ToolkitBook
Calculate the area of ten different 2D shapes, including circles, ellipses, squares, rectangles, triangles, and trapezoids. Simply enter the radius, side lengths, or base and height to get started. The calculator provides the area, the perimeter, and the specific formula used for the calculation. This tool is built for architects measuring floor space, landscapers calculating lawn square footage, students checking homework, and contractors estimating materials. You can enter any unit—results will appear in the corresponding square units. All calculations are processed locally in your browser for speed and privacy.
Need to calculate volume? Try Volume Calculator.
Choose the shape button that matches your specific project. The interface offers ten options: circles, ellipses, squares, rectangles, rhombuses, trapezoids, regular polygons, right triangles, equilateral triangles, and general triangles. Once you select a shape, a diagram will appear to show you exactly which dimensions are required, and the corresponding formula will be displayed above the input fields.
Each shape requires specific measurements to ensure accuracy. For a circle, enter the radius (the distance from the center to the edge). If you have the diameter, divide it by two before entering. For rectangles and squares, input the side lengths. For triangles, you can use the base and height, or for right triangles, the two legs that form the 90-degree angle. Trapezoids require the lengths of both parallel sides and the perpendicular height between them. For a rhombus, enter the measurements of the two diagonals. Regular polygons require the number of sides and the length of a single side.
Input all dimensions using the same unit—such as meters, feet, inches, or centimeters. The calculator maintains unit consistency: if you input your dimensions in feet, the result will be provided in square feet. If you have mixed units (for example, a room measuring 3 meters by 200 centimeters), convert them to a single unit—either 3 by 2 meters or 300 by 200 centimeters—before entering them into the calculator.
The calculated area is displayed prominently in large text. Below the area, you will find additional measurements based on the shape selected. Circles show the circumference and diameter; rectangles and squares provide the perimeter and diagonal length; triangles show the perimeter and, where applicable, the height or hypotenuse. These secondary figures are useful for material planning, such as determining the amount of edging needed for a garden or checking if furniture will fit diagonally through a space.
Flooring projects: Calculate the area of a room to determine how much material to purchase. It is standard practice to add 10% to the total to account for waste and cuts. For irregular rooms, divide the floor plan into smaller rectangles, calculate each one individually, and then add the totals together.
Landscaping: Measure the area of a lawn or garden bed to order the correct amount of seed, fertilizer, soil, or mulch. For curved or irregular areas, you can find a close approximation by combining circles, rectangles, and triangles.
Paint and materials: Calculating wall area helps you estimate how much paint you need. When measuring walls, remember to subtract the area of windows and doors for a more accurate estimate.
Property and construction: These calculations are essential for determining lot sizes in real estate or calculating floor area ratios for building permits. Contractors use these figures to provide accurate material estimates and project bids.
Always verify your measurements before entering them. A common mistake is confusing the radius with the diameter or measuring along a slanted side instead of taking the straight perpendicular height. For trapezoids, the height must be measured at a right angle to the parallel sides, not along the angled edges.
Since real-world objects are rarely perfect geometric shapes, you may encounter rooms with slightly uneven walls. In these cases, take measurements at several different points and use the average, or break the irregular space down into simpler shapes that the calculator can handle one at a time.
Circle: A = π × r² (r = radius)Ellipse: A = π × a × b (a, b = semi-axes)Square: A = s² (s = side length)Rectangle: A = length × widthRhombus: A = (d₁ × d₂) / 2 (d₁, d₂ = diagonals)Trapezoid: A = (a + b) × h / 2 (a, b = parallel sides, h = height)Regular Polygon: A = (n × s² × cot(π/n)) / 4 (n = sides, s = side length)Right Triangle: A = (a × b) / 2 (a, b = legs)Equilateral Triangle: A = (√3/4) × s² (s = side length)General Triangle: A = (base × height) / 2