Volume Calculator
Volume calculator for 12 common 3D shapes: cube, box, cylinder, cone, sphere, hemisphere, pyramid, prism, capsule, frustum, ellipsoid and tube. Pick a shape, enter its dimensions, and get the volume in cubic units, liters and gallons.
Find the Volume of Common 3D Shapes
Volume Formula
Where:
- \(V\) — volume of the shape
- \(r\) — radius of the circular base
- \(h\) — height or length of the shape
- \(\pi \approx 3.14159\)
The formula \(V = \pi r^2 h\) above is the one used for the default shape, the cylinder. Each shape in the calculator has its own formula:
| Shape | Formula |
|---|---|
| Cube | \(V = a^3\) |
| Rectangular prism (box) | \(V = a \cdot b \cdot c\) |
| Cylinder | \(V = \pi r^2 h\) |
| Cone | \(V = \tfrac{1}{3}\pi r^2 h\) |
| Sphere | \(V = \tfrac{4}{3}\pi r^3\) |
| Hemisphere | \(V = \tfrac{2}{3}\pi r^3\) |
| Pyramid (rectangular base) | \(V = \tfrac{1}{3} a b h\) |
| Triangular prism | \(V = \tfrac{1}{2} a c h\) |
| Capsule | \(V = \pi r^2 h + \tfrac{4}{3}\pi r^3\) |
| Cone frustum | \(V = \tfrac{\pi h}{3}(R^2 + Rr + r^2)\) |
| Ellipsoid | \(V = \tfrac{4}{3}\pi abc\) |
| Hollow cylinder (tube) | \(V = \pi h (R^2 - r^2)\) |
In every formula, the dimensions combine so that the result carries the cube of the length unit: if you enter centimeters, the volume comes out in \(\text{cm}^3\); if you enter inches, it comes out in \(\text{in}^3\).
Volume – Calculation Example
Example: a cylindrical water glass has a radius of 5 cm and a height of 12 cm. How much water does it hold? These are the calculator's default values, so you can reproduce the result directly.
\[ V = \pi r^2 h = \pi \times 5^2 \times 12 = 300\pi \approx 942.48 \;\text{cm}^3 \]
Result: the glass holds about 942.48 cm³, which equals roughly 0.942 liters, 57.51 cubic inches or 0.249 US gallons.
How to Use the Volume Calculator
- Open the Shape dropdown and choose the solid you are working with — the form instantly shows only the dimensions that shape needs.
- Set the Length unit (mm, cm, m, in, ft or yd). All dimensions you enter are interpreted in this unit, and the result is shown in this unit cubed.
- Fill in the visible dimension fields, for example Radius (r) and Height / length (h) for a cylinder, or the three sides for a box. For a tube, enter the outer radius in Bottom / outer radius (R) and the hole size in Inner radius (tube).
- Read the Volume result at the top, then check the conversions below it: cubic centimeters, cubic meters, cubic inches, cubic feet, cubic yards, liters and US gallons.
- The Formula with your values block shows the exact calculation with your numbers substituted, and the Shape diagram labels each dimension on a drawing so you can verify your inputs.
What Volume Means and Why It Matters
Volume is the amount of three-dimensional space a solid object occupies. It answers practical questions everywhere: how much concrete fills a footing, how much water fits in a tank, how much soil a raised bed holds, how much air a room contains, or how much liquid a bottle can carry. Whatever the shape, volume is always measured in cubic units — cubic meters, cubic feet, liters, gallons — because it is the product of three lengths.
Every volume formula reduces to the same idea: take the area of a base or cross-section and stretch it through a third dimension. A box is a rectangle swept through height \(c\), giving \(abc\). A cylinder is a circle of area \(\pi r^2\) swept through height \(h\). A cone or pyramid tapers to a point, so it holds exactly one third of the cylinder or prism with the same base and height — that is where the factor \(\tfrac{1}{3}\) in their formulas comes from. A sphere's \(\tfrac{4}{3}\pi r^3\) can be read as four stacked circle-sweeps of radius \(r\) divided by three.
When you interpret a result, pay attention to the unit. Multiplying lengths in meters gives cubic meters directly, which suits rooms, pools and construction quantities. For containers, liters and gallons are usually more meaningful: 1 liter equals 1000 cm³, and 1 US gallon equals 231 in³. The calculator performs all of these conversions for you, so you can move freely between metric and imperial figures without memorizing conversion factors.
Assumptions, Limitations and Practical Tips
- All shapes are assumed to be regular: circular bases are perfect circles, boxes have square corners, prisms have constant cross-sections. For irregular objects, volume is best measured by water displacement.
- Dimensions must be interior measurements for capacity questions. The wall thickness of a real tank, pipe or glass reduces the usable volume, so measure the inside.
- For a cone frustum, the top radius \(r\) and bottom radius \(R\) may differ, but both must be greater than zero. Set \(r = R\) only if you actually want a cylinder.
- For a hollow cylinder (tube), the inner radius must be strictly smaller than the outer radius; the calculator rejects an entry of the same size or larger because it describes an impossible shape (or zero material).
- For an ellipsoid, the inputs are semi-axes — half the full width in each direction. Entering the full diameters will overestimate the volume by a factor of 8.
- A capsule's height \(h\) is the length of the straight cylindrical middle section only, not the tip-to-tip length. The total length of the capsule is \(h + 2r\).
- Keep all dimensions in the same unit before entering them, or use the Length unit selector consistently — mixing units (for example, feet with inches) is the most common source of wrong volume results.
If you also need the surface area of the same solid — for paint, material or heat-exchange estimates — use the Surface Area Calculator. For more detail on a single shape, see the Cylinder Volume Calculator, the Sphere Volume and Surface Area Calculator and the Cone Volume and Surface Area Calculator.
Frequently Asked Questions
How do I calculate volume by hand if my shape is not in the list?
For an unknown regular solid, break it into parts the calculator already knows. If you can slice the object into thin identical cross-sections, multiply the cross-section area by the length — this covers any prism. Composite shapes (a silo, a pool with a slanted bottom) are sums and differences of simpler solids: cylinder plus hemisphere, box minus frustum, and so on. Add the part volumes for a union and subtract them for a cut-out.
Why is my result about 8 times too big?
You almost certainly entered a diameter where the calculator wants a radius. The radius is half the diameter, and since it appears squared or cubed in the formulas, using the full diameter inflates a sphere's volume by \(2^3 = 8\) or a cylinder's by \(2^2 = 4\). The same trap exists for ellipsoid inputs: they are semi-axes, so entering full widths multiplies the volume by 2 × 2 × 2.
How do I convert cubic units into liters or gallons myself?
The three key factors: 1 liter = 1000 cm³, 1 m³ = 1000 liters, and 1 US gallon = 231 in³ ≈ 3.785 liters. To convert from cubic meters, multiply by 1000 to get liters. To convert cubic inches to cubic feet, divide by 1728 (12³). Note that imperial (UK) gallons are larger, about 4.546 liters, so check which gallon a container label means before comparing numbers.
How can I find the volume of an irregular object like a rock or a vase?
Use water displacement. Fill a graduated container with enough water to submerge the object, note the level, submerge the object, and read the new level — the difference in milliliters is the volume in cm³. Make sure the object does not absorb water or trap air bubbles. For objects too large to submerge, weigh them and divide the mass by the material's density instead.
Should I measure the inside or the outside of a tank or pipe?
For capacity — how much the container actually holds — always measure the inside: inner radius, inner length, inner height. Wall thickness can matter a lot; a "40 mm" pipe with a 3 mm wall holds noticeably less than one with a 1 mm wall. Exterior dimensions only make sense when you need the displacement or the material volume of the solid itself, as when ordering concrete for a wall.
Why do cones and pyramids have a 1/3 in their formulas?
A cone is exactly one third of the cylinder that shares its base and height, and a pyramid is one third of the matching prism — this can be proved with integral calculus by summing thin slices that shrink toward the apex. That is where the factor \(\tfrac{1}{3}\) in \(V = \tfrac{1}{3}\pi r^2 h\) comes from. A frustum follows the same idea: it is the tall cone minus the cone that was cut off the top.
What is the difference between volume, capacity and surface area?
Volume is the space a solid occupies; capacity is essentially the same number but expressed for what a container can hold (liters, gallons), measured from interior dimensions. Surface area is a completely different quantity — the area of the outer skin, in square units — used for paint, wrapping or heat loss, not for how much fits inside. A tall thin glass and a short wide one can share a volume yet have very different surface areas.