⬛ Area Calculator

Calculate the area of any shape — circle, rectangle, triangle, trapezoid, ellipse, pentagon, hexagon, and more. Choose your unit and get the result instantly.

Shape

Unit

Radius (r)

What is Area?

Area is the measure of two-dimensional space enclosed within a boundary. It quantifies how much surface a shape covers, expressed in square units such as square metres (m²), square centimetres (cm²), square feet (ft²), or acres. Area is one of the most fundamental measurements in mathematics, with applications spanning construction, agriculture, physics, engineering, and everyday life — from calculating how much paint is needed for a wall to determining the size of a plot of land.

Different shapes have different area formulas derived from their geometric properties. A rectangle's area is simply length × width. A circle's area is π × radius². A triangle's area is ½ × base × height — or, when only side lengths are known, Heron's formula using the semi-perimeter. Composite or irregular shapes can be broken into standard shapes, and their areas summed.

It is important to distinguish area (a 2D measure in square units) from perimeter (a 1D measure of the boundary in linear units) and volume (a 3D measure in cubic units). When converting area between unit systems, always square the linear conversion factor — 1 m = 3.281 ft, so 1 m² = 10.764 ft².

Example — Triangle with sides 5, 6, 7

s = (5 + 6 + 7) / 2 = 9

Area = √(9 × (9−5) × (9−6) × (9−7)) = √(9×4×3×2) = √216

Area ≈ 14.70 units²

How the Area Calculator Works

Formula, assumptions, and calculation steps for this math tool.

Methodology

Math calculators apply the relevant arithmetic, algebraic, geometric, or numeric rule to the values entered and simplify the result where possible.

Calculation Steps

Read the values and operation selected.
Normalize signs, decimals, fractions, or units if needed.
Apply the mathematical rule or formula.
Format the answer and any intermediate values for checking.

Assumptions and Limits

Inputs must be within the supported domain of the operation.
Decimal answers may be rounded for readability.
Symbolic simplification is limited to the calculator scope.

Frequently Asked Questions

What is area?

Area is the amount of 2-dimensional space enclosed by a shape. It is measured in square units (m², cm², ft², etc.). Every flat shape has an area that can be calculated using its dimensions.

How do I find the area of a circle?

The area of a circle is A = π × r², where r is the radius. For example, a circle with radius 5 m has area = π × 25 ≈ 78.54 m².

How do I find area of irregular shapes?

For irregular shapes you can divide them into smaller regular shapes (rectangles, triangles, etc.), calculate each area, and add them together. Alternatively, use a coordinate-based formula like the Shoelace theorem.

What units are used for area?

Area uses square units: m², cm², mm², ft², in², yd², km², acres, hectares, etc. To convert, square the linear conversion factor — for example, 1 m = 100 cm, so 1 m² = 10,000 cm².

What is Heron's formula?

Heron's formula finds the area of a triangle from its three side lengths a, b, c. First compute s = (a+b+c)/2 (the semi-perimeter). Then Area = √(s(s−a)(s−b)(s−c)). No height measurement is needed.

Real-World Applications of Area Calculation

🏠

Flooring & Tiling

Calculate the exact area of a room or surface to determine how many tiles, floorboards, or rolls of carpet to purchase, with extra for cuts and waste.

🎨

Painting & Wall Coverage

Paint coverage is rated per m² or ft². Calculate wall area (subtract doors and windows) to estimate how many litres or gallons of paint you need.

🌱

Lawn & Garden

Determine how much grass seed, fertiliser, or mulch to buy by calculating the area of your lawn or garden beds in m² or ft².

🏗️

Construction & Architecture

Architects calculate floor area ratios, plot coverage, and material quantities. Engineers use cross-sectional areas in structural load calculations.

🔬

Physics & Engineering

Pressure is force per unit area (P = F/A). Surface area affects heat transfer, drag, and diffusion rates in engineering and scientific calculations.

🗺️

Land Surveying

Surveyors calculate plot areas for legal descriptions, real estate transactions, and tax assessments using geometry and coordinate-based methods.

Common Area Calculation Mistakes

Mixing Units Within a Calculation

Measuring one side in feet and another in metres then multiplying gives a nonsensical result. Convert all dimensions to the same unit before computing area.

Using Length Conversion Factors for Area

Since 1 m = 3.281 ft, beginners multiply m² by 3.281 to get ft². The correct factor is 3.281² = 10.764. Area conversion always uses the squared linear factor.

Forgetting to Account for Irregular Shapes

Real rooms and plots are rarely perfect rectangles or circles. Break complex shapes into standard sub-shapes, calculate each area, and sum them.

Confusing Perimeter and Area

Perimeter is the total length around a shape (linear units); area is the space inside (square units). A room with a large perimeter does not necessarily have a large area.

Not Adding a Waste Factor for Materials

Flooring, tiling, and roofing always require extra material for cuts, overlaps, and breakage. Add 10–15% to your calculated area when purchasing materials.

Area Formula Quick Reference

Shape	Formula	Variables	Example (units)
Square	a²	a = side	a=5 → 25 units²
Rectangle	l × w	l = length, w = width	4×6 → 24 units²
Triangle	½ × b × h	b = base, h = height	½×8×5 → 20 units²
Circle	π × r²	r = radius	π×3² → 28.27 units²
Trapezoid	½(a + b) × h	a,b = parallel sides, h = height	½(4+6)×5 → 25 units²
Ellipse	π × a × b	a,b = semi-axes	π×3×4 → 37.70 units²

References

Euclid. Elements. c. 300 BCE. (Foundational geometric area proofs.)
National Institute of Standards and Technology. Mathematical formulas. nist.gov
Weisstein EW. Area. MathWorld. mathworld.wolfram.com/Area.html
Khan Academy. Area and Perimeter. khanacademy.org/math/geometry
Heron of Alexandria. Metrica. c. 60 CE. (Original derivation of Heron's formula.)