How to Calculate Area: Rectangle, Triangle, Circle and Trapezoid

 

To calculate an area, identify the shape, measure the required dimensions and use one consistent length unit. Rectangle, triangle, circle and trapezoid formulas answer different geometric questions. Choosing the right formula matters as much as entering the right numbers, especially when a sloping side is confused with a height or a diameter is entered as a radius.

The Area Calculator handles these four flat shapes in feet, inches, meters, centimeters or millimeters. It reports the area in the corresponding square unit and provides square-foot and square-meter equivalents. It calculates one shape at a time, without adding waste or estimating material purchases.

Calculate rectangle and square areas

For a rectangle, area = length x width. A rectangle measuring 12 ft by 10 ft has an area of 120 square feet. The two dimensions must describe perpendicular sides, not a side and the diagonal across the rectangle.

A square is a special rectangle with equal side lengths. A square with sides of 5 m therefore has an area of 5 x 5 = 25 square meters. Length measures a line, while area measures a two-dimensional region, so the result uses squared units.

Use perpendicular height for a triangle

Triangle area = base x perpendicular height / 2. With a base of 10 ft and a height of 6 ft, the area is 30 square feet. The height meets the base, or its extended line, at a right angle.

A sloping side is not generally the height. In an obtuse triangle, the height can meet the extended base outside the triangle. The same formula still applies, provided the correct base-height pair is used. This calculator does not infer a height from three side lengths.

Distinguish a circle's radius from its diameter

Circle area = pi x radius squared. For a radius of 3 ft, the area is pi x 3 x 3, or approximately 28.274334 square feet. If you measure a diameter of 6 ft across the center, divide it by two before entering the radius.

Entering the diameter as the radius makes the calculated area four times too large. Area is also different from circumference, which measures the distance around the circle. A circle is flat; calculating the volume of a sphere requires a separate three-dimensional formula.

Calculate trapezoid area

A trapezoid has two parallel bases. Its area is their average length multiplied by the perpendicular distance between them: (base A + base B) / 2 x height. With bases of 8 ft and 12 ft and a height of 5 ft, the result is 50 square feet.

Use the perpendicular height rather than either sloping side. Reversing the names of the two parallel bases does not change the answer. Equal base lengths give the familiar base-times-height result for a parallelogram. In some regions, the word trapezium is used for the shape called a trapezoid in US terminology.

Convert area units with squared factors

One foot equals exactly 0.3048 meters. Squaring that factor gives 1 square foot = 0.09290304 square meters. The 120-square-foot rectangle is therefore 11.1483648 square meters, displayed as 11.148365.

Likewise, 1 square foot contains 144 square inches, because there are 12 inches along each of two dimensions. Dividing a square-inch area by 12 would confuse length conversion with area conversion. Choose one unit for all dimensions before calculating.

Break irregular outlines into simpler parts

For an L-shaped outline, draw nonoverlapping rectangles or triangles and calculate them separately. Add the parts and subtract relevant cutouts. Avoid counting an overlapping section twice. This version does not store earlier results, so keep a written list when combining several shapes.

For practical room measurements, see the Square Footage Calculator. Geometric area alone does not determine pack counts, coverage, installation waste or costs. Use the relevant material tool and manufacturer information for purchasing decisions. Measurements are calculated locally without being saved or transmitted by this calculator.