Pick a shape, type its measurements and read the volume in your unit, in litres, cubic metres, cubic feet and gallons. The formula is shown with your own numbers, with a labelled diagram for each shape.
Choose the shape.
Choose the unit your measurements are in.
Enter the measurements shown on the diagram.
Read the volume and its conversion to litres.
Sphere: V = 4/3 × π × r³
Cylinder: V = π × r² × h
Cone: V = 1/3 × π × r² × h
Cube: V = a³
Rectangular tank: V = l × w × h
Conical frustum: V = 1/3 × π × h × (r² + rR + R²)
Capsule: V = π × r² × h + 4/3 × π × r³
Spherical cap: V = 1/3 × π × h² × (3R − h)
Ellipsoid: V = 4/3 × π × a × b × c
Square pyramid: V = 1/3 × a² × h
Tube: V = π × (d₁² − d₂²) ÷ 4 × l
Hemisphere: V = 2/3 × π × r³
Volume is the amount of space a solid object takes up, or how much a container can hold. The volume calculator finds it for twelve common shapes: sphere, hemisphere, cube, rectangular tank, cylinder, cone, conical frustum, capsule, spherical cap, ellipsoid, square pyramid and tube. You pick the shape, choose the unit you measured in and type the sizes marked on the drawing.
The answer is given in cubic units of your choice and also in litres, cubic metres, cubic feet and gallons, because the same number is needed in different forms: litres for a water tank, cubic metres for concrete or sand, cubic feet for a room or a refrigerator. The formula is written out with your own measurements so the result can be checked by hand, which helps with Class 8 to 10 mensuration.
1. Identify the shape, or split a complicated object into simple shapes.
2. Measure every length in the same unit. For a container, measure the inside.
3. For round shapes use the radius, which is half the diameter.
4. Put the measurements into the formula for that shape, for example π × r² × h for a cylinder.
5. Write the answer in cubic units such as cm³ or m³.
6. To get litres, divide cm³ by 1,000 or multiply m³ by 1,000.
Any solid that has the same cross-section all the way up, called a prism or a cylinder, has a volume equal to the area of that cross-section multiplied by its height. A rectangular tank is length × width for the base, times the height. A cylinder is the circle area π r² times the height. A tube is the ring-shaped area between two circles times its length. This single idea covers most containers found at home and on a building site.
A cone holds exactly one third of the cylinder that has the same base and height, and a pyramid holds one third of the matching box. You can check this by filling a cone with water three times to fill the cylinder. A frustum, the bucket shape left when the tip of a cone is cut off, is the big cone minus the small cone that was removed, which gives the formula with r², rR and R² added together.
A sphere of radius r has volume four thirds π r³, a result first proved by Archimedes, who showed that a sphere fills two thirds of the cylinder that just encloses it. A hemisphere is half of that. A capsule is a cylinder with a hemisphere on each end, so its volume is a cylinder plus one whole sphere. A spherical cap, the dome sliced off a ball, depends on the ball's radius and the height of the slice.
The Reddy family has a round overhead water tank with an inside radius of 60 cm and a water height of 150 cm, and wants to know how many litres it holds.
Cylinder: formula: V = π × r² × h
Put in your measurements: V = π × 60² × 150 = 16,96,460.0329 cm³
Convert to litres: 1 cm³ = 0.001 litres 16,96,460.0329 cm³ = 1,696.46 litres
Answer: Volume 16,96,460.0329 cm³; In litres 1,696.46 L; In cubic metres 1.69646 m³
Using the diameter where the formula needs the radius, which makes the answer four times too large for a cylinder.
Mixing units, such as radius in centimetres and height in metres.
Forgetting the one third for a cone or a pyramid.
Using outside measurements for the capacity of a tank with thick walls.
Converting cm³ to m³ by dividing by 100 or 1,000 instead of 10,00,000.
Finding the capacity of water tanks, sumps and drums in litres.
Estimating concrete, sand or soil for pillars, footings and pits.
Working out how much liquid a pipe or hose holds.
Sizing packaging, storage bins and cooking vessels.
Solving mensuration problems in school and competitive exams.
How do I convert volume to litres?
1 litre is 1,000 cm³, so divide cm³ by 1,000. 1 m³ is 1,000 litres. The calculator shows litres for every shape.
How do I find the capacity of a water tank?
Use the inside measurements. For a round tank choose Cylinder and enter the inner radius and height; for a box-shaped tank choose Rectangular tank.
Why do a cone and a pyramid have 1/3 in the formula?
A cone holds exactly one third of the cylinder with the same base and height, and a pyramid one third of the matching prism.
Do I enter radius or diameter?
Radius for round shapes, which is half the diameter. The tube is the exception: it uses the outer and inner diameters.
What is a frustum?
A cone with its tip cut off parallel to the base, like a bucket or a lampshade. Enter both radii and the height.