Volume Calculator

The calculator covers 7 shapes: cube (V = s^3), rectangular prism (V = l x w x h), sphere (V = (4/3) x pi x r^3), cylinder (V = pi x r^2 x h), cone (V = (1/3) x pi x r^2 x h), square pyramid (V = (1/3) x s^2 x h), and ellipsoid (V = (4/3) x pi x a x b x c). Surface area is also shown for every shape except the ellipsoid, where no simple closed-form exists.

Use any unit you like, but keep all dimensions in the same unit throughout. Enter inches and you get cubic inches; enter centimeters and you get cubic centimeters. The calculator does not convert between unit systems, so mixing feet and inches in one calculation will produce a wrong answer.

Three practical approaches: approximate the object with the closest supported shape, break it into simpler pieces and add their volumes, or use water displacement - submerge the object in a measuring container and read off how much water it displaces. Displacement works well for small solid objects like a rock or a figurine.

Volume measures how much 3D space an object fills, expressed in cubic units (in^3, cm^3, etc.). Surface area measures the total area covering the outside of that object, expressed in square units. Think of volume as how much water a shape holds and surface area as how much paint it takes to coat the outside.

Common uses include sizing aquariums, storage tanks, and swimming pools; calculating how much concrete, soil, or gravel a landscaping project needs; optimizing packaging and shipping boxes; and solving physics problems that involve density (mass / volume). Knowing the volume of a cylinder, for example, tells you exactly how many gallons a round stock tank holds.