Cone Volume Calculator

Q: 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 .

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Hanna Pamuła, PhD

Hanna PamułaPhD

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Hanna (Hania) Pamuła holds a Ph.D. in Bioacoustics / Mechanical Engineering, obtained at AGH University of Science and Technology. She has participated in research work in labs in France and the UK and presented papers at several international conferences. Hania has a penchant for photography and graphic design. When not in the office, she’s probably traveling, hiking, or out in the field, watching birds and recording their calls. See full profile

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Bogna Szyk, Jack Bowater, and Adena Benn

Adena Benn

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Adena Benn is a Guyanese teacher with a degree in computer science who is always reading and learning. She loves problem-solving, everything tech, and working with teenagers. She has a passion for education and is especially interested in how children learn and the teaching methods that best suit their learning styles. She grew up on a farm in Pomeroon, Guyana, where she worked alongside her parents and siblings. As such, she is just as comfortable growing plants as teaching in the classroom. In her early life, she also gained expertise as a seamstress, which she learned from her mother. By grade 9, she had already acquired her dressmaker's certificate. Today she uses her skills to design many items for her family. In her free time, Adena loves to read, take long walks, write children’s stories and poetry, travel, or spend time with her family. See full profile

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This 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

Image of a cone with height and radius marked

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)

Image of a frustum with height and top and bottom radii marked

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.

FAQs

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.