Area and Volume Formulas for Common Shapes

Area measures the space inside a flat shape, in square units; perimeter is the distance around it. A rectangle's area is length times width, and its perimeter is twice the sum of the two sides. A triangle's area is one-half the base times the height.

The circle is the one everyone looks up: its area is π times the radius squared (A = πr²), and the distance around it, the circumference, is 2πr. For a radius of 5, the area is π × 25 ≈ 78.54 square units.

Volume measures the space inside a solid, in cubic units, while surface area is the total area of all its faces. A rectangular prism has a volume of length times width times height. A cylinder's volume is the area of its circular base times its height: V = πr²h.

A sphere's volume is 4/3 × πr³ and its surface area is 4πr². A cone's volume is one-third that of a cylinder with the same base and height, or 1/3 × πr²h. Each combines a base shape with a rule for extending it into three dimensions.

The key is matching the formula to the shape and keeping your units consistent — if the radius is in centimeters, the area comes out in square centimeters and the volume in cubic centimeters. Mixing units is the most common source of wrong answers.

The geometry calculator applies the right formula automatically and shows the working, so you can enter measurements and get the area, perimeter, surface area, or volume with the formula spelled out — useful for checking homework or sizing a real-world project.