a circular base that tapers to a single point called the apex. The formula V = (πr²h) ÷ 3 is derived from the fact that a cone is exactly one-third the volume of a cylinder with the same base and height. This one-third factor was first proved by Eudoxus and later formalized by Archimedes. Intuitively, if you filled a cone with water and poured it into a matching cylinder, you would need to repeat the pour three times to fill the cylinder completely. This relationship makes cones useful in engineering contexts where a tapered shape is needed to direct flow, reduce weight, or distribute force gradually.
Where cones appear in real life
Cones and cone-like shapes are everywhere in practical applications. Funnels, hoppers, and grain silos often have conical sections to guide material toward an outlet. Traffic cones, party hats, and ice cream cones are everyday examples. In construction, conical piles of sand, gravel, or soil form naturally when material is dumped from a single point, and estimating the volume of those piles is a common surveying task. Rocket nose cones use the shape for aerodynamic efficiency. Speaker cones convert electrical signals into sound by vibrating a conical diaphragm. Understanding cone volume helps in all of these scenarios, whether you are sizing a hopper, estimating a stockpile, or solving a geometry problem.
Cone volume calculator FAQs
Why is cone volume divided by 3?
A cone with the same base and height as a cylinder occupies one-third of that cylinder's volume.
What is slant height used for?
Slant height is useful when you need the side length of the cone surface, such as in material cutting or pattern layout.
Can I use diameter instead of radius?
Yes, but divide the diameter by 2 before entering it.