The Volume Of A Cone Calculator
A cone holds exactly one third of the cylinder that would fit around it, which is where the one third in the formula comes from and why it surprises people.
Volume
65.9734
- Base area
- 28.2743
- Slant height
- 7.6158
- Curved surface area
- 71.777
- Total surface area
- 100.0513
Values update as you type. This calculator covers the single scenario its formula assumes — see Common Mistakes for what it leaves out.
The formula this calculator uses
volume = pi x radius^2 x height / 3
- V
- Volume inside the cone, in cubic units
- r
- Radius of the circular base
- h
- Perpendicular height from base to apex
How to check the result by hand
- 1
Find the radius of the base
Halve the diameter if that is what you measured. The formula squares the radius, so using the diameter by mistake inflates the answer by a factor of four.
- 2
Measure the perpendicular height
This is the straight up distance from the base centre to the apex, not the distance along the slope. If you only have the slant height, recover the perpendicular height with Pythagoras.
- 3
Square the radius and multiply by pi
A radius of three squares to nine, and nine times pi is about 28.27. This is the area of the base circle, which is also the cross section of the matching cylinder.
- 4
Multiply by the height and divide by three
28.27 times seven is about 197.92, and a third of that is 65.97. The division by three is what turns the cylinder into the cone that fits inside it.
- 5
Attach cubic units
A radius and height in centimetres give cubic centimetres, which divide by a thousand for litres. A radius in metres and a height in centimetres have to be converted to match first.
For worked examples, common mistakes and the limits of this formula, read the full How To Calculate The Volume Of A Cone page.