Cone Volume Calculator
Find the volume of a cone from its radius and height.
Results update as you type.
How it works
A cone is a three-dimensional shape with a circular base that narrows smoothly to a single point called the apex. Ice cream cones, funnels, party hats, and piles of sand or gravel all take this form, so finding a cone's volume is useful in cooking, manufacturing, and construction as well as in the classroom. This cone volume calculator takes two inputs, the radius of the circular base and the perpendicular height from the base to the apex, and returns the volume, the amount of space the cone encloses. The formula is one-third of pi times the radius squared times the height, and the crucial detail is that factor of one-third: a cone holds exactly a third as much as a cylinder with the same base and height. This is a result you can demonstrate by filling a cone with water and pouring it into a matching cylinder, which takes three cones to fill. For a cone with a base radius of 3 units and a height of 4 units, the volume is about 37.70 cubic units. Students studying solid geometry, engineers designing hoppers, and anyone estimating the contents of a conical pile use a cone volume calculator to apply the formula quickly and correctly.
volume = 1⁄3 × π × r² × h
A cone's volume is one-third of pi times the radius squared times the height. The factor of one-third appears because a cone occupies exactly a third of the cylinder that shares its base radius and height, a fact proved by integration or by the classic experiment of pouring water from a cone into a matching cylinder three times to fill it. The base area, pi times the radius squared, is multiplied by the height and then divided by three.
Source:Euclidean geometry
We review all our tools from time to time to ensure accuracy.
Worked example
How to use this calculator
- 1
Enter your values
Enter base radius and height.
- 2
Adjust the options
Fine-tune any options to match your situation.
- 3
Read your result
Volume updates instantly as you type — no button to press.
Frequently asked questions
What is the formula for the volume of a cone?
The volume of a cone is one-third times pi times the radius of the base squared times the height. In symbols that is one over three times pi times r squared times h. The height must be the perpendicular distance from the base to the apex, not the slanted side. The calculator uses this formula with the built-in precise value of pi to return an accurate volume from your two inputs.
Why is there a one-third in the formula?
The one-third reflects that a cone holds exactly a third of the volume of a cylinder sharing the same base radius and height. You can see this by pouring water: it takes three full cones to fill the matching cylinder. Mathematically the factor comes from integrating the shrinking circular cross-sections from the wide base up to the single point at the apex, which averages out to a third of the full cylinder.
What is the difference between height and slant height?
The height in this formula is the vertical distance straight up from the centre of the base to the apex. The slant height is the distance measured along the sloping outer surface from the edge of the base to the apex, which is always longer. Use the perpendicular height here. If you only know the slant height and radius, find the height with the Pythagorean theorem first.
How does a cone compare to a cylinder and sphere?
For the same radius and height, a cone holds one-third of the matching cylinder's volume. A hemisphere, a cylinder, and a cone with equal radii and heights relate in a neat ratio that students often learn together. The shared factor of pi times the radius squared appears in each, with the cone scaled by one-third, making the trio a memorable set of solid-geometry results.
Can I use this for a conical pile of material?
Yes. A heap of sand, gravel, or grain settles into an approximate cone, so measuring the radius of its circular base and its peak height lets you estimate the volume with this calculator. The estimate assumes a reasonably regular cone shape. For rough stockpiles the result is an approximation, but it is often close enough for ordering materials or estimating quantities on site.