Enter values to see results
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units³
Enter values to see results
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units³
The Volume Calculator computes the three-dimensional space occupied by common geometric solids including cubes, spheres, cylinders, cones, and rectangular pyramids. Volume is one of the most fundamental measurements in solid geometry, engineering, manufacturing, and everyday life—from determining the capacity of a container to calculating how much concrete is needed for a foundation.
Volume is measured in cubic units. If lengths are given in centimeters, the volume is in cubic centimeters (cm³); if in meters, then cubic meters (m³). The concept extends naturally from area (two-dimensional measurement) to three dimensions by incorporating depth or height.
Cube — all edges equal length $$a$$:
$$V_{\text{cube}} = a^3$$
Sphere — defined by radius $$r$$:
$$V_{\text{sphere}} = \frac{4}{3}\pi r^3$$
Cylinder — circular base with radius $$r$$ and height $$h$$:
$$V_{\text{cylinder}} = \pi r^2 h$$
Cone — circular base with radius $$r$$ and height $$h$$:
$$V_{\text{cone}} = \frac{1}{3}\pi r^2 h$$
Rectangular Pyramid — rectangular base with length $$l$$, width $$w$$, and height $$h$$:
$$V_{\text{pyramid}} = \frac{1}{3} l \cdot w \cdot h$$
A cone is exactly one-third the volume of a cylinder with the same base and height. Similarly, a pyramid is one-third the volume of the prism that encloses it. These elegant ratios were first proven by Archimedes and remain central to calculus-based derivations using integration.
The sphere formula involves the irrational number $$\pi \approx 3.14159$$. Archimedes showed that a sphere’s volume is exactly two-thirds the volume of its circumscribing cylinder: $$V_{\text{sphere}} = \frac{2}{3} V_{\text{circumscribing cylinder}}$$.
Engineers use volume calculations for material estimation—how much steel for a cylindrical tank, how much water a spherical reservoir holds, or how much earth must be excavated for a conical pit. In packaging, knowing the volume of different shapes helps optimize storage. In medicine, tumor volumes (often modeled as ellipsoids or spheres) guide treatment decisions. Architects compute volumes to determine heating and cooling loads for buildings.
Select your shape, enter the required dimensions, and the calculator instantly returns the volume in cubic units.
Choose a shape from the dropdown. Enter the relevant dimensions: for a cube, only Dimension 1 (edge length) is used; for a sphere, only Dimension 1 (radius); for a cylinder or cone, Dimension 1 (radius) and Dimension 2 (height); for a rectangular pyramid, all three dimensions (length, width, height). The calculator applies the corresponding formula and displays the result in cubic units.
The output is the volume in cubic units matching your input units. If you entered dimensions in centimeters, the result is in cm³. To convert to liters, note that 1 liter = 1000 cm³. To convert cm³ to m³, divide by 1,000,000.
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A cylinder with radius 3 m and height 10 m has volume V = π(3)²(10) ≈ 282.74 m³, equivalent to about 282,743 liters.
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A sphere of radius 7 cm has volume V = (4/3)π(7)³ ≈ 1436.76 cm³.
Cube: edge length (Dim 1). Sphere: radius (Dim 1). Cylinder/Cone: radius (Dim 1) and height (Dim 2). Rectangular Pyramid: length (Dim 1), width (Dim 2), height (Dim 3).
Divide by 1000. For example, 5000 cm³ = 5 liters. One liter equals exactly 1000 cm³ or 1 dm³.
By Cavalieri’s principle or integration, the cross-sectional area of a cone at height $$y$$ is proportional to $$y^2$$. Integrating from 0 to $$h$$ yields exactly $$\frac{1}{3}$$ of the cylinder’s volume with the same base and height.
This calculator handles five standard solids. For irregular shapes, you can approximate by decomposing the object into simpler components and summing their volumes, or use water displacement methods.
Use any consistent unit (cm, m, inches, feet). The result will be in the cube of that unit. Do not mix units—convert all dimensions to the same unit first.
The formula $$V = \frac{4}{3}\pi r^3$$ is exact for a perfect mathematical sphere. Real-world objects have manufacturing tolerances, so the computed volume is an idealized value.
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