Area Calculator — Calculate Area of Any Shape Instantly
Find the area of circles, triangles, rectangles, trapezoids, ellipses, and more. Includes formulas, unit conversions, and real-world examples.
Area calculations come up constantly in the real world — figuring out how much paint to buy, how much flooring you need, or how large a garden bed you're planning. The formulas aren't complicated individually, but remembering which formula applies to which shape, and handling the unit conversions afterward, is where things get tedious. The CalcHub Area Calculator covers all common shapes and handles the math cleanly.
Supported Shapes and Formulas
| Shape | Formula | Variables |
|---|---|---|
| Square | A = s² | s = side length |
| Rectangle | A = l × w | l = length, w = width |
| Triangle | A = ½ × b × h | b = base, h = height |
| Circle | A = πr² | r = radius |
| Ellipse | A = π × a × b | a, b = semi-axes |
| Trapezoid | A = ½(a + b) × h | a, b = parallel sides, h = height |
| Parallelogram | A = b × h | b = base, h = perpendicular height |
| Rhombus | A = ½ × d₁ × d₂ | d₁, d₂ = diagonals |
| Sector | A = ½ × r² × θ | r = radius, θ = angle in radians |
| Regular Polygon | A = (n × s² × cot(π/n)) / 4 | n = sides, s = side length |
How to Use It
Select the shape from the dropdown, enter the required measurements, and specify your units (cm, m, inches, feet). The result appears in the same units squared, with an option to convert — like getting your answer in both square feet and square meters.
Practical Examples
How much tile for a kitchen floor? Room is 12 ft × 15 ft = 180 square feet. Add 10% for waste and cuts → buy enough for 198 sq ft. Paint coverage for a circular feature wall? Radius 2.4 meters → A = π × 2.4² ≈ 18.1 m² Most paint covers about 10–12 m² per liter → need roughly 1.5–1.8 liters. Area of a triangle with no height given: If you know all three sides (a, b, c), use Heron's formula:s = (a + b + c) / 2
A = √(s(s−a)(s−b)(s−c))
For sides 5, 7, 8:
- s = 10
- A = √(10 × 5 × 3 × 2) = √300 ≈ 17.32
Unit Conversions Reference
| From | To | Multiply By |
|---|---|---|
| ft² | m² | 0.0929 |
| m² | ft² | 10.764 |
| in² | cm² | 6.452 |
| acres | m² | 4,046.86 |
| hectares | acres | 2.471 |
Tips for Real-World Projects
- Irregular shapes: Break them into regular shapes (rectangles + triangles), calculate each area separately, then add.
- Always add waste factor: For tiling and flooring, budget 10–15% extra. Odd-shaped rooms need more cuts.
- Perimeter ≠ Area: These are different measurements. Doubling the perimeter doesn't double the area (it quadruples it for a square).
- Diameter vs. Radius: The most common mistake with circles. Diameter is the full width; radius is half that. Plugging in diameter as radius gives you 4× the correct area.
How do I find the area of an irregular polygon?
The shoelace formula works for any polygon if you know the coordinates of all vertices. Input the x,y coordinates in order, and it calculates the area regardless of how irregular the shape is. The CalcHub tool includes this for custom polygons.
What's the difference between area and surface area?
Area is for 2D flat shapes. Surface area is for 3D objects — it's the total area of all the faces. A cube with side 4 cm has a face area of 16 cm² per face, and a total surface area of 96 cm². The volume calculator covers surface area for 3D shapes.
Why does doubling a shape's dimensions quadruple the area?
Because area is a two-dimensional measurement. When you double both length and width, you multiply by 2 twice: A = l × w → 2l × 2w = 4(l × w). A shape twice as wide and twice as tall has four times the area, not twice.
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