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Select a shape, enter dimensions, and click Calculate// calculate area for any 2D shape instantly
Free online area calculator for rectangle, circle, triangle, trapezoid, ellipse, parallelogram, and more. Instant results with formula explanations.
Ready to calculate
Select a shape, enter dimensions, and click CalculateClick the shape tab for the geometry you want to calculate — rectangle, circle, triangle, and more.
Fill in the required measurements like width, height, radius, or base and height.
Click Calculate to see the area, formula used, step-by-step substitution, and unit conversions.
The Area Calculator is a free online tool for computing the surface area of common 2D geometric shapes. It shows the formula used, the step-by-step substitution, and automatically converts the result across multiple units of measurement.
All calculations run entirely in your browser — no data is sent to any server.
The area of a rectangle is calculated by multiplying its length by its width: Area = length × width. For example, a rectangle 5m × 3m has an area of 15 m².
The area of a circle is A = π × r², where r is the radius. This tool uses π ≈ 3.14159265. For example, a circle with radius 4cm has area = π × 16 ≈ 50.27 cm².
The standard formula is Area = ½ × base × height, where height is the perpendicular distance from the base to the opposite vertex. This tool uses base and height inputs for the triangle.
A trapezoid (also called a trapezium) is a quadrilateral with one pair of parallel sides. Its area is: A = ½ × (a + b) × h, where a and b are the lengths of the parallel sides and h is the height.
This tool supports meters, centimeters, millimeters, kilometers, inches, feet, yards, and miles. Results are automatically shown in the selected unit and converted to common alternatives.
The area of an ellipse is A = π × a × b, where a is the semi-major axis (half the longer diameter) and b is the semi-minor axis (half the shorter diameter).
A rhombus has all four sides equal in length. A parallelogram has opposite sides equal and parallel. Both have the same area formula: A = base × height. A rhombus can also use the diagonal formula: A = (d1 × d2) / 2.
This calculator uses JavaScript's native floating-point math with up to 10 significant digits. Results are displayed rounded to 4 decimal places for readability. For π, the full double-precision value is used.
Whether you're measuring a room for new flooring, calculating the size of a garden bed, or solving a geometry homework problem, having a fast and reliable area calculator saves time and reduces mistakes. This free tool supports nine of the most common 2D geometric shapes and shows you not just the answer, but the formula and step-by-step working behind it.
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The rectangle is the most commonly used shape in everyday area calculations. To find the area of a rectangle, multiply the length by the width:
Area = length × width
For example, a room that is 5 meters long and 4 meters wide has an area of 20 square meters. This formula applies to any right-angled quadrilateral with two pairs of parallel sides of equal length.
The area of a circle depends on its radius — the distance from the center to the edge. The formula uses pi (π ≈ 3.14159):
Area = π × r²
If you know the diameter instead, divide it by two to get the radius first. A circle with a 10 cm radius has an area of approximately 314.16 cm². Circles appear constantly in engineering, architecture, and natural science.
For a triangle, you need the base and the perpendicular height (not the slant side). The formula is:
Area = ½ × base × height
This works for all triangle types — right-angled, isosceles, scalene, or equilateral — as long as you measure the height perpendicularly from the base. A triangle with base 8m and height 5m has area = ½ × 8 × 5 = 20 m².
A trapezoid (or trapezium) has two parallel sides called the bases, and a height measured perpendicularly between them. The area formula averages the two bases and multiplies by height:
Area = ½ × (a + b) × height
This formula appears frequently in land surveying, where irregular plots are often approximated as a series of trapezoids.
An ellipse is a stretched circle with two axes: the semi-major axis (a) and the semi-minor axis (b). Its area is:
Area = π × a × b
When both axes are equal, this simplifies to the standard circle formula. Ellipses appear in orbital mechanics, optical lenses, and architectural arches.
A parallelogram has opposite sides parallel and equal. Its area equals the base multiplied by the perpendicular height (not the side length):
Area = base × height
A rhombus is a special case of the parallelogram where all sides are equal. Its area can also be computed from its diagonals: Area = (d1 × d2) / 2, which is particularly useful when the diagonal measurements are easier to obtain than the height.
A sector is a "pie slice" of a circle, defined by a radius and a central angle. The area is a proportion of the full circle's area:
Area = ½ × r² × θ (where θ is in radians)
Equivalently, in degrees: Area = (θ/360) × π × r². Sectors are used in pie charts, gear design, and any rotational geometry problem.
Area is measured in square units — square meters, square feet, square inches, and so on. When converting between units, remember that the conversion factor is squared. For instance, 1 meter = 100 centimeters, so 1 m² = 10,000 cm² (not 100). This tool handles all these conversions automatically when you select a unit.
Area calculations are essential across many fields. In construction and renovation, knowing the floor area determines how much flooring, paint, or tiles to buy. In agriculture, field area calculations determine irrigation needs, fertilizer quantities, and crop yield estimates. In graphic design, understanding canvas area matters for print sizing and resolution. In education, area problems form a core part of middle and high school geometry curricula worldwide.
This tool is designed to be fast, accurate, and educational — showing the formula alongside the result so you always understand how the number was derived, not just what it is.