What this calculator does
The volume of a cone is exactly one third of the volume of a cylinder with the same base and height, a relationship that holds for any cone regardless of how tall or wide it is. It answers a simple, practical question: how much can this cone-shaped container or pile actually hold.
This calculator keeps that one question at the front, taking just a base radius and a height and returning the volume of a cone as the headline result, with the base area and litre capacity given underneath. For slant height and surface area as well, the full cone calculator covers that side of the same shape.
The formula
The cone volume formula is V = ⅓πr²h: the area of the circular base, πr², multiplied by the height, then divided by three. The one-third factor is what distinguishes a cone from a cylinder of the same base and height, which has no such reduction.
| Term | Meaning |
|---|---|
| V | Volume: the space enclosed inside the cone, ⅓πr²h. |
| r | Radius of the circular base. |
| h | Height, measured perpendicular from the base to the apex. |
The inputs explained
| Field | What to enter |
|---|---|
| Base radius | The radius of the circular base. |
| Height | The vertical height from the base to the apex, not the slant length along the side. |
When to use it
Sizing a funnel or hopper
A funnel, hopper or silo outlet is usually cone-shaped, so the volume of a cone from its base radius and height gives the capacity or the rate material drains at a known fill level.
Estimating a conical pile of loose material
Sand, gravel and grain heaped from a single point naturally settle into a rough cone shape, and the cone volume formula gives a reasonable estimate of the quantity from a measured base and height.
Working a cone volume formula problem
Given a base radius and height directly, this replaces the two-step process of finding the base area by hand before multiplying by the height and dividing by three.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How does cone volume change with radius?
A fixed height of 12, across a range of base radius values.
| Radius | Volume | Base area |
|---|---|---|
| 2 | 50.265 | 12.566 |
| 5 | 314.159 | 78.540 |
| 8 | 804.248 | 201.062 |
| 10 | 1,256.64 | 314.159 |
| 15 | 2,827.43 | 706.858 |
| 20 | 5,026.55 | 1,256.64 |
How does cone volume change with height?
A fixed radius of 5, across a range of height values.
Questions
What is the volume of a cone formula?
V = ⅓πr²h, the area of the circular base multiplied by the height, divided by three. It applies to any right circular cone, from an ice-cream cone to a hopper.
Why is a cone volume formula one third of a cylinder’s?
A cone tapers to a point while a cylinder keeps its full cross-section all the way up, and the calculus behind the shapes works out to exactly one third for any cone sharing a cylinder’s base and height.
Does the cone volume calculator need the slant height or the vertical height?
The vertical height, measured straight up from the base to the apex. The slant height, measured along the sloped side, is longer and would overstate the volume if used by mistake.
How do you find cone volume in litres?
Measure the radius and height in centimetres, calculate V = ⅓πr²h to get cubic centimetres, then divide by 1,000, since 1 litre equals 1,000 cubic centimetres.
For slant height and total surface area as well as volume, see the full cone calculator. For the volume of a sphere instead, see the sphere volume calculator.