Calculate the volume of a cube, rectangular prism, cylinder, sphere, cone or square pyramid — instantly, with the formula shown.
Choose a shape, enter its dimensions, and calculate to see the volume
This free volume calculator finds the volume of six common 3D solids — cube, rectangular prism, cylinder, sphere, cone, and square pyramid — showing the exact formula behind every result. Volume measures the three-dimensional space a solid encloses, always expressed in cubic units, whether cubic feet for a room, cubic meters for a shipping container, or cubic centimeters for a small part. Instead of memorizing six separate solid-geometry formulas, this volume calculator lets you pick a shape, enter its dimensions, and get an instant, formula-transparent answer — useful for construction, packaging, science, or any project where getting capacity right the first time matters.
Volume is a three-dimensional measurement — it quantifies how much space a solid occupies or how much it could hold, unlike area (2D surface) or perimeter/circumference (1D boundary length). Because volume multiplies three linear measurements together (or their geometric equivalent), the result is always reported in cubic units: cm³, m³, ft³, or liters, for example. Doubling every linear dimension of a solid doesn't double or quadruple its volume — it multiplies it by eight, since volume scales with the cube of length.
This volume calculator is built for students checking solid-geometry homework, contractors and DIYers estimating concrete, soil, or fill material, shipping and logistics teams calculating container or box capacity, manufacturers and 3D-printing hobbyists sizing molded or printed parts, and cooks, brewers, or scientists determining tank or vessel capacity. Anyone who needs a fast, formula-transparent volume calculation without deriving it from scratch can use it.
Volume translates directly into cost and material quantity: concrete for a foundation, water for a tank, packing material for a box, or filament for a 3D print all depend on an accurate volume figure. Because volume scales with the cube of linear size, small measurement errors compound quickly — a modest error in a tank's radius becomes a much larger error in its cubed volume, which is why this calculator shows the exact substitution used for every solid.
Contractors use rectangular prism and cylinder volume to order concrete, gravel, or soil. Shipping and logistics teams use cube and rectangular prism volume for container and box capacity. Manufacturers use cone and pyramid volume for hoppers, funnels, and molded parts. Scientists and engineers use sphere volume for tanks, ball bearings, and displacement calculations. Cooks and brewers use cylinder volume to size pots, kegs, and fermenters.
How this volume calculator turns your dimensions into a cubic-unit result, shape by shape
Every volume result is expressed in cubic units (cm³, m³, ft³, liters). Never mix units — convert all dimensions first, then compute.
Cylinder, sphere, and cone formulas use JavaScript's full-precision Math.PI (≈3.14159265358979), more accurate than 3.14 or 22/7 shortcuts.
A cone is exactly ⅓ the volume of a cylinder with the same base and height; a pyramid is exactly ⅓ the volume of a prism with the same base and height.
From picking a solid to reading a verified result
Open the Shape dropdown and select cube, rectangular prism, cylinder, sphere, cone, or square pyramid.
The input fields update automatically for your chosen solid — side length, radius, or length/width/height — all in the same unit, using the perpendicular height for cones and pyramids.
The calculator substitutes your values into that solid's volume formula and computes the result instantly.
The result panel shows the numeric volume in cubic units alongside the exact formula and substitution used to reach it.
Pick a different solid from the dropdown to reset the input fields and calculate another volume without reloading the page.
Compare against a related solid — for example, confirm a cone's volume equals one-third of a cylinder sharing the same base and height.
Finding the volume of a cube with side length 4 — the calculator's default shape
A storage cube has a side length of 4 units. What volume can it hold?
Explanation: The result is in cubic units because volume multiplies three linear dimensions together — here, the side length by itself three times. If the side length were measured in feet, 64 would be reported in cubic feet. Doubling the side to 8 would not double or quadruple the volume; it would increase it eightfold to 512, since volume scales with the cube of a linear dimension.
Unit conventions and sanity checks for each solid
| Solid | Unit Convention | Sanity Check |
|---|---|---|
| Cube | Cubic units of the side length entered (e.g. s in m → m³) | Always a perfect cube of the side length — s×s×s |
| Rectangular prism | Cubic units of length × width × height | Should equal the base area (l×w) multiplied by height |
| Cylinder | Cubic units of radius × height | Should equal the circular base area (πr²) multiplied by height |
| Sphere | Cubic units of the radius entered | Roughly 4.19 × r³ — always larger than a cube of the same radius |
| Cone | Cubic units of radius × height | Exactly ⅓ of a cylinder sharing the same base radius and height |
| Square pyramid | Cubic units of base side × height | Exactly ⅓ of a rectangular prism sharing the same base and height |
Reading the result: the number shown is always in whatever unit you entered, cubed — enter meters and get cubic meters, enter feet and get cubic feet.
Typical ranges: volume should always be a positive number; a result of zero or an error message signals a zero, negative, or invalid input.
Manual verification: for a cone or pyramid, calculate the equivalent cylinder or prism volume and confirm your result is exactly one-third of it — a quick and reliable cross-check.
Where a fast, accurate volume calculation genuinely helps
Check solid-geometry homework for cubes, prisms, cylinders, spheres, cones, and pyramids.
Estimate concrete, gravel, or fill volume for a rectangular or cylindrical foundation.
Calculate box, crate, or container capacity for packing and logistics planning.
Size cylindrical or spherical tanks for water, fuel, or chemical storage capacity.
Determine pot, keg, or fermenter capacity for recipes and batch sizing.
Estimate material (filament or resin) volume needed for a printed part before slicing.
Compute material volume for molded parts, hoppers, and funnel-shaped components.
Calculate displacement volume for density, buoyancy, or fluid-mechanics problems.
Estimate soil or fill volume removed or added for a rectangular or trapezoidal excavation.
Calculate mulch, gravel, or sand volume for a rectangular or cylindrical garden bed.
Size cube or prism packaging to match a product's own volume with minimal wasted space.
Estimate cylindrical or spherical vessel capacity for lab equipment and reagent storage.
Quickly size a planter, storage bin, or custom-built container for any home project.
What this volume calculator does well, and where manual judgment is still needed
Formula and typical use, side by side
| Solid | Formula | Typical Use |
|---|---|---|
| Cube | V = s³ | Dice, ice cubes, storage bins |
| Rectangular prism | V = l × w × h | Rooms, shipping boxes, rectangular tanks |
| Cylinder | V = πr²h | Pipes, cans, silos, drums |
| Sphere | V = (4/3)πr³ | Balls, bearings, spherical tanks |
| Cone | V = ⅓πr²h | Funnels, hoppers, ice cream cones |
| Square pyramid | V = ⅓s²h | Roof sections, monuments, hoppers |
Summary: This volume calculator gives you an instant, free way to find the volume of a cube, rectangular prism, cylinder, sphere, cone, or square pyramid — with the formula and substitution shown for every result. Pair it with the Surface Area Calculator and Area Calculator for a complete picture of a solid's capacity, coverage, and cross-section.
Common questions about volume formulas and this volume calculator
Trusted educational references to go deeper on the math behind volume formulas
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