Area Calculator
Select a shape, enter dimensions, and get instant area, perimeter, and full step-by-step working
Area = Length × Width | Perimeter = 2(L + W)Summary
Step-by-Step Working
Unit Conversions
Related Measurements
Full Details
What Is Area? A Complete Guide to 2D Measurement
The definition of area, why it matters, how to measure it, and the fundamentals behind every shape formula
Area is the measure of the two-dimensional space enclosed within a flat shape or surface. It answers the question: "How much surface does this shape cover?" Area is always expressed in square units — square metres (m²), square centimetres (cm²), square feet (ft²), square inches (in²) — because you are multiplying one length by another.
The concept is universal: whether you're calculating the floor space of a room, the amount of grass in a garden, the cross-section of a pipe, or the face area of a tile, you're always computing area. Area is one of the most practically useful measurements in everyday life — from interior design and construction to agriculture, engineering, and physics.
The area of a rectangle naturally emerges from counting unit squares — a 4 m × 3 m rectangle contains exactly 12 unit squares of 1 m² each. All other formulas follow: a triangle is half a rectangle, a circle is the limit of infinitely many thin rectangles (integration), and complex shapes decompose into simple ones.
Area Formulas for All 2D Shapes — Complete Reference Table
Every common shape formula with variables defined, perimeter formulas, and special notes
| Shape | Area Formula | Perimeter / Circumference | Key Variables | Notes |
|---|---|---|---|---|
| Square | A = s² | P = 4s | s = side | Diagonal = s√2 |
| Rectangle | A = L × W | P = 2(L+W) | L = length, W = width | Diagonal = √(L²+W²) |
| Triangle (base/height) | A = ½bh | P = a+b+c | b = base, h = height | Height must be perpendicular to base |
| Triangle (Heron's) | A = √(s(s-a)(s-b)(s-c)) | P = a+b+c | s = (a+b+c)/2 | Works for any triangle with known sides |
| Triangle (SAS) | A = ½ab·sin(C) | Requires all sides | a, b = sides, C = included angle | C in radians for sin() |
| Circle | A = πr² | C = 2πr | r = radius | d = 2r; A = π(d/2)² |
| Semicircle | A = πr²/2 | P = πr + 2r | r = radius | Half of full circle |
| Ellipse | A = π × a × b | ≈ π√(2(a²+b²)) | a = semi-major, b = semi-minor | No exact perimeter formula; Ramanujan approximation |
| Trapezoid (Trapezium) | A = ½(a+b)h | P = a+b+c+d | a,b = parallel sides, h = height | c,d = non-parallel legs |
| Parallelogram | A = b × h | P = 2(a+b) | b = base, h = perpendicular height | Or A = ab·sin(θ) |
| Rhombus | A = (d₁ × d₂)/2 | P = 4a | d₁,d₂ = diagonals, a = side | Also A = a²sin(θ) |
| Regular Polygon | A = (ns²)/(4·tan(π/n)) | P = n × s | n = sides, s = side length | Or A = ½ × P × apothem |
| Sector of Circle | A = ½r²θ | P = rθ + 2r | r = radius, θ = angle in radians | θ(°) to radians: θ × π/180 |
| Annulus (Ring) | A = π(R²-r²) | Two circles | R = outer radius, r = inner radius | Area between two concentric circles |
How to Use the Area Calculator — Step-by-Step
Instructions for all six shape modes, tips for accurate measurement, and when to use each method
- 1
Select Your Shape
Click the shape button that matches what you're measuring: Rectangle for rooms, gardens, walls, fields; Circle for circular pools, tables, trees; Triangle for triangular plots, roofs, sails; Trapezoid for irregular plots with two parallel sides; Ellipse for oval shapes; Polygon for any regular shape with equal sides (hexagonal rooms, octagonal features).
- 2
Choose Your Unit
Select the unit you're measuring in (m, cm, mm, ft, in, or yd) using the unit buttons. The calculator automatically shows results in that unit squared (e.g., m²) AND converts to all other common units in the results panel. For large outdoor spaces use metres; for rooms use metres or feet; for small objects use centimetres.
- 3
Enter Your Dimensions
Type your measurements into the input fields. Use decimal points for non-integer values (e.g., 3.75 not 3¾). For triangles, choose the input method that matches the measurements you have: base+height is simplest, Heron's formula if you know all three sides, SAS if you know two sides and the angle between them, or coordinate method if you have x,y points from a map or drawing.
- 4
Click Calculate
Press the green "Calculate Area" button. The results panel shows the area in your chosen unit, perimeter/circumference, full step-by-step working with the exact formula applied, unit conversions to m², cm², ft², and in², related measurements, and a complete details breakdown. Use the quick example tabs to try sample calculations instantly.
- 5
Use the Results
For practical applications: multiply m² by litres-per-m² to get paint, fertiliser, or water quantities. For flooring: your m² result × price per m² = material cost. For tiles: area ÷ tile area = number of tiles. Use the Share buttons to send the result via WhatsApp, tweet it, or copy to clipboard for pasting into a quote or document.
Area Unit Conversion Table — m², cm², ft², in², and More
Convert between any square area units instantly with this comprehensive conversion reference
| From ↓ / To → | m² | cm² | mm² | ft² | in² | yd² | acre | hectare |
|---|---|---|---|---|---|---|---|---|
| 1 m² | 1 | 10,000 | 1,000,000 | 10.7639 | 1,550 | 1.196 | 0.000247 | 0.0001 |
| 1 cm² | 0.0001 | 1 | 100 | 0.001076 | 0.155 | 0.0001196 | — | — |
| 1 ft² | 0.0929 | 929.03 | 92,903 | 1 | 144 | 0.1111 | 0.0000229 | 0.00000929 |
| 1 in² | 0.000645 | 6.4516 | 645.16 | 0.00694 | 1 | 0.000772 | — | — |
| 1 yd² | 0.8361 | 8,361 | 836,127 | 9 | 1,296 | 1 | 0.000207 | 0.0000836 |
| 1 acre | 4,047 | 40,468,564 | — | 43,560 | 6,272,640 | 4,840 | 1 | 0.4047 |
| 1 hectare | 10,000 | 100,000,000 | — | 107,639 | 15,500,031 | 11,960 | 2.471 | 1 |
Real-World Area Calculations — Practical Applications & Examples
How area calculations are used in everyday life, construction, agriculture, science, and design
Floor Area & Room Planning
Calculating floor area is essential for buying flooring, tiles, or carpet. A 4.5 × 3.2 m bedroom = 14.4 m². If carpet costs £25/m², that's £360 for the room. Always add 10% for cuts and waste. For irregular rooms, break into rectangles and add up.
Garden & Landscaping
Lawn area determines how much seed or fertiliser to buy. A 10 × 8 m rectangular lawn = 80 m². At 35 g/m² of seed, you need 2.8 kg. For turf at £5/m², the lawn costs £400. Circular flower beds (radius 2 m) = π × 4 ≈ 12.57 m² of planting area.
Painting & Decorating
Calculate wall area to buy the right amount of paint. A room 5 × 4 m with 2.4 m ceilings has wall area ≈ 43.2 m² (minus doors and windows). Standard paint covers 12–16 m²/litre; you'd need about 3–4 litres per coat. Ceiling area = 5 × 4 = 20 m² additional.
Agriculture & Land Management
Farmers calculate field area for planting density, yield projections, and chemical application rates. 1 hectare = 10,000 m² ≈ 2.47 acres. A 100 × 100 m square field = 1 ha. Herbicide at 2 litres/ha means ordering exactly the right quantity based on precise field measurements.
Construction & Building
Architects and builders calculate surface areas constantly — for roofing felt, insulation, cladding, and rendering. A hip roof might have four trapezoidal faces; each requires the formula A = ½(a+b)h. Concrete for a circular pad (r = 3 m) = π × 9 ≈ 28.27 m² × depth.
Science & Engineering
Area appears in physics as cross-sectional area for calculating fluid flow rates, heat transfer, structural stress, and electrical resistance. The formula for pressure (Force ÷ Area) shows why high-heeled shoes damage floors — concentrating force on a tiny area (≈ 1 cm²) creates enormous pressure.
Land & Property
Property measurements are one of the most financially significant area calculations. Residential properties are measured in m² (UK) or ft² (US). A difference of 10 m² at £5,000/m² means £50,000. Always verify floor area using our calculator against estate agent figures — errors are common.
Surprising Everyday Uses
A 16-inch pizza has area = π × 8² ≈ 201 in². A 12-inch pizza = π × 6² ≈ 113 in². The 16-inch pizza is 78% bigger, yet often only 50% more expensive — making it the better value. Similarly, a 10 cm cookie is 4× the area of a 5 cm cookie (area scales as radius squared).
Area Calculator — Frequently Asked Questions
Expert answers to the most common questions about calculating area, perimeter, and unit conversion