Area Calculator
Calculate the area of common geometric shapes.
Understanding Area Calculator
The Area Calculator finds the area of common two-dimensional geometric shapes from the dimensions you provide. Select a shape and enter its required measurements to calculate the amount of space enclosed by the figure.
The calculator supports squares, rectangles, triangles, circles, and trapezoids. Each shape uses its corresponding geometric area formula, and the result is expressed in square units.
How to work through the calculation
Area Calculator is designed to make unit changes easier to verify without doing the conversion by hand. Start with the quantity and source unit, then select the destination unit when the calculator provides that choice. The available units or options include Square, Rectangle, Triangle, Circle.
How to interpret the result
A conversion changes the way a quantity is expressed; it does not change the underlying quantity. Pay attention to squared or cubed units, prefixes such as kilo- or milli-, and regional measurement conventions. Keeping the original value visible while checking the converted value is a simple way to catch a mistaken unit selection.
Area Calculator
The Area Calculator finds the area of common two-dimensional geometric shapes from the dimensions you provide. Select a shape and enter its required measurements to calculate the amount of space enclosed by the figure.
The calculator supports squares, rectangles, triangles, circles, and trapezoids. Each shape uses its corresponding geometric area formula, and the result is expressed in square units.
What Is Area?
Area measures the amount of two-dimensional surface enclosed by a geometric figure. Unlike length or perimeter, which are measured in linear units, area is measured in squared units.
For example, if dimensions are measured in meters, the calculated area is expressed in square meters (m²). If dimensions are measured in feet, the area is expressed in square feet (ft²).
Square Area
A square has four equal sides. Its area is calculated by multiplying the side length by itself.
The square's side length is represented by s.
Rectangle Area
The area of a rectangle is found by multiplying its length by its width.
The length and width must be expressed using compatible units before calculating the area.
Triangle Area
The area of a triangle is half the product of its base and its perpendicular height.
The height must be measured perpendicular to the selected base. It is not necessarily the length of one of the triangle's sloping sides.
Circle Area
The area of a circle depends on its radius, which is the distance from the center of the circle to its edge.
The calculator uses the mathematical constant π when calculating the area. The diameter of a circle is twice its radius.
Trapezoid Area
A trapezoid has two parallel bases. Its area is calculated using the two base lengths and the perpendicular distance between them.
The height is the perpendicular distance between the two parallel bases. It is not the length of a slanted side.
Example Calculations
For a square with a side length of 5 units:
A = 25 square units
For a rectangle measuring 5 units by 3 units:
A = 15 square units
For a triangle with a base of 5 units and a height of 4 units:
A = 10 square units
For a circle with a radius of 5 units:
A ≈ 78.5398 square units
For a trapezoid with bases of 6 and 4 units and a height of 3 units:
A = 15 square units
Area vs. Perimeter
Area and perimeter measure different properties of a shape. Area measures the surface enclosed by a figure, while perimeter measures the total distance around its boundary.
For example, a rectangle that is 5 units long and 3 units wide has an area of 15 square units, while its perimeter is 16 units.
Perimeter = 2(5 + 3) = 16 units
Understanding Square Units
Area is expressed in square units because it represents two dimensions: length and width. A square measuring 1 meter by 1 meter has an area of 1 square meter.
When converting between area units, the conversion factor must also be squared. For example, converting a length from meters to centimeters uses a factor of 100, while converting an area from square meters to square centimeters uses a factor of 10,000.
How to Use the Calculator
Select the geometric shape you want to calculate. The calculator will automatically display the dimensions required for that shape. Enter positive values and select Calculate to receive the area and the relevant calculation details.
Depending on the selected shape, the result may also include useful related measurements such as perimeter, circumference, diameter, diagonal, or average base length.
Disclaimer
This calculator is intended for informational purposes only. While we strive for accuracy, we cannot guarantee that every result is correct for every situation.