# Cone Volume Calculator

Table of contents

Cone volume formulaHow to find the volume of a coneTruncated cone volume (volume of frustum)Oblique cone volumeFAQsThis cone volume calculator can help in solving your math problems or can answer your weird day-to-day questions. How much ice cream fits into my cone? How much cream can I put into the pastry bag? Or what's the volume of my conical champagne glass? If these are the questions that you would like answered, keep reading!

## Cone volume formula

A cone is a solid that has a circular base and a single vertex. To calculate its volume, you need to multiply the base area (area of a circle: π × r²) by height and by 1/3:

`volume = (1/3) × π × r² × h`

A cone with a polygonal base is called a pyramid – see pyramid volume calculator.

## How to find the volume of a cone

Let's calculate how much water fits into the conical part of the funnel.

**Determine the height of the cone**(can be found using the slant height calculator). For our funnel, it's**4 in**.**Enter the base radius**. It may be equal to**3 in**.- The calculator now displays the
**volume of the cone**– in our case, it's**37.7 cu in**.

Remember that you can change the units to meet your exact needs – click on the unit and select it from the list. Check out our volume converter tool if you need a simple volume unit conversion.

## Truncated cone volume (volume of frustum)

A truncated cone is the cone with the top cut off, with a cut perpendicular to the height. You can calculate frustum volume by subtracting the smaller cone volume (the cut one) from the bigger cone volume (base one) or use the formula:

`volume = (1/3) × π × depth × (r² + r × R + R²)`

, where`R`

is the radius of the base of a cone and`r`

of the top surface radius.

An example of the volume of a truncated cone calculation can be found in our potting soil calculator, as the standard flower pot is a frustum of a cone.

## Oblique cone volume

An oblique cone is a cone with an apex that is not aligned above the center of the base. It "*leans*" to one side, similar to the oblique cylinder. The cone volume formula of the oblique cone is the same as for the right one.

### How do I calculate a cone volume by hand?

To calculate the volume of a cone, follow these instructions:

- Find the cone's
**base area**`a`

. If unknown, determine the cone's**base radius**`r`

. - Find the cone's
**height**`h`

. - Apply the
**cone volume formula**:`volume = (1/3) × a × h`

if you know the base area, or`volume = (1/3) × π × r² × h`

otherwise. **Congratulations**, you've successfully computed the volume of your cone!

### What is the relationship between the volume of a cone and a cylinder?

If a cone and cylinder have the same height and base radius, then the volume of a cone is equal to one-third of that of the cylinder. That is, you would need the contents of three cones to fill up this cylinder. The same relationship holds for the volume of a pyramid and that of a prism (given that they have the same base area and height).

### What is the volume of a typical ice cream cone?

The size of an ice cream waffle varies quite widely, yet there are a few sizes that are typical:

Radius | Height | Volume |
---|---|---|

1 in | 6 in | 6.3 cu in |

3 cm | 11 cm | 103.7 cm³ |

2.5 cm | 11.5 cm | 75.3 cm³ |

1 7/8 in | 4 5/8 in | 17 cu in |

1 3/16 in | 6 in | 8.9 cu in |

### What is the volume of cone with radius one and height three?

Recall that the cone volume formula reads:

`volume = (1/3) × π × r² × h`

So in our case, we have the following:

`volume = (1/3) × π × 1² × 3`

So the volume of our cone is exactly `π`

! As we all know, this can be approximated as `volume ≈ 3.14159`

.