Volume Calculator – Find Volume & Surface Area of 3D Shapes

Volume measures the three-dimensional space enclosed by a solid. The formula depends on the solid. Prisms and cylinders can be understood as base area × perpendicular height; pyramids and cones with the same base and height have one-third of the corresponding prism or cylinder volume.

A good volume calculator also keeps surface area separate from volume. Volume uses cubic units such as cm³, m³ or ft³, while surface area uses square units. Learn Mode explains the geometry behind the selected formula, not just the arithmetic.

Multiply length, width and height: V = LWH. A box 4 m long, 3 m wide and 2 m high has V = 4 × 3 × 2 = 24 m³.

The formula can be understood in layers: L × W gives the area of one rectangular base layer, and multiplying by H counts how many such layers fill the solid. Make sure all three dimensions are expressed in compatible units before multiplying.

First find the area of the circular base, πr², then multiply by the perpendicular height: V = πr²h. With r = 3 cm and h = 10 cm, V = π × 9 × 10 = 90π ≈ 282.743 cm³.

If diameter is given, divide by 2 before squaring. A common mistake is to use diameter in place of radius, which makes the volume four times too large.

A cone has one-third the volume of a cylinder with the same circular base and perpendicular height: V = ⅓πr²h. This one-third factor is a geometric result, not an arbitrary adjustment.

For surface area, slant height is also needed. If radius and vertical height are known for a right cone, slant height can be found with Pythagoras: l = √(r²+h²). The calculator shows these relationships separately so volume and surface area are not mixed.

Use V = 4/3 πr³. If r = 5 cm, V = 4/3 × π × 125 ≈ 523.599 cm³.

The radius must be cubed, not squared. Squaring r is associated with circular area and spherical surface area; cubing is what gives the three-dimensional volume. If diameter is supplied, first use r = d/2.

If the dimensions are already in feet, multiply the three perpendicular dimensions to obtain ft³. For a 10 ft × 8 ft × 2 ft rectangular space, V = 160 ft³.

If dimensions are mixed—for example feet and inches—convert them to one unit before multiplying or enter the explicit units in the calculator. Cubic conversion factors are the cube of linear conversion factors, so converting ft³ to m³ is not the same as converting feet to metres.

Yes. Once a geometric volume is known, it can be expressed as a capacity. One cubic metre equals 1,000 litres. The calculator also shows common equivalents such as millilitres, cubic feet, US gallons and Imperial gallons.

Be careful with the word “gallon”: the US liquid gallon and Imperial gallon are different sizes. The result labels them separately. For real tanks, usable capacity can differ from ideal geometric volume because of wall thickness, heads, fittings, dead space or operating level.

Volume measures the space inside a solid and uses cubic units. Surface area measures the total outside covering and uses square units. They answer different questions even though they use the same dimensions.

For example, tank capacity depends on volume, while paint or cladding required for its outside depends on surface area. Dimensional units are a quick check: m³ is volume; m² is area.

Volume combines three independent length dimensions. For a rectangular prism, cm × cm × cm becomes cm³. Geometrically, cubic units represent how many unit cubes fit inside the solid.

This also affects conversions. If 1 m = 100 cm, then 1 m³ = 100³ cm³ = 1,000,000 cm³. Using only the linear factor would produce a major error.

Total surface area includes every outside face or surface. Lateral surface area usually excludes the bases of a prism or pyramid; curved surface area describes the curved side of solids such as cylinders and cones.

For a closed cylinder, total surface area is 2πr² + 2πrh, while curved surface area is only 2πrh. The calculator labels these separately so you can use the result that matches the physical task.

For an ideal upright cylindrical tank or rectangular tank, the corresponding cylinder or cuboid formula gives the geometric volume. That can be useful for basic planning.

However, real tanks may have dished heads, cones, rounded ends, wall thickness, internal components or partial fill levels. Horizontal-cylinder fill calculations are also different from full-cylinder volume. Those cases deserve a dedicated tank-volume calculator rather than being hidden inside a general geometry tool.

A closed cylinder has two circular ends and one curved side. The two ends contribute 2πr². If the curved surface is unwrapped, it becomes a rectangle with width equal to circumference 2πr and height h, so its area is 2πrh.

Therefore total surface area is 2πr² + 2πrh. Seeing the curved surface as an unwrapped rectangle is often the easiest way to remember where the formula comes from.