Area Calculator

Area is the size of a surface on a plane covered by a particular geometric shape. This calculator allows you to calculate the area for nine different commonly used geometric shapes. Select a shape and enter dimensions to instantly get the area. If the selected shape can also calculate perimeter from the entered values, it will be shown as well.

Because area is a two-dimensional measurement, it will always be expressed in square units - such as square meters, square feet or acres. You can change the unit in either field and the tool will automatically convert between them. So you could measure in inches and get an answer in square feet without doing any math yourself.

Here's how to use this calculator.

Select a geometric shape in the Shapes menu. The input fields change accordingly so that only values actually required for this shape are shown.

Enter the respective measurements and set the unit. While entering, the area is updated in real time and shown in two formats: as a readable number and as a copyable field. If the shape can also calculate the perimeter from the entered values, it will be displayed as well.

To try a different shape simply select a new shape from the menu. The values entered are saved separately for each shape so you can quickly switch between shapes.

Formulas for calculating the area of various geometric shapes.

For each shape there is a simple formula to calculate it. This calculator uses the following formulas. If you know them then you can check the results manually.

For triangles, use Heron's formula.

The area formula for triangles that many people learn is half the product of base and height, but in reality one rarely measures the height. With Heron's Formula, the area can be calculated using only the lengths of the three sides, without needing a height. These are values which can be measured with a tape measure.

where s is the semiperimeter of the triangle. For a triangle with sides 3, 4 and 5, the semiperimeter (s) is (3+4+5)/2 = 6. The area of the triangle is then A=sqrt(6*3*2*1) = sqrt(36) = 6.

Circle and circular segment.

The area of a circle is calculated by multiplying π with the square of its radius. If you cut out a wedge-shaped region, what remains is called a sector. The area of the sector corresponds to only a certain part of the total area of the circle.

A quarter circle is a sector with a central angle of 90 degrees. So the area will be one fourth of the total area of the circle. If the radius is 6, then the total area of the circle is approximately 113.10, and the area of a 90-degree sector would be about 28.27.

Examples of calculations:

Since these examples use the default values, they can be reproduced individually. Please note that the method of calculating area is different depending on the geometric shape.

Select and convert area units:

The unit you choose to measure with will determine the units of the calculated area. If a room is measured in meters, then the resulting area will be in square meters, while if it is measured in feet, then the resulting area will be in square feet. Because the area unit is the square of the length unit, the two units cannot be directly converted into each other without conversion.

A meter is a little longer than three feet, but one square meter is about eleven square feet. This is because the length has to be squared. For land areas, an acre is 43,560 square feet and a hectare is 10,000 square meters, which is about 2.5 acres. The calculator will do all of the conversions for you when changing units. So if you enter the area of your garden in meters, it will give you the result in acres.

Areas of application for area calculations:

Area is one of the most useful mathematical concepts. Since flooring, tiles and carpets are sold in square meters or feet, calculating the area of a room allows you to determine how much material you will need. Paint cans give an indication of the area they can cover so that you can compare this with the area of your wall.

Gardeners and farmers measure the area of plots, lawns and fields, usually in acres or hectares. Construction workers and landscape architects calculate the area of patios, driveways and ponds. Even a pizza is essentially an area problem. A 16-inch pizza has more than twice as much edible surface as a 10-inch pizza, but not 1.6 times as much. The area comes from squaring the diameter.

Dividing irregular shapes:

In reality, spaces and plots are rarely laid out in a single regular shape. Surveyors and builders break irregular contours into simple geometric figures, calculating the area of each piece individually with this tool, then adding them together. An L-shaped room is divided into two rectangles, for example. A plot might have the shape of a rectangle with triangles added to its sides.

Instead of adding a part, another part is subtracted. For example, if there is a circular flower bed in a rectangular lawn, calculate the area of both shapes and subtract the smaller from the larger. The Shapes menu has options such as squares, rectangles, triangles, and circles so you can measure almost any real shape using this method.

Tips for accurate area calculation:

Make sure all measurements of the same shape are in the same units before you calculate. Measure height and radius from their respective defined reference points. The height of a triangle or parallelogram is the vertical distance, not the hypotenuse, and the radius is the exact distance from the center of the circle to its edge.

Note that since area scales with the square of length, a small error in measurement will result in a large error in the calculated area. If accuracy is required, measure twice.

This tool should only be used for general educational purposes and everyday planning. For architectural, surveying or other high risk work please verify the values against the required standards and tolerances for your project.