Area Calculator

Pick the shape that matches what you are measuring, then enter its dimensions. Only the boxes that shape needs are used.

1. Choose a shape in the first box. Rectangle is the default.
2. Enter the first measurement. For a rectangle it is the length, for a circle it is the radius, for a square it is the side.
3. Enter the second measurement, and the height if you picked a trapezoid. The example is a rectangle 12 by 8, so you can press Calculate right away.
4. Press Calculate, or press Enter. The area appears first and large, with the perimeter or circumference below.

Every shape has its own formula, but all six are short. A rectangle is length x width. A square is side squared, which is the rectangle formula with both sides equal. A triangle is 1/2 x base x height, where the height is the perpendicular distance from the base to the opposite corner, not the slanted side.

A circle is pi x radius squared, with pi about 3.14159. A trapezoid is (base 1 + base 2) / 2 x height, where the two bases are the parallel sides and the height is the distance between them. A parallelogram is base x height, again with the perpendicular height. Our square footage calculator does the same job for rooms in square feet, and our area converter converts the answer between square feet, square meters and acres.

Find the area of a rectangle 12 by 8.

1. Pick Rectangle in the shape box.
2. Enter the length, 12, and the width, 8.
3. Multiply. Area = 12 x 8 = 96 square units.
4. Check the perimeter. Perimeter = 2 x (12 + 8) = 40.

As a second check, a circle with radius 5 has an area of pi x 5 squared = 3.14159 x 25 = 78.54, and a circumference of 2 x pi x 5 = 31.42. A triangle with base 10 and height 6 has an area of 1/2 x 10 x 6 = 30. The same steps work for any shape, so try your own numbers in the tool above.

Measure twice and write the numbers down before you type them in. For a rectangle, measure two adjacent sides at right angles. For a circle, measure the diameter across the middle and halve it to get the radius. A radius of 5 comes from a diameter of 10.

For a triangle, the height is the straight line from the base to the opposite corner at a right angle. The slanted edge is longer than the height, so using it gives an answer that is too big. For a trapezoid, measure both parallel sides and the perpendicular distance between them, not the slanted ends.

Keep every measurement in the same unit. Mixing feet and inches is the most common measuring error, and the calculator cannot catch it. If you measured in feet, the area comes back in square feet. If you measured in meters, it comes back in square meters.

The most common mistake is using the diameter as the radius. A circle with a diameter of 10 has a radius of 5, and an area of 78.54. Using 10 as the radius gives 314.16, four times too big, because the radius is squared.

A second mistake is using the slanted side as the height in a triangle or a parallelogram. The height is always the perpendicular distance. For a triangle with base 10 and a slanted side of 8, the height is less than 8, so 1/2 x 10 x 8 = 40 is wrong.

A third mistake is forgetting that area is in square units. A room 12 feet by 8 feet is 96 square feet, not 96 feet. The perimeter is 40 feet, and the two numbers measure different things.

Flooring, paint and sod are all sold by area. A room 12 by 8 needs 96 square feet of flooring, plus a little extra for cuts and waste. Paint covers a stated area per gallon, so the wall area tells you how many gallons to buy. Our paint calculator and flooring calculator work out the materials from the same measurements.

Gardens and plots use the same formulas. A triangular flower bed, a round patio and a trapezoidal lawn section each need their own formula, and an odd shaped plot can be split into rectangles and triangles whose areas add up. A plot split into a 12 by 8 rectangle and a triangle with base 10 and height 6 has a total area of 96 + 30 = 126 square units.