Area Calculator - Shapes Area Formula Tool
Calculate the area of squares, rectangles, circles, triangles, parallelograms, and trapezoids with the correct formula.
Select a shape, enter the required dimensions, and get the area instantly with the formula displayed.
Area Calculator - Shapes Area Formula Tool
Calculate the area of squares, rectangles, circles, triangles, parallelograms, and trapezoids with the correct formula.
About the area calculator
Area is the measure of the two-dimensional space enclosed by a shape. It tells you how much surface a flat figure covers, expressed in square units — square meters, square feet, square centimeters, and so on. Area is one of the most practically important measurements in everyday life: you need it to buy flooring, seed a lawn, paint a wall, design a room layout, or calculate the footprint of a building.
This calculator supports six of the most common geometric shapes: square, rectangle, circle, triangle, parallelogram, and trapezoid. Each shape has a specific formula derived from basic principles of geometry, and the calculator applies the correct formula automatically based on the shape you select.
A square has all four sides equal, so its area is the side length multiplied by itself: A = s². A rectangle has two pairs of equal sides, giving A = length × width. A circle's area is determined by its radius: A = π × r², where π ≈ 3.14159. This formula reflects the fact that the area grows with the square of the radius — doubling the radius quadruples the area.
A triangle's area is half the product of its base and its perpendicular height: A = ½ × b × h. The factor of ½ arises because a triangle is exactly half of a parallelogram with the same base and height. A parallelogram's area is simply A = b × h, without the halving factor. A trapezoid has two parallel sides (bases) of different lengths, and its area is the average of the two bases multiplied by the height: A = ½ × (b₁ + b₂) × h.
In real-world problems, always use consistent units. If the dimensions are in meters, the area is in square meters. If you mix meters and centimeters without conversion, the result will be meaningless. Convert all measurements to the same unit before entering them into the calculator.
Area calculations appear in countless fields. In construction and real estate, area determines material quantities and property values. In agriculture, field area determines fertilizer and seed requirements. In medicine, body surface area influences drug dosing. In manufacturing, surface area affects material cost and coating coverage. In environmental science, habitat area is a primary factor in biodiversity and conservation planning.
For irregular shapes, the standard approach is to decompose them into a combination of the regular shapes this calculator handles, compute each area separately, and add the results together. For example, a floor plan that is an L-shape can be split into two rectangles, each calculated independently.
Area calculation examples
Practical examples for each major shape type using real-world dimensions.
| Shape and Dimensions | Area | Explanation |
|---|---|---|
| Square, side = 8 m | 64 m² | A = 8² = 64. The area of a square garden with 8-meter sides is 64 square meters. |
| Rectangle, 12 ft × 10 ft | 120 ft² | A = 12 × 10 = 120. A room 12 feet long and 10 feet wide has an area of 120 square feet. |
| Circle, r = 5 m | ≈ 78.5398 m² | A = π × 5² ≈ 78.54. The area of a circular pool with 5-meter radius is about 78.54 square meters. |
| Triangle, base = 15 m, height = 8 m | 60 m² | A = ½ × 15 × 8 = 60. A triangular plot with base 15 m and height 8 m has an area of 60 square meters. |
| Trapezoid, b₁ = 10 m, b₂ = 6 m, h = 4 m | 32 m² | A = ½ × (10 + 6) × 4 = ½ × 16 × 4 = 32. Average width 8 m over 4 m height gives 32 square meters. |
How to use the area calculator
- Click the button for the shape you want to calculate: Square, Rectangle, Circle, Triangle, Parallelogram, or Trapezoid.
- Enter the required dimensions in the fields that appear. Each shape shows only the fields it needs — side for a square, length and width for a rectangle, and so on.
- Click Calculate Area to compute the result. The area is displayed in square units (the same unit as the dimensions you entered).
- The formula used for the chosen shape appears below the result so you can verify the calculation or use it manually.
- Click Reset to clear all fields and select a new shape for a fresh calculation.
Area calculator FAQ
What units does the area calculator use?
The calculator does not impose any specific unit. The area result is in the square of whatever unit you enter for the dimensions. If you enter the radius in centimeters, the area is in square centimeters. If the dimensions are in feet, the area is in square feet. Ensure all inputs use the same unit.
How do I calculate the area of an irregular shape?
Decompose the irregular shape into combinations of regular shapes — rectangles, triangles, circles, and so on. Calculate the area of each component separately using this calculator, then add them together. For example, an L-shaped room can be divided into two rectangles, and the total area is the sum of both rectangle areas.
What is the formula for the area of a circle?
The area of a circle is A = π × r², where r is the radius and π ≈ 3.14159. The radius is half the diameter. If you know the diameter d, use r = d/2, giving A = π × (d/2)² = π × d² / 4. For a circle with diameter 10 m, the area is π × 25 ≈ 78.54 m².
Why is the triangle area formula ½ × base × height?
Any triangle can be embedded in a parallelogram with the same base and height by placing a copy of the triangle alongside it. The parallelogram has area base × height, and the triangle occupies exactly half of it. This geometric argument explains the factor of ½ and holds for all triangles, not just right triangles.
How is the trapezoid area formula derived?
A trapezoid with parallel sides b₁ and b₂ and height h can be thought of as a shape with average width (b₁ + b₂)/2. Multiplying this average width by the height gives A = (b₁ + b₂)/2 × h = ½ × (b₁ + b₂) × h. This formula reduces to the rectangle formula when b₁ = b₂.
Can I calculate the area of a sector or a ring?
Sectors and rings are not directly in the shape list, but you can derive them. A circular sector with radius r and central angle θ (in degrees) has area A = (θ/360) × π × r². A ring (annulus) between outer radius R and inner radius r has area A = π × (R² - r²). Both use the circle area formula as a starting point.