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Volume is the three-dimensional space an object occupies — a measure of how much fits inside. How many litres an aquarium holds, a tank's capacity, how many cubic metres of concrete you need, a parcel's shipping volume: all start with a volume calculation. Every solid has its own formula, and placing the height and radius correctly determines the result.
Pick a solid, enter the dimensions, and the volume is calculated instantly in the cube of your unit (cm³, m³…).
Volume Calculator: step-by-step worked example
A cylindrical water tank with a 0.6 m radius and 1.5 m height
- Solid
- Cylinder
- Radius
- 0.6
- Height
- 1.5
- 1
Radius squared
r²
0.6 × 0.6 = 0.36 m²
- 2
Base area
Base = π × r²
3.14159265 × 0.36 = 1.131 m²
- 3
Cylinder volume
V = π × r² × h
1.130973 × 1.5 = 1.6965 m³
- 4
In litres
1 m³ = 1,000 L
1.69646 × 1000 = 1,696.46 L
- Cylinder (πr²h)1.6965 m³
- Cone (πr²h ÷ 3)0.5655 m³
- Sphere (4/3 πr³)0.9048 m³
Good to know: Tanks are usually specified by diameter — the radius is half of it. The result is in cubic input units: metres give m³ (× 1,000 = litres), centimetres give cm³ (= ml).
Volume Calculator — how it works
Formulas
| Solid | Volume formula |
|---|---|
| Cube | side³ |
| Rectangular prism | length × width × height |
| Cylinder | π × radius² × height |
| Sphere | (4 ÷ 3) × π × radius³ |
| Cone | (1 ÷ 3) × π × radius² × height |
Units and litre conversion
- The volume comes out in the cube of whatever unit you enter: metres → m³, centimetres → cm³.
- 1 m³ = 1,000 litres, 1 litre = 1,000 cm³ (1 dm³). For an aquarium or tank, convert to litres: 0.3 m³ = 300 litres.
Common mistakes
- Radius vs diameter: the cylinder, sphere and cone formulas use the radius; if you have the diameter, halve it.
- Cone and sphere coefficients: a cone is one-third of a cylinder with the same base and height; forget the 4/3 in the sphere formula and the result is wrong.
- Correct height axis: in a cylinder and cone the height is the length perpendicular to the base.
For a surface calculation use an area calculator.
Worked example
A cylindrical water tank with a radius of 3 m and a height of 10 m: π × 3² × 10 = 3.14159 × 9 × 10 = 282.74 m³ — that is, it holds 282,743 litres. For comparison, a sphere of radius 6 m is 904.78 m³, and a cone with a 4 m radius and 9 m height is 150.80 m³. Note that the cone is exactly one-third of a cylinder with the same base and height: forgetting that 1/3 coefficient is the most common calculation error.
Volume by side or radius length
| a (side / radius) | Cube (a³) | Sphere (r = a) | Cylinder (r = h = a) | Cone (r = h = a) |
|---|---|---|---|---|
| 1 | 1 | 4.19 | 3.14 | 1.05 |
| 2 | 8 | 33.51 | 25.13 | 8.38 |
| 3 | 27 | 113.1 | 84.82 | 28.27 |
| 4 | 64 | 268.08 | 201.06 | 67.02 |
| 5 | 125 | 523.6 | 392.7 | 130.9 |
| 6 | 216 | 904.78 | 678.58 | 226.19 |
| 7 | 343 | 1,436.76 | 1,077.57 | 359.19 |
| 8 | 512 | 2,144.66 | 1,608.5 | 536.17 |
| 9 | 729 | 3,053.63 | 2,290.22 | 763.41 |
| 10 | 1,000 | 4,188.79 | 3,141.59 | 1,047.2 |
| 12 | 1,728 | 7,238.23 | 5,428.67 | 1,809.56 |
| 15 | 3,375 | 14,137.17 | 10,602.88 | 3,534.29 |
| 20 | 8,000 | 33,510.32 | 25,132.74 | 8,377.58 |
Same unit throughout: sides in cm give cm³ (1,000 cm³ = 1 litre).
Frequently asked questions
How is volume calculated?+
By solid type: cube is side³, prism is length × width × height, cylinder is π × radius² × height, sphere is (4/3)πr³, cone is (1/3)πr² × height. Pick the solid and enter the dimensions.
How do I convert cubic metres to litres?+
1 cubic metre = 1,000 litres. So 282.74 m³ = 282,743 litres. For small volumes use 1 litre = 1,000 cm³ (1 dm³).
What is the formula for the volume of a cylinder?+
The base circle area (πr²) times the height: π × radius² × height. A cylinder with radius 3 and height 10 is 282.74 cubic units.
How are cone and cylinder volumes related?+
A cone with the same base and height is exactly one-third of the cylinder. That is why the cone formula has the 1/3 coefficient; omit it and the volume comes out three times too large.
How do I find how many litres an aquarium holds?+
For a rectangular aquarium, length × width × height, then convert to litres: 50 cm × 30 cm × 40 cm = 60,000 cm³ = 60 litres. If it is not full to the top, use the actual water height.
What unit does volume come out in?+
The cube of the length unit you enter: metres → m³, centimetres → cm³. For litres, multiply an m³ result by 1,000 or divide a cm³ result by 1,000.
Related guides
About this page
- Publisher:
- Kalkoro — Teknolojig Bilişim Teknolojileri A.Ş., İstanbul
- Written by:
- Ahmet Tur — Editor (Math, date & time, unit conversion, physics & chemistry, everyday tools)
- Reviewed by:
- Kübra Yıldız — Editor
Parameters come from official sources; the last update date is shown at the bottom of the page.
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Results are for information only. For official matters the relevant authority's calculation prevails.
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