Volume Calculator
Pick a shape and type its sizes in any mix of units to get the volume in litres, gallons or cubic units, plus the surface area and the working.
The size you pick is worked out from this volume and the other sizes, and filled in below.
For example 12 identical jars or 4 fence posts.
Typical values: real materials vary with temperature, moisture and mix. The shape is treated as solid all the way through (a tube counts only its wall).
Working: volume
Working: surface area
How your volume is worked out
Put every size in one unit, use the shape’s formula, then convert to litres or gallons.
- 1
Sizes in cm
30, 20, 10 cm
- 2
Find the volume
l × w × h30 × 20 × 10= 6,000 cm³
- 3
Add up the surface
2 × (lw + lh + wh)2 × (600 + 300 + 200)= 2,200 cm²
- 4
Turn it into litres
6,000 cm³ ÷ 1,000= 6 litres= 1.58503 US gal
Read more: every formula, a worked example and unit tables
Volume is how much space a shape takes up, measured in cubic units (cm³, m³, in³, ft³) or in litres and gallons. Every size must be in the same unit before you multiply, so the calculator first changes them all to the unit you used most.
The formula
cube = side³ · surface = 6 × side²
box = length × width × height · surface = 2 × (lw + lh + wh)
cylinder = π × radius² × height · surface = 2π × r × (r + h)
cone = π × r² × h ÷ 3 · surface = π × r × (r + slant), slant = √(r² + h²)
sphere = 4/3 × π × r³ · surface = 4 × π × r²
hemisphere = 2/3 × π × r³ · surface = 3 × π × r²
pyramid = base length × base width × height ÷ 3
triangular prism = triangle area × length, triangle area = √(s(s − a)(s − b)(s − c)), s = (a + b + c) ÷ 2
capsule = π × r² × middle length + 4/3 × π × r³
frustum = π × h ÷ 3 × (R² + R × r + r²)
tube = π ÷ 4 × (outside diameter² − inside diameter²) × length
ellipsoid = 4/3 × π × a × b × c
spherical cap = π × h² × (3r − h) ÷ 3
torus = 2 × π² × R × r² · surface = 4 × π² × R × r
litres = cm³ ÷ 1,000 · weight = volume × density
Worked example
A box 30 cm long, 20 cm wide and 10 cm high. The volume is 30 × 20 × 10 = 6,000 cm³. The surface area is 2 × (30 × 20 + 30 × 10 + 20 × 10) = 2 × (600 + 300 + 200) = 2,200 cm². As 1,000 cm³ is 1 litre, the box holds 6,000 ÷ 1,000 = 6 litres, which is 6 ÷ 3.785411784 = 1.58503 US gallons or 6 ÷ 4.54609 = 1.31981 UK gallons. Filled with water (about 1 kg per litre) it would weigh about 6 kg.
Volume units
| Unit | In litres | Note |
|---|---|---|
| 1 cm³ (1 mL) | 0.001 | 1,000 mm³ |
| 1 m³ | 1,000 | 1,000,000 cm³ |
| 1 in³ | 0.016387064 | 2.54 cm cubed |
| 1 ft³ | 28.316846592 | 1,728 in³ |
| 1 yd³ | 764.554857984 | 27 ft³ |
| 1 US gallon | 3.785411784 | 231 in³, 128 US fl oz |
| 1 UK gallon | 4.54609 | 160 UK fl oz |
| 1 US fl oz | 0.0295735295625 | 1/128 US gallon |
| 1 UK fl oz | 0.0284130625 | 1/160 UK gallon |
These are exact definitions (the inch is exactly 2.54 cm).
Typical densities for the weight
Weight = volume × density. Water is about 1,000 kg/m³ (1 kg per litre), sea water about 1,025, ice 917, petrol about 740, diesel about 840, concrete about 2,400, dry sand about 1,600, pine about 500, glass about 2,500, aluminium 2,700, steel about 7,850, copper 8,960 and gold 19,300 kg/m³. These are typical figures; the real value depends on temperature, moisture, mix and grade.
Notes
- The ellipsoid's surface area has no simple exact formula. The calculator uses Knud Thomsen's approximation (p = 1.6075), which is within about 1.06% of the exact value; when all three semi-axes are equal it is exact (a sphere).
- A tube's volume is the material in its wall. The space inside (what a pipe holds) is shown in the note, as π ÷ 4 × inside diameter² × length.
- "A missing size" finds the size that gives the volume you type, keeping the other sizes, by narrowing it down step by step until it matches.
Common questions
How do I calculate volume?
Multiply the sizes that give the space inside, all in the same unit. For a box it's length × width × height: 30 cm × 20 cm × 10 cm = 6,000 cm³. Because 1,000 cm³ is 1 litre, that box holds 6 litres. Other shapes have their own formula, shown in the working.
How do I find the volume of a cylinder?
Multiply π by the radius squared and by the height: V = π × r² × h. A cylinder with a 5 cm radius and 20 cm height holds π × 25 × 20 = 1,570.8 cm³, or about 1.57 litres. If you know the diameter, halve it first to get the radius, or switch the calculator to diameter.
How do I find the volume of a sphere?
Use V = 4/3 × π × r³. A ball with a 10 cm radius has a volume of 4/3 × π × 1,000 = 4,188.79 cm³, which is about 4.19 litres. Its surface area is 4 × π × r² = 1,256.64 cm².
How many litres are in a cubic metre or a gallon?
1 cubic metre is 1,000 litres and 1 litre is 1,000 cm³ (millilitres). A US gallon is 3.785411784 litres and a UK (imperial) gallon is 4.54609 litres, so the two gallons are not the same. 1 cubic foot is about 28.3168 litres.
How do I work out how much something weighs from its volume?
Multiply the volume by the material's density. Water is about 1,000 kg per m³, so 6 litres of water weighs about 6 kg. Concrete is typically about 2,400 kg per m³ and steel about 7,850 kg per m³. Pick a material in Advanced mode, or type your own density.
What is the difference between volume and surface area?
Volume is the space inside a shape, in cubic units such as cm³ or litres. Surface area is the total area of its outside, in square units such as cm². The 30 × 20 × 10 cm box holds 6,000 cm³ and has 2,200 cm² of outside surface, which is what you'd paint or wrap.
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