Volume Calculator
Volume and surface area of cubes, boxes, cylinders, cones, spheres, pyramids, capsules, frustums and tubes, with the result in litres and US or UK gallons.
The interactive tool loads here when JavaScript runs.
About this toolWhat is the Volume Calculator?
Volume is how much space a solid fills, and for a container it is how much it holds. This volume calculator covers ten solids: cube, rectangular box, cylinder, cone, sphere, hemisphere, rectangular pyramid, capsule, conical frustum (a bucket or flower pot shape) and tube. It reports the volume in cubic units together with total surface area, so the same entry tells you both how much liquid a tank holds and how much paint or sheet it takes to cover.
Measurements can be in millimetres, centimetres, metres, kilometres, inches, feet, yards or miles. The answer is converted to litres, millilitres, cubic metres, cubic inches, feet and yards, US gallons, UK (imperial) gallons and US fluid ounces. Default values show a cylinder 10 cm in radius and 30 cm tall, which holds 9.42 litres.
For shapes with a curved side the calculator also gives the lateral area (the curved part only), which is what you need for a label wrapped around a can or the outside of a pipe.
- Ten solids including capsule, frustum and tube
- Volume and total surface area, plus lateral area for curved solids
- Litres, millilitres, US and UK gallons, US fluid ounces and cubic units
- Eight input length units
- Labelled sketches, formula panel, copy and share
How to use the Volume Calculator
- Choose the solid. The sketch labels each dimension it needs.
- Choose the length unit your measurements are in.
- Enter the dimensions. Radii are half the diameter; for a tube, enter the outer and inner radius.
- Read the volume and surface area, plus litres and gallons, then check the full unit table if you need cubic feet or yards.
- Copy the summary or share a link to the same calculation.
Worked examples
Fish tank
Input
Rectangular box, 40 × 30 × 30 cm
Output
36,000 cm³ = 36 L = 9.51019 US gal = 7.91889 UK gal; surface area 6,600 cm²
Length × width × height. Real tanks hold a little less because of glass thickness and the gap at the top.
Water in a pipe
Input
Cylinder, radius 0.25 ft, height (length) 100 ft
Output
19.635 ft³ = 556 L = 146.88 US gal
A 6 in inside diameter pipe 100 ft long. π × 0.25² × 100 = 19.635 ft³, and 1 ft³ is 7.48 US gallons.
Plant pot
Input
Conical frustum, R = 15 cm, r = 10 cm, h = 30 cm
Output
14,922.6 cm³ = 14.92 L
A tapered pot holds noticeably less than a cylinder of the bottom radius (21.2 L) and more than one of the top radius (9.4 L).
A ball
Input
Sphere, radius 4.5 in
Output
381.704 in³ = 6.255 L; surface 254.469 in²
A 9 in ball. ⁴⁄₃π × 4.5³ = 381.7 in³, and multiplying by 16.387 cm³ per in³ gives litres.
Background and insight
Most of the formulas follow from one principle: a prism or cylinder is its base area times its height, and a pointed solid on the same base (a pyramid or cone) holds exactly one third of that. A sphere holds two thirds of the cylinder that just encloses it, a result Archimedes is said to have wanted carved on his tomb. The capsule is a cylinder with a hemisphere on each end, so its volume is πr²·a + ⁴⁄₃πr³.
The frustum formula ⅓πh(R² + Rr + r²) is the difference between two cones. Setting the top radius to 0 turns it back into a cone, and setting both radii equal gives a cylinder, which makes it a handy check. The tube is the outer cylinder minus the inner one, so it measures the material in a pipe wall, not the water inside; use the cylinder with the inner radius for that.
The liquid units are fixed by law. A litre is exactly 1,000 cm³. The US gallon is defined as 231 cubic inches, exactly 3.785411784 litres, and the imperial gallon used in the UK is exactly 4.54609 litres, about 20% larger. Mixing them up is a common source of error in recipes, fuel figures and aquarium sizing.
Common use cases
Tanks, pools and aquariums
Find capacity in litres or gallons to size pumps, heaters, water treatment doses or fill times.
Shipping and storage
Work out cubic feet or cubic metres of a box or crate for freight quotes and storage space.
Cooking and brewing
Check how much a cylindrical pot or a hemispherical bowl really holds before scaling a recipe.
Paint, wrap and coating
Use the surface or lateral area to estimate paint, insulation or label material.
Tips and limitations
- Measure inside dimensions for capacity and outside dimensions for material or displacement.
- Cubic units scale with the cube of the length: doubling the radius of a sphere multiplies its volume by eight.
- US and UK gallons differ by about 20%. Check which one a product label or recipe uses.
- For concrete, gravel or soil orders in cubic yards, use the dedicated concrete or gravel calculators, which add waste and bag counts.
- Surface area here includes flat ends. Use the lateral area if a can has no lid or a pipe has open ends.
Frequently asked questions
How do you calculate the volume of a cylinder?
Multiply the area of the circular base by the height: V = πr²h. A cylinder with a 10 cm radius and 30 cm height holds π × 100 × 30 = 9,424.78 cm³, which is 9.42 litres.
How many litres are in a cubic foot?
One cubic foot is 28.3168 litres, because a foot is exactly 30.48 cm and 30.48³ is 28,316.85 cm³. It is also 7.4805 US gallons.
What is the volume formula for a sphere?
V = ⁴⁄₃πr³. A sphere with radius 1 has a volume of 4.18879, and its surface area is 4πr², or 12.566. Doubling the radius makes the volume eight times larger.
How do I convert cubic metres to US gallons?
Multiply by 264.172. A cubic metre is 1,000 litres and a US gallon is exactly 3.785411784 litres. For imperial gallons multiply by 219.969 instead.
Why is a cone one third of a cylinder?
A cone and a cylinder with the same base and height compare as 1 : 3 because the cone's cross-section shrinks steadily to a point. Adding up those shrinking slices (by calculus or Cavalieri's principle) gives exactly one third of πr²h.
What is the difference between volume and surface area?
Volume measures the space inside a solid in cubic units, such as litres or ft³. Surface area measures the skin around it in square units, such as cm² or ft². A tank's capacity depends on volume, the paint to cover it on surface area.
Is there an in-depth guide to the Volume Calculator?
Yes. “Area and Volume Formulas, and Why They Work” covers the background, how it works, common pitfalls and worked examples. Read the full guide.
Related Tools You May Like
Free, in-browser tools that pair well with this one.