Volume Guides & Formulas
The calculators give you an answer. These guides explain where it comes from — every formula, every unit, and the methods that work when no formula fits.
- ✓ Every formula in one place
- ✓ Units explained properly
- ✓ Worked examples throughout
Start here
2 guidesNew to this? These two cover the whole subject — the method, then every formula in one place.
Units & conversion
3 guidesCubic versus liquid measures, and the US–imperial gap that quietly breaks calculations.
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Volume Conversion Calculator
Convert between 17 units at once — cubic inches to gallons, litres to cubic feet, cups to millilitres.
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Cubic Feet, Yards & Metres Explained
Why a cubic yard is 27 cubic feet and not 9 — the error that costs contractors money.
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Gallons, Litres & Fluid Ounces
The US and imperial systems, why they differ, and which one a recipe means.
Concepts & methods
3 guidesThe ideas behind the arithmetic — and what to do when no formula fits your object.
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Volume vs Capacity
Why a tank's outside volume and its capacity are different numbers, and when the difference matters.
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Measuring Irregular Objects
Water displacement, sectioning and averaging — how to measure things no formula covers.
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Density, Mass & Volume
The relationship that turns a volume into a weight, and why bulk density differs from solid density.
For students
2 guidesPractice material — worked examples first, then problems with full solutions.
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If you read one thing: volume calculation reduces to two rules. Anything with a constant cross-section — a box, a cylinder, a pipe, an extruded beam — has volume = cross-section area × length. Anything that tapers to a point — a cone, a pyramid — holds exactly one third of that. Almost every formula below is one of those two, or a sphere.
The two rules, and the one exception
Tapering to a point: V = ⅓ × base area × height
Sphere: V = (4/3) π r³
The first rule covers boxes, cubes, cylinders, prisms of any cross-section, pipes and tubes. The second covers cones, all pyramids regardless of base shape, and tetrahedra. Between them they account for most of the geometry anyone needs.
The one-third in the second rule is not an approximation — it is exact, and it applies no matter what shape the base is. You can demonstrate it physically: a cone-shaped cup fills its matching cylinder in exactly three pours. The sphere is the genuine outlier, and Archimedes proved its volume is exactly two-thirds of the cylinder that encloses it.
Quick formula reference
| Shape | Formula | Calculator |
|---|---|---|
| Cube | a³ | Cube |
| Box / rectangular prism | l × w × h | Box |
| Cylinder | π r² h | Cylinder |
| Sphere | (4/3) π r³ | Sphere |
| Hemisphere | (2/3) π r³ | Hemisphere |
| Cone | (1/3) π r² h | Cone |
| Pyramid | (1/3) × base area × h | Pyramid |
| Triangular prism | ½ b h l | Triangular prism |
| Ellipsoid | (4/3) π a b c | Ellipsoid |
| Capsule | π r² a + (4/3) π r³ | Capsule |
| Tube (hollow cylinder) | π (R² − r²) h | Tube |
| Truncated cone | (1/3) π h (R² + Rr + r²) | Frustum |
All seventeen shape calculators are indexed on the shape volume calculators hub, each with its own diagram, worked examples and reference tables.
The units, in brief
Volume answers come in two families, and the bridges between them are worth knowing by heart:
| Remember this | Because |
|---|---|
| 1 yd³ = 27 ft³ | 3 × 3 × 3 — the most common construction error is using 9 |
| 1 ft³ = 1,728 in³ | 12 × 12 × 12 |
| 1 ft³ = 7.4805 US gal | 1,728 ÷ 231 |
| 1 US gal = 231 in³ | Defined exactly, from the English wine gallon |
| 1 mL = 1 cm³ | Identical by definition — no conversion needed |
| 1 L = 1,000 cm³ | A 10 cm cube |
| 1 m³ = 1,000 L | And weighs one tonne, if it is water |
| 1 imp gal = 1.201 US gal | About 20% larger |
The volume conversion calculator handles all seventeen units at once if you would rather not do it by hand.
Frequently asked questions
How do you calculate volume?
Identify the shape, then apply its formula with all measurements in the same unit. For anything with a constant cross-section — a box, a cylinder, a pipe — volume is cross-section area × length. For anything tapering to a point, it is one third of that. For a sphere it is (4/3)πr³. The answer comes out in whatever unit you measured, cubed.
What is the difference between area and volume?
Area measures a flat surface in square units and needs two dimensions; volume measures space in cubic units and needs three. A 10 × 12 ft floor has an area of 120 ft², but the room above it has a volume of 120 × the ceiling height. Flooring is bought by area, paint by area, concrete and soil by volume.
How do I find the volume of an irregular object?
Use water displacement: submerge the object in a container of water and measure how much the level rises. That rise is the object's volume. For irregular spaces rather than objects, split the space into simple shapes, calculate each, and add them together.
Why is a cubic yard 27 cubic feet?
Because a yard is three feet, and volume scales with the cube of length: 3 × 3 × 3 = 27. The same logic makes a cubic foot 1,728 cubic inches (12³) and a cubic metre a million cubic centimetres (100³). Confusing this with the 9 square feet in a square yard is the most common estimating error in construction.