Volume Calculator

About the Volume Calculator

A volume calculator computes the volume of any three-dimensional shape — rectangular prism (box), cube, cylinder, sphere, cone, pyramid, triangular prism, ellipsoid, capsule, or frustum (truncated cone) — from its dimensions. Volume calculations are essential for a wide range of practical tasks: calculating the capacity of tanks and containers, determining concrete, soil, or gravel quantities for construction, sizing aquariums and pools, computing material volumes for manufacturing, solving geometry problems, and scaling up recipes. Our free volume calculator handles all common 3D shapes with step-by-step formula display, accepts any length unit (metres, feet, inches, centimetres), and converts the result to volume units including cubic metres, cubic feet, cubic inches, litres, gallons (US and UK), and cubic centimetres. It also includes a liquid capacity converter showing how many standard containers the calculated volume fills.

How It Works

Key volume formulas: Rectangular prism (box): V = length x width x height. Example: 3m x 4m x 2.5m room = 30 m^3 of air space. Cylinder: V = pi x r^2 x height. A 2-foot radius, 4-foot tall tank: V = pi x 4 x 4 = 50.27 cubic feet = 376 gallons. Sphere: V = (4/3) x pi x r^3. Basketball (diameter 9.4 in, r=4.7 in): V = (4/3) x pi x 103.8 = 434 cubic inches. Cone: V = (1/3) x pi x r^2 x height. Note: cone volume is exactly 1/3 of the cylinder with same base and height. Pyramid: V = (1/3) x base area x height. This 1/3 factor is true for any pyramid or cone. Triangular prism: V = 0.5 x base x height_of_triangle x length_of_prism. Sphere versus cylinder of same diameter and height: sphere volume = (2/3) x cylinder volume — Archimedes proved this 2,200 years ago.

Tips & Best Practices

• ✓The 1/3 rule: cone and pyramid volumes are always exactly 1/3 of the corresponding cylinder or prism with the same base dimensions and height. This is a profound geometric relationship that makes volume comparison intuitive.
• ✓Aquarium volume calculation: L(in) x W(in) x H(in) / 231 = US gallons. A 24"x12"x16" aquarium = 24x12x16/231 = 19.9 gallons.
• ✓Concrete for a cylindrical column: pi x r^2 x height in cubic feet, divided by 27 = cubic yards. A 12-inch diameter, 8-foot column: pi x 0.25 x 8 / 27 = 0.233 cubic yards.
• ✓Water weight: 1 US gallon of fresh water weighs 8.34 lbs; 1 litre weighs exactly 1 kg. Volume-to-weight conversion is direct for water: 100 litres = 100 kg.
• ✓Pool volume: a standard 12ft x 24ft rectangular pool averaging 5 feet deep = 12x24x5 = 1,440 cubic feet = 10,769 gallons. Chemical dosing, pump sizing, and heating calculations all depend on accurate pool volume.
• ✓Partial filling: the volume of a horizontally oriented cylinder (like a storage tank) filled to height h requires integration — our calculator handles this partial cylinder calculation.
• ✓Scale models: volumes scale as the cube of the linear dimension. A model at 1:10 scale has 1/1000 the volume of the original. This explains why scale models look small even when linear dimensions look similar.
• ✓Volume versus capacity: volume is a measurement of 3D space; capacity is how much liquid a container can hold. They are numerically equal for perfect containers but differ in practice due to wall thickness and fill lines.

Who Uses This Calculator

Homeowners calculate room air volumes for HVAC sizing, humidifier capacity, and paint coverage calculations. Construction contractors estimate concrete volumes for columns, slabs, and footings. Aquarium hobbyists calculate tank volume for stocking capacity and chemical dosing. Pool owners calculate pool volume for chlorine dosing, heating costs, and pump sizing. Engineers size storage tanks, pressure vessels, and industrial containers. Students solve geometry volume problems in school. Farmers calculate grain bin and silo capacities. Manufacturers calculate material volumes for cost estimation and production planning.