Volume Calculator
What is the volume formula for each 3D shape?
| Shape | Formula | Variables |
|---|---|---|
| Cube | V = s³ | s = side length |
| Rectangular prism (cuboid) | V = l × w × h | length × width × height |
| Sphere | V = (4/3) × π × r³ | r = radius |
| Cylinder | V = π × r² × h | r = radius, h = height |
| Cone | V = (1/3) × π × r² × h | r = base radius, h = height |
| Pyramid (square base) | V = (1/3) × a² × h | a = base side, h = height |
| Ellipsoid | V = (4/3) × π × a × b × c | a, b, c = three semi-axes |
| Triangular prism | V = 0.5 × b × h × l | b = base, h = height of triangle, l = length |
How do you convert volume units?
| Unit | Cubic Metres | Litres | US Gallons |
|---|---|---|---|
| 1 cubic metre (m³) | 1 | 1,000 | 264.17 |
| 1 litre (L) | 0.001 | 1 | 0.2642 |
| 1 US gallon | 0.003785 | 3.785 | 1 |
| 1 cubic foot (ft³) | 0.02832 | 28.32 | 7.481 |
| 1 cubic inch (in³) | 0.0000164 | 0.01639 | 0.004329 |
Real-world volume examples
A standard bathtub holds approximately 300 litres. An Olympic swimming pool: 2,500 m³ (2.5 million litres). A standard shipping container (20ft): 33.2 m³. The human body: approximately 0.067 m³ (67 litres). Earth's volume: 1.083 × 10¹² km³. Use the volume calculator for any construction, cooking, engineering, or science problem requiring 3D measurement. Related: use the Area Calculator to go further, or the Concrete Calculator for a different angle.
Volume for concrete and construction
For concrete slabs, multiply length × width × depth (all in metres) to get cubic metres. 1 cubic metre = approximately 45 bags of 80 lb pre-mixed concrete, or order ready-mix by the cubic metre. See also the concrete calculator. — see also: area calculator
Frequently asked questions
How do you calculate the volume of a cylinder?
Volume = π × r² × h where r is the radius of the circular base and h is the height. Example: water tank with radius 0.5m and height 2m: π × 0.25 × 2 = 1.571 m³ = 1,571 litres.
How do you find the volume of a sphere?
Volume = (4/3) × π × r³ where r is the radius. A sphere with radius 5cm: (4/3) × π × 125 = 523.6 cm³. In terms of diameter: V = (π/6) × d³.
What is the difference between volume and capacity?
Volume is the total 3D space an object occupies. Capacity is the amount of substance a container can hold — usually slightly less than its volume due to wall thickness. A 1-litre bottle has 1-litre capacity but slightly more than 1 litre of total volume.
How do you calculate volume from weight?
Volume = Mass ÷ Density. Water density = 1 kg/L. So 5 kg of water = 5 litres. Steel density = 7,850 kg/m³. So 100 kg of steel = 100 ÷ 7850 = 0.01274 m³ = 12.74 litres. Use this for any material with a known density.
How is volume used in cooking and baking?
Volume measurements in cooking: 1 tablespoon = 15 ml. 1 cup = 240 ml. 1 US pint = 473 ml. 1 UK pint = 568 ml. Note: cup sizes differ between US (240ml), UK (284ml), and metric (250ml) — always check which system a recipe uses.
Sources & References
Sources: Euclid, Elements; Archimedes, On the Sphere and Cylinder; BIPM SI Units — volume definition (cubic metre); ISO 80000-3.
What is the difference between volume and capacity?
Volume is the total 3D space an object occupies — including its walls. Capacity is the amount a container can hold — the interior space only. A 1-litre plastic bottle has a capacity of 1,000 ml but a volume slightly greater (the plastic walls add ~5–10 ml). In everyday use the terms are interchangeable, but in science and engineering the distinction matters. A fuel tank rated at 60 litres capacity holds 60 litres of fuel — but its total volume including the tank walls is slightly more.
| Volume Units | Litres | Cubic Metres | US Gallons |
|---|---|---|---|
| 1 cubic metre (m³) | 1,000 L | 1 | 264.17 |
| 1 cubic foot (ft³) | 28.317 L | 0.02832 | 7.481 |
| 1 litre | 1 | 0.001 | 0.2642 |
| 1 US gallon | 3.785 L | 0.003785 | 1 |
| 1 UK gallon | 4.546 L | 0.004546 | 1.201 |
| 1 cubic inch (in³) | 0.01639 L | 0.0000164 | 0.00433 |
Volume in cooking: cups, tablespoons, and recipe conversions
Cooking uses volume for liquids and some dry ingredients. Key conversions for recipe scaling:
| Unit | Millilitres | Teaspoons | Tablespoons |
|---|---|---|---|
| 1 US cup | 240 ml | 48 tsp | 16 tbsp |
| 1 UK cup | 284 ml | 57 tsp | 19 tbsp |
| 1 metric cup (Australia) | 250 ml | 50 tsp | 16.7 tbsp |
| 1 US tablespoon | 14.79 ml | 3 tsp | 1 |
| 1 US teaspoon | 4.93 ml | 1 | 1/3 |
| 1 fluid ounce (US) | 29.57 ml | 6 tsp | 2 tbsp |
Warning: US and UK cups differ by 18%. An American recipe calling for "1 cup of flour" means 240 ml — a UK cook using a UK cup (284 ml) will use 18% more flour and the recipe will be off. Always check which cup system a recipe uses.
Real-world volume reference: tanks, pools, and rooms
| Object | Volume | Formula Used |
|---|---|---|
| Standard bathtub | ~300 litres | Approximate cuboid |
| Olympic swimming pool | 2,500 m³ (2.5M litres) | 50m × 25m × 2m = 2,500 m³ |
| Standard shipping container (20ft) | 33.2 m³ | 5.9m × 2.35m × 2.39m |
| Car fuel tank (typical) | 45–70 litres | Measured as capacity |
| Average room (3m × 4m × 2.7m) | 32.4 m³ | Cuboid: l × w × h |
| Football (FIFA standard) | ~5,800 cm³ | Sphere: (4/3)πr³, r=11cm |
Related calculators: Area Calculator for 2D measurements · Concrete Calculator for construction volumes.
Frustum volume: truncated cone or pyramid
A frustum is the portion of a cone or pyramid remaining after the top is cut off with a plane parallel to the base. This shape appears in buckets, flower pots, cooling towers, and drinking cups. Volume of a frustum: V = (πh/3) × (r₁² + r₁r₂ + r₂²), where h = height, r₁ = bottom radius, r₂ = top radius. Example: a bucket with bottom radius 15cm, top radius 20cm, height 30cm: V = (π×30/3) × (225 + 300 + 400) = 31.416 × 925 = 29,059 cm³ = 29.1 litres.
Cavalieri's principle: slicing for volume
Cavalieri's principle states: if two 3D solids have the same cross-sectional area at every height, they have the same volume. This is why a cylinder and an oblique cylinder (tilted) with the same base and height have equal volume. It is also why the formula for a pyramid (V = ⅓Bh) works for oblique pyramids. The principle enables integration-based volume calculations in calculus — cutting a complex solid into infinitely thin slices and summing their areas.
Aquarium and swimming pool volume for chemical dosing
Knowing exact water volume is critical for accurate chemical dosing. Fish tanks are rectangular prisms (length × width × height, all in cm ÷ 1,000 for litres). A 90cm × 40cm × 45cm tank: 90 × 40 × 45 = 162,000 cm³ = 162 litres. For chemical dosing, subtract ~10% for gravel and decorations: effective water volume ≈ 146 litres. Swimming pools: most are combination shapes. A rectangular pool 8m × 4m with depth varying from 1.0m (shallow end) to 1.8m (deep end): average depth = 1.4m → V = 8 × 4 × 1.4 = 44.8 m³ = 44,800 litres.
Capacity vs volume: why your 1-litre bottle holds slightly more
Volume and capacity measure the same thing — three-dimensional space — but the terms are used differently. Volume refers to the amount of space an object occupies. Capacity refers to the maximum amount a container can hold. A 1-litre bottle has a capacity of 1 litre, but its physical volume (including the glass or plastic walls) is slightly more. In cooking and science, "capacity" means how much liquid the container can hold; "volume" is used for solids and gases too.
| Context | Common Units | Key Conversions |
|---|---|---|
| Cooking (liquid) | Cup, tablespoon, teaspoon, ml | 1 cup = 240 ml; 1 tbsp = 15 ml; 1 tsp = 5 ml |
| Science | Litre (L), millilitre (mL), cubic centimetre (cc) | 1 mL = 1 cc exactly |
| Engineering (large) | Cubic metre (m³), cubic foot (ft³) | 1 m³ = 1,000 litres; 1 ft³ = 28.317 litres |
| US cooking | Fluid ounce, pint, quart, gallon | 1 US gallon = 3.785 litres; 1 UK gallon = 4.546 litres |
Cooking volume conversions: scaling a recipe
To scale a recipe from 4 servings to 6 servings, multiply each ingredient by 1.5 (6÷4). Volume conversions most cooks need:
| From | To Cups | To Tablespoons | To Millilitres |
|---|---|---|---|
| 1 cup | 1 | 16 | 240 ml |
| ¾ cup | 0.75 | 12 | 180 ml |
| ½ cup | 0.5 | 8 | 120 ml |
| ⅓ cup | 0.33 | 5⅓ | 80 ml |
| ¼ cup | 0.25 | 4 | 60 ml |
| 1 tablespoon | 0.0625 | 1 | 15 ml |
| 1 teaspoon | 0.021 | ⅓ | 5 ml |
Indian cooking measures: 1 katori ≈ 150–180 ml. 1 glass ≈ 200–250 ml. 1 tumbler ≈ 300–350 ml.
Practical volume applications
Swimming pool volume: A standard residential pool (12m × 5m × 1.5m average depth) = 90,000 litres. A 50m Olympic pool = 2,500 m³ = 2.5 million litres. Pool chemical dosing (chlorine) is typically calculated per 10,000 litres — use the volume calculator to find your pool's volume, then divide by 10,000 for chemical quantities.
Fish tank stocking density: General guideline: 1 cm of adult fish length per 4–5 litres of water. A 100-litre tank (50cm × 40cm × 50cm) can comfortably hold fish totalling 20–25 cm in adult length. Calculate tank volume first, then plan stocking accordingly.
Attic or basement volume for insulation: Measure length × width × average height. A 10m × 8m attic with 1.5m average height = 120 m³. Insulation is sold by coverage area — divide volume by the insulation depth (in metres) to get the floor area to cover. Example: 120 m³ ÷ 0.3m thickness = 40 m² of insulation needed.