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Basic Geometry Formulas: Area, Perimeter, and Volume

Tap a shape to see its key formulas.

Rectangle

Area = length × width. Perimeter = 2 × (length + width). A square is simply a special case of a rectangle where all four sides are equal in length.

Triangle

Area = ½ × base × height. Perimeter = the sum of all three side lengths. The height used in the area formula must be measured perpendicular to the chosen base.

Circle

Area = π × radius². Circumference (perimeter) = 2 × π × radius. The constant π (pi) is approximately 3.14159, representing the ratio of a circle's circumference to its diameter.

Trapezoid

Area = ½ × (base 1 + base 2) × height, where base 1 and base 2 refer to the lengths of the two parallel sides.

Cube and Rectangular Prism

Volume = length × width × height. Surface area = 2 × (length×width + width×height + length×height). A cube is simply a special case where all three dimensions are equal.

Cylinder

Volume = π × radius² × height. Surface area = 2 × π × radius × (radius + height), accounting for both circular ends and the curved side surface.

Sphere

Volume = (4/3) × π × radius³. Surface area = 4 × π × radius². Unlike most other shapes, a sphere's dimensions are described entirely by a single radius value.

A quick reference for the formulas people forget most often

While area, perimeter, and volume formulas are typically taught in school, they're also some of the most commonly forgotten mathematical facts in daily life, which is why having a quick, organized reference on hand can be useful for everything from home improvement projects to helping with schoolwork.

Frequently Asked Questions

What is the difference between area and perimeter?

Perimeter measures the total distance around the outside edge of a two-dimensional shape, while area measures the total amount of space enclosed within that shape — perimeter is measured in linear units (like meters), while area is measured in square units (like square meters).

Why does a sphere only need one measurement (radius) to calculate its volume and surface area?

Because a sphere is perfectly symmetrical in every direction from its center, a single radius value is sufficient to fully define its size, unlike shapes such as rectangular prisms that require separate length, width, and height measurements.