Volume of solids
Pick a shape, enter its measurements, and get the volume and total surface area — along with the exact formulas used for the calculation.
Formulas:
Use the same unit for every measurement. Enter inches and the volume is in cubic inches (in³) with the surface area in square inches (in²); enter cm and you get cm³ and cm². Handy conversions: 1,728 in³ = 1 cubic foot, 1,000 cm³ = 1 liter.
The volume formulas, demystified
For solids with flat faces, you simply multiply the dimensions: a cube is s³, a box is a·b·c. Round solids bring π into play: a cylinder is π·r²·h (base area times height) and a sphere is 4/3·π·r³. Cones and pyramids follow the "one-third rule": each holds exactly 1/3 of the volume of the cylinder or prism with the same base and height — that's why their formulas divide by 3. For the surface area of cones and pyramids, this tool works out the slant height for you using the Pythagorean theorem, starting from the radius (or base side) and the height.
From cubic inches to gallons (and cm³ to liters)
Volume answers practical questions: how much water an aquarium holds, how much potting soil a planter needs, how much room a package takes up. In US units, 1 gallon = 231 in³ and 1 cubic foot = 7.48 gallons; in metric, 1,000 cm³ = 1 liter and 1 m³ = 1,000 liters. Example: a 20×10×12-inch aquarium has a volume of 2,400 in³ — about 10.4 gallons. As with areas, convert everything to the same unit before you calculate.