Volume
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3D Volume Calculator (Sphere, Cylinder, Cone, Prism)
Volume for a sphere, cylinder, cone, or rectangular prism from radius, height, length, and width.
Page updated 2026-09-04.
Calculator
Calculated Results
A cylinder's volume from radius and height
A cylinder with radius 3 and height 10 has a volume of 282.74 -- calculated as pi x r² x h = 3.14159 x 9 x 10 = 282.74.
A cylinder's volume formula is essentially the circular base's area (pi x r²) multiplied by how far that circular cross-section extends (the height) -- the same basic 'base area times height' logic that applies to any prism-like solid with a constant cross-section along its length.
Switching the shape selector changes both which fields are used and which formula applies -- a sphere uses only r (volume = 4/3 x pi x r³), a cone uses r and h with an extra one-third factor compared to a cylinder of the same dimensions, and a rectangular prism uses length, width, and height multiplied directly together.
Why a cone's volume is exactly one-third of the equivalent cylinder
Sphere uses r. Cylinder and cone use r and h. Prism uses l, w, and h. A cone with the same radius and height as this cylinder would have exactly one-third its volume (94.25 instead of 282.74) -- this one-third relationship between a cone and its enclosing cylinder is a well-known geometric fact, not a coincidence specific to these particular numbers.
Each shape's fields are shown or hidden based on what that shape actually needs -- a sphere doesn't need a height field at all (since it's defined by radius alone), while a rectangular prism doesn't need a radius field, since it's defined by three straight-line dimensions instead of a curved one.
All volume results come out in cubic units matching whatever linear unit you used for the inputs -- if radius and height are in centimeters, the resulting volume is in cubic centimeters, and consistency across all input fields matters for the result to be meaningful.
Related geometry and measurement tools
For the 2D circular cross-section this cylinder and cone are built from, the Circle Area, Perimeter & Arc Calculator covers that flat-shape calculation.
For converting the resulting volume into different units (like liters or gallons), a general unit converter would be the next step beyond this shape-specific calculation.
Frequently Asked Questions (FAQ)
How is the cylinder volume of 282.74 calculated?
Volume = pi x r² x h = 3.14159 x 3² x 10 = 3.14159 x 9 x 10 = 282.74 (rounded), the circular base's area multiplied by the height.
Why is a cone's volume exactly one-third of a cylinder with the same radius and height?
Sphere uses r. Cylinder and cone use r and h. Prism uses l, w, and h. This is a well-established geometric relationship: a cone tapers to a point, and integrating its cross-sectional area from base to tip produces exactly one-third the volume of a cylinder with the same base and height -- true for any radius and height combination, not just this example.
Why doesn't the sphere option use a height field?
Sphere uses r. Cylinder and cone use r and h. Prism uses l, w, and h. A sphere is fully defined by its radius alone -- there's no separate height dimension for a sphere the way there is for a cylinder or cone, so that field is hidden when sphere is selected.
What units does the volume result come out in?
Whatever cubic unit matches your linear input units -- if you entered radius and height in centimeters, the volume is in cubic centimeters. The calculator doesn't perform unit conversion; it assumes consistent units across all your inputs.
Does the rectangular prism option use the same radius field as the other shapes?
No. Sphere uses r. Cylinder and cone use r and h. Prism uses l, w, and h. A rectangular prism is defined by length, width, and height (straight-line dimensions), not a radius, since it has no curved surface -- the radius field is hidden and the length/width fields appear instead when prism is selected.
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