Calculate volume for cubes, spheres, cylinders, cones, and other 3D shapes with formula display.
Pick a shape from the list - cube, rectangular box, sphere, cylinder, cone, and other common solids - enter the dimensions it asks for, and the tool returns the volume with the formula written out and your values substituted in, so you can see exactly where the number comes from. The mistake users most often make is entering a diameter where the tool asks for a radius, or mixing units. Because dimensions are squared or cubed, a factor of 2 on one dimension multiplies a volume by 4 or 8, not 2. The tool multiplies what you type, in the units you type it, and reports the result in that unit cubed.
A concrete input and expected output from the current implementation.
Input
Cylinder, radius 3 cm, height 7 cm
Expected output
V = pi x r^2 x h = pi x (3 cm)^2 x 7 cm = 63 x pi cm^3 ~ 197.92 cm^3
The cylinder formula multiplies the base area pi x r^2 (about 28.27 cm^2) by the height 7 cm, giving 63 x pi. With pi = 3.14159... that is 197.920..., which rounds to 197.92 cm^3.
Each shape in the list has one fixed volume formula, and the fields change to match: a cube asks for one edge length, a cylinder for radius and height, a sphere for radius alone. Only the numbers the formula needs are collected, and they plug straight into that formula, so nothing in the result depends on estimation or iteration.
The result shows the formula with your numbers written into it: for a cylinder, V = pi r^2 h becomes V = pi x 3^2 x 7, then the intermediate product and the final value. This display is the way to check which dimension you actually used: enter a diameter where the radius belongs and the arithmetic on screen will disagree with what you intended.
No. It works in whatever unit you enter and returns the volume in that unit cubed. Convert before entering or after: 1 L = 1000 cm^3, so the example cylinder holding 197.92 cm^3 holds about 0.198 L; 1 m^3 = 1000 L; one US gallon is about 3785 cm^3. For water, cubic centimeters and milliliters are the same thing.
The standard named solids are covered - cube, rectangular box, sphere, cylinder, cone, and similar common shapes - and the entry fields change to match the one you select. If what you need is not listed, it may not have a simple closed-form formula; irregular solids typically require calculus or water displacement, which this tool does not attempt.
The example and behavioral notes were checked against the browser implementation. Standards and primary references below define the relevant format, formula, or platform behavior.
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