Area Calculator
Calculate the area of square, rectangle, triangle (base-height or Heron), circle, trapezoid, parallelogram and ellipse with step-by-step formulas.
This free area calculator finds the area of any common shape — square, rectangle, triangle, circle, trapezoid and parallelogram — with the full area calculation formula shown step by step. Pick a shape, enter the measurements, and the result appears instantly. Below you will find every area calculation formula and clear guidance on how to calculate the area of each shape.
Area Calculation Formula by Shape
| Shape | Area Formula | Required Measurements | Example |
|---|---|---|---|
| Square | A = a² | Side (a) | a=6 → 36 cm² |
| Rectangle | A = a × b | Length a, width b | 5×4 = 20 m² |
| Triangle | A = (base × h) / 2 | Base, height (h) | 8×5/2 = 20 units² |
| Circle | A = π × r² | Radius (r) | r=7 → ≈153.94 cm² |
| Trapezoid | A = ((a+b) × h) / 2 | Top base (a), bottom base (b), height (h) | (4+8)×5/2 = 30 units² |
| Parallelogram | A = base × h | Base, height (h) | 10×6 = 60 units² |
| Ellipse | A = π × a × b | Semi-major (a), semi-minor (b) | 6×4 → ≈75.4 units² |
| Equilateral △ | A = (√3/4) × a² | Side (a) | a=10 → ≈43.3 units² |
| Triangle (Heron) | A = √(s(s-a)(s-b)(s-c)) | 3 sides; s=(a+b+c)/2 | 3,4,5 → 6 units² |
Rectangle Area Calculator
How to calculate the area of a rectangle: Formula A = a × b — multiply length by width. A room 12 m × 8 m has an area of 96 m². As a rectangle area calculator, this is the mode to use for flooring, carpet or paint coverage of rectangular spaces. A square is just a special rectangle, so the same idea powers the square area calculator mode with A = a².
Triangle Area Calculator
How to calculate the area of a triangle: Formula A = (base × height) / 2. If the height is not directly measurable, this triangle area calculator also offers Heron's formula using all three sides: s = (a+b+c)/2, then A = √(s(s-a)(s-b)(s-c)). There is an equilateral-triangle mode too, where A = (√3 ÷ 4) × a².
Circle Area Calculator
How to calculate the area of a circle: Formula A = π × r² — square the radius and multiply by π (≈ 3.14159). If only the diameter is given, radius = diameter / 2. A circular pool with diameter 10 m: r = 5, A = π × 25 ≈ 78.54 m². This circle area calculator also has a semicircle mode (half of πr²) for arches and rounded edges.
Trapezoid Area Calculator
How to calculate the area of a trapezoid: Formula A = ((a + b) × h) / 2, where a = top base, b = bottom base, h = height (perpendicular distance between the two bases). Example: top 6 m, bottom 10 m, height 4 m → ((6+10)×4)/2 = 32 m². The trapezoid area calculator mode does this automatically, and a parallelogram (A = base × height) is available as well.
Common Uses of the Area Calculator
- Construction & renovation: Calculate flooring, tiles, wallpaper or paint for rooms and surfaces.
- Gardens & land: Find the area of plots, fields or garden beds for irrigation, seeding and fertiliser planning.
- Maths & school: Solve geometry problems for square, rectangle, triangle, circle and trapezoid quickly with step-by-step formulas.
- Design: Determine the surface area of elements in graphic and web design projects.
Tips to Avoid Mistakes
- Radius vs diameter: The circle formula uses the radius (r), not the diameter. Divide the diameter by 2 first.
- Triangle height: The height is perpendicular to the base — not the slant side length.
- Consistent units: Use the same unit for all measurements. Mixing cm and m gives wrong results.
- Trapezoid bases: Only the two parallel sides are the bases; height is the perpendicular distance between them.
Area vs Surface Area
People often look for a surface area calculator when they actually need a flat area, so it helps to know the difference. Area measures a flat (2D) shape — a floor, a field, a piece of paper. Surface area measures the total outside of a 3D solid — for example, a cube's surface area is the sum of its six square faces (6 × a²). This tool calculates 2D area; to find the surface area of a 3D object, add up the area of each face using the relevant 2D formula. For a box, that is 2 × (length × width + width × height + height × length); for a cylinder, 2πr² + 2πrh. The same flat-area formulas above are the building blocks for every surface-area calculation.
Calculating Area in Square Meters
For rooms, land and construction, area is usually expressed in square metres, so this tool also works as an area in square meters calculator. The key is to convert every length to metres before multiplying: a wall measured as 250 cm is 2.5 m, and a room of 2.5 m × 4 m is 10 m². If you measure in centimetres and want square metres, divide the final cm² result by 10,000 (since 1 m² = 10,000 cm²). Common conversions: 1 m² = 10,000 cm² = 1,000,000 mm², and 1 hectare = 10,000 m². Keeping units consistent is the single most important step for an accurate result.
Whether you are estimating paint for a wall, flooring for a room, fabric for a project or land for a plot, the workflow is the same: choose the shape that matches your object, measure the required lengths in a single unit, and read the result with its formula. For irregular shapes, split the space into simple shapes — rectangles, triangles and circle segments — calculate each one separately, then add the results together. See the frequently asked questions below for more worked examples.
Frequently Asked Questions About the Area Calculator
Rectangle area: A = a × b. Multiply length (a) by width (b). A room 5 m × 3 m has area 15 m². Select Rectangle in the tool and enter the two side lengths.
Triangle area: A = (base × height) / 2. If only the three sides are known, use Heron's formula: s = (a+b+c)/2, A = √(s(s-a)(s-b)(s-c)).
Circle area: A = π × r². Square the radius and multiply by π (≈ 3.14159). A circle with radius 5 cm has area ≈ 78.54 cm².
Trapezoid area: A = ((a + b) × h) / 2. Top base a + bottom base b, multiplied by height h, divided by 2. E.g. a=4, b=8, h=5 → ((4+8)×5)/2 = 30 units².
Square area: A = a². Square the side length. A square with side 6 m has area 36 m².
Square: a², Rectangle: a×b, Triangle: (base×h)/2, Circle: π×r², Trapezoid: ((a+b)×h)/2, Parallelogram: base×h, Ellipse: π×a×b, Equilateral triangle: (√3/4)×a².
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