# Volume Calculator > Free volume calculator to find the volume of any 3D shape. Calculate volume of cube, sphere, cylinder, cone, pyramid, prism with step-by-step formulas and unit. **URL:** https://calculators.im/volume-calculator **Category:** math **Last updated:** 2026-07-04 Calculate the volume and surface area of any 3D shape including cube, sphere, cylinder, cone, pyramid, prism, ellipsoid, and torus. See step-by-step formulas and unit conversions. This volume calculator helps you find the volume of any common 3D shape. Select your shape, enter the dimensions, and get instant results with detailed step-by-step calculations, formulas, surface area as a bonus, and liquid capacity conversions (liters, gallons). Supports 10 different 3D shapes with metric and imperial unit conversions. ## Formula ``` Cube: V = s³ | Sphere: V = (4/3)πr³ | Cylinder: V = πr²h | Cone: V = (1/3)πr²h | Prism: V = l×w×h ``` **Variables:** - **** — - **** — - **** — - **** — Volume measures the amount of three-dimensional space enclosed by a shape. Each 3D shape has its own formula based on its defining dimensions. Results can be converted to liquid capacity (liters, gallons). ## Worked Example ### Cylinder Volume Example A cylinder with radius 5cm and height 10cm has a volume of π × 25 × 10 = 785.40 cm³, which equals about 0.79 liters. The total surface area (top + bottom + side) is 471.24 cm². ## Pro Tips - Volume is measured in cubic units (cm³, m³, ft³) — not square or linear units - 1 liter = 1,000 cm³ = 0.001 m³ - 1 US gallon ≈ 3.785 liters ≈ 231 in³ - Sphere has the smallest surface area for a given volume - Doubling all dimensions multiplies the volume by 8 (cubic scaling) ## Frequently Asked Questions ### What is the difference between volume and capacity? Volume measures the 3D space an object occupies, expressed in cubic units (cm³, m³). Capacity refers to the amount of substance (usually liquid) a container can hold, expressed in liters or gallons. They're related: 1 liter = 1,000 cm³. ### How do you convert cubic centimeters to liters? Divide cubic centimeters by 1,000 to get liters. For example, 5,000 cm³ = 5 liters. For gallons, divide cm³ by 3,785.41 (US gallon) or 4,546.09 (imperial gallon). ### How do you calculate the volume of an irregular shape? For irregular shapes, you can use water displacement: submerge the object in water and measure the volume of water displaced. For mathematical problems, you can break the shape into simpler shapes, calculate each volume, and add them together. ### What is surface area and how does it relate to volume? Surface area is the total area of all faces/surfaces of a 3D object. While volume measures the space inside, surface area measures the outside. A sphere has the minimum surface area for a given volume, making it the most efficient shape for containers. ### How do I calculate the volume of a cube? Cube the side length: V = s³. A cube with 5 cm sides holds 5 × 5 × 5 = 125 cm³. Because all sides are equal, you only need one measurement. ### How do I calculate the volume of a cylinder? Use V = πr²h: square the radius, multiply by π (≈3.1416), then by the height. A cylinder with radius 5 cm and height 10 cm holds π × 25 × 10 ≈ 785.4 cm³. Remember the radius is half the diameter. ### How do I calculate the volume of a sphere? Use V = (4/3)πr³: cube the radius, multiply by π, then by 4/3. A sphere of radius 6 cm holds (4/3)π × 216 ≈ 904.8 cm³. If you know the diameter, halve it first to get the radius. ### How do I calculate the volume of a cone? Use V = (1/3)πr²h — exactly one-third of a cylinder with the same base and height. A cone with radius 3 cm and height 9 cm holds (1/3)π × 9 × 9 ≈ 84.8 cm³. ### How do I calculate the volume of a rectangular box? Multiply length × width × height: V = l × w × h. A box 30 × 20 × 15 cm holds 9,000 cm³, which equals 9 litres. Use the same unit for all three dimensions. ### How do I calculate the volume of a pyramid? Use V = (1/3) × base area × height. For a square base, base area = side². A pyramid with a 6 m square base and 9 m height holds (1/3) × 36 × 9 = 108 m³. ### How many gallons does my tank hold? Compute the tank's volume in cubic feet, then multiply by 7.481 (US gallons per ft³). A cylindrical tank 6 ft in diameter and 5 ft tall holds π × 3² × 5 = 141.4 ft³ × 7.481 ≈ 1,058 gallons. The calculator does this conversion automatically. ### How do I convert cubic feet to gallons? Multiply cubic feet by 7.481 for US gallons (or 6.229 for imperial gallons). For example, 40 ft³ = 40 × 7.481 ≈ 299 US gallons. To go from cubic feet to litres, multiply by 28.32. ### How do I convert cubic meters to cubic feet? Multiply cubic metres by 35.31. For example, 2 m³ = 70.6 ft³. One cubic metre also equals exactly 1,000 litres or about 264.2 US gallons. ### How do I work out how many cubic yards of concrete I need? Calculate the volume in cubic feet (length × width × thickness, all in feet) and divide by 27. A 10 × 12 ft slab 4 inches (0.333 ft) thick needs 10 × 12 × 0.333 = 40 ft³ ÷ 27 ≈ 1.48 cubic yards. Order a little extra for waste. ## Deep Dive Volume calculation is essential across construction, manufacturing, shipping, cooking, aquariums, landscaping, and countless practical applications where you need to determine how much space a three-dimensional object occupies or how much material it can contain. From basic shapes like cubes (V = s³), cylinders (V = πr²h), and spheres (V = 4/3πr³) to complex forms like truncated cones, ellipsoids, and irregular prisms, each geometry requires its own formula. Our volume calculator supports over 15 common 3D shapes with instant computation in both metric and imperial units, including automatic conversion between cubic inches, cubic feet, cubic meters, liters, gallons, and fluid ounces. Whether you are calculating concrete needed for a foundation, soil for a garden bed, water for a pool, gravel for a driveway, or packaging dimensions for shipping, this tool handles the math and unit conversions that make volume problems surprisingly tricky to solve by hand. ### Volume formulas for common shapes The most frequently used volume formulas all hinge on squaring or cubing a dimension — the kind of power an exponent calculator evaluates instantly: - **Cube:** V = s³ (a 2-foot cube holds 8 cubic feet or 59.8 gallons). - **Rectangular prism:** V = l × w × h. - **Cylinder:** V = πr²h — a 4-foot diameter, 3-foot tall cylindrical tank holds π(2²)(3) = 37.7 ft³ = 282 gallons. - **Sphere:** V = (4/3)πr³. - **Cone:** V = (1/3)πr²h — exactly one-third of a cylinder with the same base and height. - **Pyramid:** V = (1/3) × base area × h. For irregular shapes, break them into simpler components, calculate each separately, and sum the results. A swimming pool with a shallow end (3ft) and deep end (8ft) can be approximated as a rectangular prism with average depth: V = length × width × (3+8)/2. ### Practical volume conversions and estimates Key conversion factors: - 1 cubic foot = 7.481 US gallons = 28.317 liters. - 1 cubic yard = 27 cubic feet = 202 gallons — the standard unit for ordering concrete, mulch, and gravel. - 1 cubic meter = 264.2 gallons = 35.31 cubic feet. **Quick estimation shortcuts:** a standard bathtub holds 40-60 gallons, a hot tub 300-500 gallons, and an average swimming pool 10,000-20,000 gallons. For landscaping, mulch and soil are sold by the cubic yard — a 2-inch layer over a 10×20 foot area requires (10 × 20 × 2/12) / 27 = 1.23 cubic yards. Concrete trucks typically carry 8-10 cubic yards. Always add 10-15% waste factor when ordering materials — irregular shapes, spillage, and settling inevitably consume more material than the pure mathematical volume. ### Volume in shipping and packaging Shipping costs often depend on **dimensional weight** rather than actual weight. Dimensional weight = (L × W × H in inches) / dimensional factor (typically 139 for domestic US, 166 for international). A 24×18×12 inch box has dimensional weight of 24×18×12/139 = 37.3 lbs — if the actual package weighs only 15 lbs, you pay for 37.3 lbs. This makes efficient packaging critical: reducing box dimensions by just 2 inches in each direction (22×16×10) drops dimensional weight to 25.3 lbs — a 32% cost reduction. Cubic capacity utilization matters for truckload shipping: a standard 53-foot trailer holds approximately 3,489 cubic feet or 2,390 cubic feet of palletized freight (accounting for air gaps). Stackability, pallet patterns, and void fill all affect how much of that theoretical capacity you actually use. ### Cube and Rectangular Box Volume Calculator A **cube's** volume is V = s³ — the side length cubed. A 5 cm cube holds 5³ = 125 cm³. A **rectangular box** (rectangular prism) uses V = length × width × height: a 30 × 20 × 15 cm box holds 9,000 cm³ = 9 litres. These two shapes cover most everyday containers, rooms, and shipping boxes. Select 'Cube' or 'Rectangular Prism', enter the dimensions, and the calculator returns volume plus surface area and liquid capacity. ### Cylinder Volume Calculator for Tanks and Pipes A **cylinder's** volume is V = πr²h — the circular base area (πr²) times the height. A tank 4 ft across (radius 2 ft) and 3 ft tall holds π × 2² × 3 = 37.7 ft³ ≈ 282 US gallons. Use this for water tanks, pipes, cans, and silos. Enter the radius (half the diameter) and the height; the tool converts the result to litres and gallons automatically. ### Sphere and Hemisphere Volume Calculator A **sphere's** volume is V = (4/3)πr³. A ball of radius 10 cm holds (4/3)π × 10³ ≈ 4,189 cm³ ≈ 4.19 litres. A **hemisphere** (half a sphere) is exactly half of that: V = (2/3)πr³. Spheres enclose the most volume for the least surface area, which is why bubbles and pressure tanks are round. Enter the radius or diameter to compute it. ### Cone and Pyramid Volume Calculator A **cone** holds exactly one-third of the cylinder that surrounds it: V = (1/3)πr²h. A **pyramid** follows the same one-third rule over its base: V = (1/3) × base area × height — for a triangular base, work out that base area with a triangle calculator first. An ice-cream cone 3 cm across (radius 1.5 cm) and 12 cm tall holds (1/3)π × 1.5² × 12 ≈ 28.3 cm³. Pick 'Cone' or 'Pyramid' and enter the base dimensions and the height. ### Tank Volume in Gallons and Liters To size a tank or container, compute its volume in cubic units, then convert to capacity: - 1 ft³ = 7.481 US gallons = 28.32 litres - 1 m³ = 264.2 gallons = 1,000 litres A cylindrical tank 5 ft tall and 6 ft in diameter holds π × 3² × 5 = 141.4 ft³ ≈ 1,058 gallons. The calculator shows litres and gallons alongside the cubic result so you can order or fill accurately. ### Cubic Meters, Feet, and Yards: Volume Unit Conversion Volume scales with the cube of the linear unit, which is why the volume factors below dwarf the length ratios you would reach for in a general unit converter. Key factors: - 1 m³ = 35.31 ft³ = 1,000 litres - 1 cubic yard = 27 ft³ = 202 gallons (the unit for ordering concrete, mulch, and gravel) - 1 ft³ = 1,728 in³ To order concrete for a 10 × 12 ft slab 4 inches thick: 10 × 12 × (4/12) = 40 ft³ ÷ 27 = 1.48 cubic yards — round up and add a 10% waste factor. ### How to Calculate the Volume of Irregular Shapes Two methods handle irregular objects. - **Water displacement:** submerge the object and measure the water it pushes up — the displaced volume equals the object's volume. - **Decomposition:** split the shape into cubes, cylinders, and cones, compute each, and add them (subtracting any hollows). A bottle, for instance, is a cylinder body plus a cone neck. This is how you estimate volume for real-world objects the standard formulas don't directly cover. ## Related Calculators - [area-calculator](https://calculators.im/area-calculator) - [perimeter-calculator](https://calculators.im/perimeter-calculator) - [concrete-calculator](https://calculators.im/concrete-calculator) - [triangle-calculator](https://calculators.im/triangle-calculator) ## Authoritative Sources - [Khan Academy - Volume](https://www.khanacademy.org/math/geometry/hs-geo-solids) — Educational resource for volume concepts and 3D geometry - [Math is Fun - Volume](https://www.mathsisfun.com/geometry/volume.html) — Clear explanations of volume formulas for various 3D shapes - [Wolfram MathWorld - Volume](https://mathworld.wolfram.com/Volume.html) — Volume formulas for 3D solids - [NIST - Weights and Measures](https://www.nist.gov/pml/owm) — US authority on units of volume and measurement --- *Source: https://calculators.im/volume-calculator — calculators.im, 299+ free online calculators.*