What is the Area Calculator?
Area is a quantity that describes the size or extent of a two-dimensional figure or shape in a plane. It can be visualized as the amount of paint that would be necessary to cover a surface, and is the two-dimensional counterpart of the one-dimensional length of a curve, and the three-dimensional volume of a solid.
The standard unit of area in the International System of Units (SI) is the square meter (m²). This Area Calculator allows you to quickly evaluate the area of seven common shapes. The area of more complex shapes can usually be obtained by breaking them down into their aggregating simple shapes and totaling their areas.
Formulas for Calculating Area
Depending on the shape of the surface, different mathematical formulas apply. Here is a breakdown of the standard formulas used in this calculator:
- Rectangle: A rectangle is a quadrilateral with four right angles. The formula is:
Area = length × width - Triangle: Using Heron's formula based on the three edge lengths (a, b, c):
Area = √(s(s - a)(s - b)(s - c))wheresis the semi-perimeter(a + b + c) / 2. - Trapezoid: A trapezoid is a simple convex quadrilateral that has at least one pair of parallel sides. The formula is:
Area = ((b₁ + b₂) / 2) × height - Circle: A circle is a closed shape formed by points equidistant from a center. The formula is:
Area = π × r² - Sector: A sector is a proportion of a circle enclosed by two radii and an arc. If the angle θ is in degrees:
Area = (θ / 360) × π × r² - Ellipse: An ellipse is a generalized form of a circle with a semi-major axis (a) and a semi-minor axis (b). The formula is:
Area = π × a × b - Parallelogram: A simple quadrilateral with two pairs of parallel sides. The formula is:
Area = base × height
1 square meter (m²) = 10.7639 square feet (sq ft)
1 hectare = 10,000 square meters
1 acre = 43,560 square feet
How to Use This Calculator
To use the Area Calculator, follow these simple steps:
- Select the Shape: Use the dropdown menu to select the geometric shape you are measuring (e.g., Rectangle, Circle, Triangle).
- Choose Your Units: Select the unit of measurement you are inputting (Meters, Feet, Inches, etc.). The calculator will automatically process the final output in the corresponding squared unit.
- Input Dimensions: Enter the specific lengths, widths, radii, or angles required for the chosen shape.
- Calculate: Click "Calculate Area." The tool will instantly provide the total area, formula used, and standard conversions across other common area units.
Frequently Asked Questions
Area refers to the total space occupied by a two-dimensional flat surface or shape, measured in square units. Perimeter refers to the total length of the continuous line forming the boundary of a closed geometric figure, measured in linear units.
The easiest way to calculate the area of a complex or irregular shape is to decompose it into simpler, standard shapes (like rectangles and triangles). Calculate the area of each individual simpler shape, and then add them all together to find the total area.
The standard unit of area in the International System of Units (SI) is the square meter (m²). In the United States, square feet (sq ft) and acres are more commonly used for everyday measurements and real estate.
Heron's formula allows you to calculate the area of a triangle when you do not know the height, but you do know the lengths of all three sides. It calculates the semi-perimeter first, then uses it alongside the three sides to determine the area without needing an altitude measurement.
A circle is a special type of ellipse where the semi-major axis and the semi-minor axis are equal (this equal distance is called the radius). An ellipse has two focal points and resembles a flattened circle, requiring two different radial measurements (the major and minor axes) to calculate its area.