Shape Volume Calculators
Nineteen dedicated calculators — one for every geometric shape you'll meet in a classroom, a workshop or a job site. Each page shows the formula, a labeled diagram, worked examples and the mistakes to avoid.
- ✓ 19 shapes covered
- ✓ Formula & diagram on every page
- ✓ Or use the all-in-one tool
Round shapes
Anything with a circular or elliptical cross-section. These formulas all carry a π.
- Cylinder Volume Calculator
V = πr²h — tanks, pipes, drums and posts. Radius or diameter input.
- Sphere Volume Calculator
V = (4/3)πr³ — balls, domes and planets, from radius, diameter or circumference.
- Hemisphere Volume Calculator
V = (2/3)πr³ — half-spheres: bowls, domes and tank end caps.
- Cone Volume Calculator
V = (1/3)πr²h — funnels, hoppers and stockpiles of gravel or sand.
- Truncated Cone Volume Calculator
Frustum: buckets, planters, lampshades — a cone with the tip cut off.
- Tube Volume Calculator
V = π(R²−r²)h — the material in a hollow cylinder: pipes, sleeves, rings.
- Capsule Volume Calculator
A cylinder with hemispherical ends — pills, propane tanks, submarines.
- Spherical Cap Volume Calculator
V = ⅓πh²(3R−h) — domes, dished tank heads and liquid in a spherical vessel.
- Ellipsoid Volume Calculator
V = (4/3)πabc — stretched spheres: eggs, melons and clinical estimates.
Flat-sided shapes (prisms & boxes)
Straight sides, constant cross-section: volume is always base area × length.
- Cube Volume Calculator
V = a³ — one edge length is all you need.
- Rectangular Prism / Box Volume Calculator
V = l×w×h — boxes, rooms, aquariums, slabs. The workhorse formula.
- Triangular Prism Volume Calculator
V = ½bhl — ramps, roof spaces, Toblerone-shaped solids.
- Trapezoidal Prism Volume Calculator
Ditches, ramps and footings with sloped sides.
- Prism Volume Calculator (general)
Any base shape: enter the base area and length directly.
Pointed shapes (pyramids)
Flat base, single apex: always one-third of the matching prism.
- Pyramid Volume Calculator
V = (1/3) × base area × height — any base shape.
- Square Pyramid Volume Calculator
V = (1/3)a²h — the Giza shape: square base, four triangular faces.
- Rectangular Pyramid Volume Calculator
V = (1/3)lwh — a pyramid over a rectangular base.
- Triangular Pyramid Volume Calculator
Tetrahedra: four triangular faces, including the regular tetrahedron.
- Truncated Pyramid Volume Calculator
A pyramid with its tip cut off — hoppers, planters and battered excavations.
How to choose: look at the profile of your object. Parallel flat sides → a prism (base area × length). Round with parallel sides → cylinder. Tapers to a point → cone or pyramid (one-third of the matching prism). Round everywhere → sphere. Combinations — like a silo (cylinder + hemisphere) — are calculated part by part and added.
All 17 formulas side by side
| Shape | Formula | Typical real-world object |
|---|---|---|
| Cube | a³ | Dice, shipping crates |
| Rectangular prism (box) | l × w × h | Boxes, rooms, aquariums |
| Cylinder | π r² h | Tanks, pipes, cans |
| Sphere | (4/3) π r³ | Balls, bubbles |
| Hemisphere | (2/3) π r³ | Bowls, domes |
| Cone | (1/3) π r² h | Funnels, stockpiles |
| Truncated cone | (1/3) π h (r₁² + r₁r₂ + r₂²) | Buckets, planters |
| Tube (hollow cylinder) | π (R² − r²) h | Pipe walls, sleeves |
| Capsule | π r² a + (4/3) π r³ | Pills, propane tanks |
| Spherical cap | (1/3) π h² (3R − h) | Domes, dished tank heads |
| Ellipsoid | (4/3) π a b c | Eggs, melons |
| Prism (any base) | base area × l | Extrusions, beams |
| Triangular prism | ½ b h l | Ramps, roof spaces |
| Trapezoidal prism | ½ (b₁ + b₂) h l | Ditches, sloped footings |
| Pyramid (any base) | (1/3) × base area × h | Monuments, roof hips |
| Square pyramid | (1/3) a² h | The Great Pyramid |
| Rectangular pyramid | (1/3) l w h | Skylights, hoppers |
| Triangular pyramid | (1/3) × base area × h | Tetrahedra |
| Truncated pyramid | (h/3)(A₁ + A₂ + √(A₁A₂)) | Hoppers, battered pits |
Notice the pattern: prisms are base × length, and anything tapering to a point is exactly one-third of its matching prism. Master those two rules and the whole table follows. The full derivations live in our volume formulas cheat sheet.
Real objects are combinations
Most manufactured things are two or three of these shapes glued together, and their volume is just the sum of the parts:
- Grain silo = cylinder + hemisphere on top. A 10-ft-diameter silo, 20 ft to the eaves: cylinder π × 25 × 20 = 1,570.8 ft³, plus half-dome (2/3) π × 125 = 261.8 ft³ → 1,832.6 ft³.
- Propane tank = capsule (cylinder + two hemispheres = cylinder + one full sphere). That's why the capsule calculator exists as its own tool.
- Water tower = cylinder stem + truncated cone + hemisphere cap, each calculated separately.
- House attic = triangular prism over the rectangular living space.
For hollow objects, subtract instead of add: the concrete in a pipe is the tube volume — outer cylinder minus inner cylinder. And when the object is genuinely irregular — a rock, a machine part — skip formulas entirely and use water displacement.
Frequently asked questions
Which volume formula should I use?
Match the shape's profile. Flat sides all around: box, cube or prism (base area × length). Round with parallel sides: cylinder. Round and tapering to a point: cone. Perfectly round all over: sphere. Flat base tapering to a point: pyramid. If your object combines shapes — a silo is a cylinder plus a hemisphere — calculate each part and add them.
Why do cones and pyramids have 1/3 in their formulas?
Any shape that tapers linearly from a full base to a single point holds exactly one-third of the prism or cylinder that shares its base and height. You can verify it physically: a cone-shaped cup fills its matching cylinder in exactly three pours. The 1/3 comes from integrating the shrinking cross-section, and it applies to every pyramid regardless of base shape.
What units do these calculators support?
Every shape calculator on this site accepts millimeters, centimeters, meters, inches, feet and yards — mixed freely between fields — and outputs cubic units (cm³, m³, in³, ft³, yd³) plus liquid units (mL, L, US and UK gallons).
How accurate are the results?
The formulas are mathematically exact; results are computed in double precision and displayed to four decimal places. Real-world accuracy therefore depends on your measurements — measure twice, and for containers remember to use inside dimensions.