Calculate the volume of common 3D shapes instantly with formulas, diagrams, worked examples, cubic unit conversions and step-by-step solutions.
Volume is the amount of space a 3D object occupies, measured in cubic units. For any prism or cylinder, multiply the base area by the height — a cuboid is l × w × h and a cylinder is πr²h. Cones and pyramids taper, so they hold exactly one third as much: ⅓πr²h and ⅓b²h. A sphere is ⁴⁄₃πr³. Pick a shape below, enter its dimensions, and the calculator returns the volume, the surface area, litres and gallons, fill time, and material weight estimates.
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Enter the dimensions — results update as you type. Every measurement must use the same unit.
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| Unit | Value |
|---|
Need to convert a capacity you already know? Use the volume converter.
| Measurement | Value |
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How long to fill the volume above at a given flow rate. A standard garden tap runs roughly 15–20 L/min.
Convert the volume above into an approximate delivered weight. Densities are typical values — confirm with your supplier.
Freight is charged on whichever is greater: actual weight or volumetric (cubic) weight.
Volume is the amount of three-dimensional space an object occupies. Because it measures three dimensions multiplied together, it is always expressed in cubic units — cubic millimetres, cubic metres, cubic feet. One cubic metre is the space filled by a cube measuring one metre on every edge, and a volume of 12 m³ means twelve of those cubes would fill the shape exactly.
Nearly every volume formula reduces to one idea: base area × height. That is exactly true for anything with parallel ends — a cuboid, a cylinder, any prism. Shapes that taper to a point hold precisely one third as much, which is where the ⅓ in the cone and pyramid formulas comes from. Curved solids like the sphere have their own constants, worked out by Archimedes long before calculus existed.
Volume is how much space something takes up; capacity is how much it can hold. In practice the two are measured with different units for the same physical quantity, and the metric system links them perfectly:
That equivalence is not a coincidence — the litre was defined as a cubic decimetre, a cube 10 cm on each side. It is why a 1,000 mm × 1,000 mm × 1,000 mm water tank holds 1,000 litres, and why converting a tank's dimensions straight into litres is a single step. Strictly, capacity refers to the internal space, so a tank's capacity uses internal dimensions while its external volume includes the wall thickness. For thin-walled tanks the difference is negligible; for thick concrete structures it is not.
| Aspect | Volume | Surface area |
|---|---|---|
| Measures | Space inside | Skin outside |
| Units | Cubic — m³, litres | Square — m² |
| Answers | How much fits in it? | How much to cover it? |
| Buy by it | Concrete, water, soil, gravel | Paint, cladding, insulation, wrapping |
| Scaling | Double the size → 8× the volume | Double the size → 4× the area |
Because they scale differently, the surface-area-to-volume ratio falls as objects grow. A cube of side 1 has a ratio of 6; at side 10 it is 0.6. That single fact explains why small animals lose heat faster and eat proportionally more, why crushed ore dissolves faster than rock, and why a large water tank loses proportionally less heat than a small one. The calculator reports this ratio for every shape. For covering rather than filling, use the surface area calculator.
Cubic conversion factors are the cube of the length factors, which is where most conversion errors come from. Since 1 m = 100 cm, it follows that 1 m³ = 100³ = 1,000,000 cm³ — not 100, and not 10,000.
| Conversion | Factor | Where it is used |
|---|---|---|
| 1 m³ | = 1,000,000 cm³ = 1,000,000,000 mm³ | The metric chain, cubed |
| 1 m³ | = 1,000 litres | Tanks, pools, concrete, irrigation |
| 1 litre | = 1,000 cm³ = 1,000 mL | Everyday capacity |
| 1 ft³ | = 0.0283168 m³ = 28.3168 litres | Imperial plans, US freight |
| 1 m³ | ≈ 35.3147 ft³ | Converting imperial drawings |
| 1 yd³ | = 0.764555 m³ | Concrete and soil in the US |
| 1 US gallon | = 3.785412 litres | US fuel and liquids |
| 1 imperial gallon | = 4.54609 litres | UK and older Australian figures |
| 1 in³ | = 16.3871 cm³ | Engine capacity, machining |
V = s³. All three dimensions are equal, so multiply the side by itself three times. A cube of side 5 holds 125 cubic units. Note that s³ means s × s × s, not s × 3 — a mistake that turns 125 into 15.
V = l × w × h. The base area is l × w, and multiplying by the height stacks that base all the way up. For 8 × 5 × 4 the volume is 160 cubic units. This is the formula behind concrete slabs, shipping cartons, excavations and rectangular tanks — probably the most used volume formula in the building trades.
V = πr²h. Again base area times height, with the base being a circle of area πr². For r = 5 and h = 10 the base is 78.54 and the volume is 785.40 cubic units. Cylinders cover water tanks, pipes, columns, silos, drums and post holes. Remember to halve the diameter first: a 3 m diameter tank has r = 1.5.
V = ⅓πr²h. A cone holds exactly one third of the cylinder with the same base and height — a classroom experiment worth doing once with sand, because it makes the ⅓ memorable. Note that volume uses the vertical height, unlike surface area, which needs the slant height.
V = ⁴⁄₃πr³. For r = 10 the volume is about 4,188.79 cubic units. Because the radius is cubed, volume grows very fast: double the radius and the volume becomes eight times larger. That is why a 600 mm diameter ball holds eight times as much as a 300 mm one, not twice.
V = ⅔πr³ — exactly half the sphere. A hemisphere of radius 8 holds about 1,072.33 cubic units. Dome roofs, bowl-shaped tank ends and hemispherical caps all use it, and it combines with the cylinder formula to handle the domed ends of pressure vessels.
V = base area × length. Any prism follows this rule, whatever the cross-section — triangular, hexagonal, L-shaped, irregular. For a triangular prism with base sides 5, 6 and 7 and a length of 10, Heron's formula gives a base area of about 14.70, so the volume is about 146.97. This is also the practical method for oddly shaped channels and gutters: find the cross-sectional area once, then multiply by the run.
V = ⅓ × base area × h. Like the cone, a pyramid is one third of the prism sharing its base and height. A square pyramid with b = 6 and h = 8 holds ⅓ × 36 × 8 = 96 cubic units. The height must be the perpendicular distance from base to apex, not the sloping edge.
The remaining shapes handle the cases that come up in engineering and manufacturing:
| Field | What volume is used for | Example |
|---|---|---|
| Construction | Concrete, fill, excavation and screed quantities | A 6 × 4 m slab at 100 mm = 2.4 m³ of concrete |
| Civil engineering | Earthworks cut and fill, culvert and pipe capacity | Balancing cut against fill minimises truck movements |
| Architecture | Room volumes for ventilation and heating loads | Air changes per hour are calculated from room volume |
| Water storage | Rainwater tanks, dams, reservoirs | A 2 m × 2.5 m round tank holds about 7,854 L |
| Swimming pools | Capacity for chemical dosing and heating | An 8 × 4 m pool at 1.5 m average = 48,000 L |
| Agriculture | Silo capacity, spray tanks, irrigation volumes | Grain silos are quoted in cubic metres or tonnes |
| Chemical storage | Vessel capacity, bunding requirements | Bunds must hold a set percentage of tank volume |
| Manufacturing | Material per unit, mould and casting volumes | Injection shot size comes from part volume |
| Packaging | Carton sizing and fill efficiency | Cubic efficiency decides how many fit on a pallet |
| Warehousing | Storage capacity in cubic metres | Racking is planned by cubic space, not floor area |
| Freight and logistics | Volumetric weight and container loading | Air freight charges 1 m³ as 167 kg |
| Mining | Ore and overburden volumes, stockpiles | A conical stockpile uses ⅓πr²h |
| Mistake | Why it goes wrong | How to avoid it |
|---|---|---|
| Mixing units | Metres × millimetres produces nonsense | Convert everything first — 100 mm becomes 0.1 m |
| Not cubing the conversion factor | 1 m³ is 1,000,000 cm³, not 100 or 10,000 | Cube the length factor every time |
| Reading s³ as s × 3 | Cubing means multiplying by itself three times | 5³ = 125, not 15 |
| Using diameter instead of radius | πr² becomes four times too large | Halve the diameter before squaring |
| Forgetting the ⅓ for cones and pyramids | Gives three times the real volume | Tapered shapes always carry the ⅓ |
| Using slant height for volume | Volume needs the perpendicular height | Slant height belongs to surface area, not volume |
| Giving the answer in square units | Volume is cubic | Check the unit: m³ or litres, never m² |
| Assuming double size means double volume | Volume scales with the cube of length | Double the dimensions → eight times the volume |
| Using external dimensions for capacity | Wall thickness reduces the usable space | Measure internally for tanks and vessels |
| Ordering exactly the calculated amount | Spillage, over-excavation and settlement all consume extra | Add around 5–10% for concrete and bulk fill |
V = s³ | Cuboid: V = lwhV = πr²h | Cone: V = ⅓πr²hV = ⁴⁄₃πr³ | Hemisphere: V = ⅔πr³V = A × h | Pyramid: V = ⅓ × A × hV = πr²h + ⁴⁄₃πr³ | Ellipsoid: V = ⁴⁄₃πabcV = 2π²Rr²V = ⅓πh(r₁² + r₁r₂ + r₂²)1 m³ = 1,000 L = 1,000,000 cm³ | 1 L = 1,000 cm³ = 1,000 mL1 ft³ = 28.3168 L | 1 m³ = 35.3147 ft³ | 1 yd³ = 0.764555 m³1 US gal = 3.785412 L | 1 imp gal = 4.54609 L×k on lengths → ×k³ on volume2.4 t/m³ | Water = 1 t/m³ | Gravel ≈ 1.6 t/m³
1) 4³ = 64 cm³ 2) 10 × 5 × 2 = 100 cm³ 3) π × 9 × 10 ≈ 282.74 cm³ 4) 1,000 litres 5) ⁴⁄₃π × 27 ≈ 113.10 cm³
1) r = 1.2, V = π × 1.44 × 2 ≈ 9.0478 m³ ≈ 9,048 L 2) 7 × 5 × 0.125 = 4.375 m³, about 10.5 t at 2.4 t/m³ 3) Cylinder = π × 36 × 10 ≈ 1,130.97; cone = ⅓ of that ≈ 376.99; ratio 3 : 1 4) 2,500 L, about 88.29 ft³, about 660.43 US gallons 5) Average depth 1.6 m, so 10 × 5 × 1.6 = 80 m³ = 80,000 L 6) 27 versus 216 — eight times larger, because 2³ = 8 7) πr²h = π × 0.25 × 2 ≈ 1.5708, plus ⁴⁄₃π × 0.125 ≈ 0.5236, total ≈ 2.0944 m³ ≈ 2,094 L 8) 0.05 m³ × 167 = 8.35 kg, which exceeds the 7 kg actual weight, so it is charged as 8.35 kg
What is volume?
Volume is the amount of three-dimensional space an object occupies, measured in cubic units such as cm³ or m³. Because it multiplies three dimensions together, the units are cubed. A volume of 12 m³ means twelve cubes each measuring one metre on every edge would exactly fill the shape.
How do you calculate volume?
For anything with parallel ends — a cuboid, cylinder or any prism — multiply the base area by the height. For shapes that taper to a point, such as cones and pyramids, take one third of that: V = ⅓ × base area × height. Curved solids have their own formulas: a sphere is ⁴⁄₃πr³ and a hemisphere half of that. Convert every dimension to the same unit before multiplying.
What is the volume formula?
Each shape has its own, but they share a pattern. Cube V = s³, cuboid V = lwh, cylinder V = πr²h, cone V = ⅓πr²h, sphere V = ⁴⁄₃πr³, hemisphere V = ⅔πr³, prism V = base area × length, pyramid V = ⅓ × base area × height. The general rule is base area × height, with a factor of ⅓ for anything that tapers.
How do you calculate the volume of a cube?
Cube the side length: V = s³. A cube with sides of 5 has a volume of 5 × 5 × 5 = 125 cubic units. Remember that s³ means the side multiplied by itself three times, not the side times three — 5³ is 125, not 15.
How do you calculate the volume of a cylinder?
V = πr²h, where r is the radius of the circular base and h the height. Find the base circle area first, then multiply by the height. For r = 5 and h = 10: π × 25 = 78.54, times 10 gives about 785.40 cubic units. If you were given the diameter, halve it first — a 3 m diameter tank has a radius of 1.5 m.
How do you calculate the volume of a sphere?
V = ⁴⁄₃πr³. For a radius of 10: r³ = 1,000, so V = ⁴⁄₃ × π × 1,000 ≈ 4,188.79 cubic units. Because the radius is cubed, volume grows very quickly — doubling the radius multiplies the volume by eight, since 2³ = 8.
How do you calculate the volume of a cone?
V = ⅓πr²h. A cone holds exactly one third of the cylinder that shares its base radius and height, which is why the ⅓ appears. For r = 4 and h = 9 the volume is about 150.80 cubic units against the cylinder's 452.39. Use the vertical height here, not the slant height — slant height belongs to surface area calculations.
How do you calculate the volume of a prism?
V = base area × length, whatever the cross-section. Work out the area of one end, then multiply by how long the prism runs. For a triangular prism with base sides 5, 6 and 7 and a length of 10, Heron's formula gives a base area of about 14.70, so the volume is about 146.97 cubic units. The same method handles hexagonal, L-shaped and irregular cross-sections such as gutters and channels.
How do you calculate the volume of a pyramid?
V = ⅓ × base area × perpendicular height. A square pyramid with a base side of 6 and a height of 8 holds ⅓ × 36 × 8 = 96 cubic units. As with the cone, a pyramid is exactly one third of the prism sharing its base and height, and the height must be measured straight up from the base, not along a sloping edge.
What units are used for volume?
Cubic units: cubic millimetres, cubic centimetres and cubic metres in metric, or cubic inches, cubic feet and cubic yards in imperial. Capacity is usually given in millilitres and litres, which link exactly to the metric chain — 1 mL = 1 cm³ and 1 litre = 1,000 cm³. Australia uses the metric system, so tanks and pools are quoted in litres and concrete in cubic metres.
What is cubic volume?
"Cubic volume" simply means volume expressed in cubic units, and the phrase is common in freight and storage, where space is sold by the cubic metre. One cubic metre — often written CBM — is a cube one metre on each side, and it is the unit warehouses, shipping lines and removalists price against.
What is the difference between volume and capacity?
Volume is how much space something takes up; capacity is how much it can hold. They measure the same quantity in different units, linked by the definition of the litre as a cubic decimetre: 1 litre = 1,000 cm³ and 1 m³ = 1,000 litres. Strictly, capacity uses internal dimensions while volume may include the walls, which matters for thick-walled concrete structures but is negligible for a thin plastic tank.
What is the difference between area and volume?
Area measures a flat surface in square units; volume measures space inside a solid in cubic units. A floor has an area of 20 m²; the room above it has a volume of 48 m³. Area answers how much surface to cover, volume answers how much fits inside.
What is the difference between surface area and volume?
Surface area is the total of all the outer surfaces of a 3D object, in square units; volume is the space inside, in cubic units. Paint, cladding and wrapping are surface-area problems, while concrete, water and soil are volume problems. They scale differently too: double every dimension and surface area quadruples while volume grows eightfold.
How do you convert litres to cubic metres?
Divide litres by 1,000, since 1 m³ = 1,000 litres. So 7,854 litres is 7.854 m³. Going the other way, multiply cubic metres by 1,000. For smaller quantities, 1 litre = 1,000 cm³ = 1,000 mL, and 1 mL equals exactly 1 cm³.
How do you convert cubic feet to cubic metres?
Multiply cubic feet by 0.0283168, because a foot is 0.3048 m and 0.3048³ = 0.0283168. So 100 ft³ ≈ 2.83 m³. In reverse, multiply cubic metres by about 35.3147. One cubic foot also holds about 28.32 litres.
How do you calculate water tank volume?
Most tanks are cylinders, so use V = πr²h with internal dimensions, then multiply cubic metres by 1,000 for litres. A tank 2 m across and 2.5 m tall has r = 1 m, giving π × 1 × 2.5 ≈ 7.854 m³, or about 7,854 litres. Allow some freeboard at the top, since a tank is rarely filled to the very brim, and remember that the rated capacity of a commercial tank is usually the usable figure rather than the geometric one.
How do you calculate concrete volume?
Multiply length by width by thickness, converting the thickness to metres first. A 6 m × 4 m slab at 100 mm is 6 × 4 × 0.1 = 2.4 m³. Concrete weighs roughly 2.4 tonnes per cubic metre, so that slab is about 5.76 tonnes. Order about 5–10% extra to cover spillage, uneven subgrade and over-excavation — running short mid-pour is far more costly than a small excess.
How do you calculate swimming pool volume?
For a rectangular pool, multiply length × width × average depth. A pool 8 m × 4 m with an average depth of 1.5 m holds 48 m³, which is 48,000 litres. If the floor slopes evenly, the average depth is simply the shallow and deep measurements averaged — 1.2 m and 1.8 m gives 1.5 m. Capacity matters because chemical dosing and heater sizing are both calculated per litre.
How do you estimate excavation volume?
Multiply the plan area by the average depth for a rectangular dig, or split irregular excavations into simpler blocks and add them. Two practical adjustments matter: excavated soil bulks up by roughly 20–30% once loosened, so the truck volume exceeds the hole volume, and material that will be compacted back needs more than the neat volume suggests.
How do you calculate shipping volume?
Multiply length × width × height in metres to get cubic metres, then compare against the carrier's volumetric conversion. Air freight commonly charges 1 m³ as 167 kg, sea LCL as 1,000 kg, and Australian road freight often around 333 kg. A 600 × 400 × 300 mm carton is 0.072 m³, giving an air-freight volumetric weight of about 12 kg — so a 9 kg carton is billed as 12 kg.
How do builders and engineers calculate volume?
By breaking the structure into standard shapes and adding the parts. Slabs, footings and beams are cuboids; columns, piles and post holes are cylinders; stockpiles are cones; hoppers and tapered silos are frustums. Engineers use the same figures for capacity, mass, buoyancy and flow, and volume converts to weight through material density — concrete at about 2.4 t/m³, water at exactly 1 t/m³.
How do you find the volume of an irregular shape?
Either split it into standard shapes and add the volumes, or use water displacement — submerge the object and measure how much the water level rises. That displacement method is Archimedes' original insight, and it remains the most practical approach for genuinely irregular objects. For long irregular runs like a gutter or channel, find the cross-sectional area once and multiply by the length.
What are common volume calculation mistakes?
Mixing units, especially millimetres with metres; forgetting to cube the conversion factor, so 1 m³ becomes 100 cm³ instead of 1,000,000; reading s³ as s × 3; using the diameter as the radius; leaving out the ⅓ for cones and pyramids; using slant height instead of perpendicular height; giving the answer in square units; and assuming that doubling the dimensions doubles the volume when it actually multiplies it by eight.
Does this volume calculator show the formula and steps?
Yes. For every shape it shows the formula, the working line by line, the surface area and base area, the surface-area-to-volume ratio and a labelled diagram. It converts the result into cubic millimetres, centimetres and metres, litres, millilitres, cubic inches, feet and yards, and both US and imperial gallons. It also estimates tank fill time from a flow rate, converts the volume into tonnes of concrete, soil or gravel, and calculates air, road and sea freight volumetric weight.
A one-page reference with volume and surface area for all twelve shapes plus every cubic conversion. Use the button to print it or save it as a PDF — the rest of the page is hidden from the printout.
MegaCalcOnline.com · 3D shape volumes, surface areas and cubic conversions
| Shape | Volume | Surface area |
|---|---|---|
| Cube | V = s³ | 6s² |
| Cuboid | V = l × w × h | 2(lw + lh + wh) |
| Cylinder | V = πr²h | 2πr(r + h) |
| Cone | V = ⅓πr²h | πr(r + l), l = √(r² + h²) |
| Sphere | V = ⁴⁄₃πr³ | 4πr² |
| Hemisphere | V = ⅔πr³ | 3πr² |
| Prism (any) | V = A × h | 2A + Ph |
| Pyramid | V = ⅓A × h | A + ½Pl |
| Capsule | V = πr²h + ⁴⁄₃πr³ | 4πr² + 2πrh |
| Ellipsoid | V = ⁴⁄₃πabc | No simple exact formula |
| Torus | V = 2π²Rr² | 4π²Rr |
| Frustum | V = ⅓πh(r₁² + r₁r₂ + r₂²) | π(r₁+r₂)l + πr₁² + πr₂² |
| Conversions & densities | Value |
|---|---|
| 1 m³ | = 1,000 L = 1,000,000 cm³ = 1,000,000,000 mm³ |
| 1 litre | = 1,000 cm³ = 1,000 mL (1 mL = 1 cm³) |
| 1 ft³ | = 0.0283168 m³ = 28.3168 L |
| 1 m³ | ≈ 35.3147 ft³ |
| 1 yd³ | = 0.764555 m³ |
| 1 US gallon | = 3.785412 L |
| 1 imperial gallon | = 4.54609 L |
| 1 in³ | = 16.3871 cm³ |
| Scaling | ×k on lengths → ×k³ on volume |
| Concrete / water / gravel | ≈ 2.4 / 1.0 / 1.6 tonnes per m³ |
| Freight volumetric weight | air 167, road ~333, sea 1,000 kg per m³ |
Educational use only. Volume uses perpendicular height, never slant height. Add 5–10% when ordering concrete or bulk fill.