Area Calculator – Rectangle, Square, Triangle & Circle

Use this free online Area Calculator to find the two-dimensional surface area of rectangles, squares, triangles, and circles in metric or imperial units. Select your shape in the calculator card, enter your measurements, and view the exact square-unit area alongside the geometric formula and step-by-step math.

Below the calculator, you will also find complete geometric formulas, unit conversion tables (including square millimeters, acres, and hectares), worked project examples, and reference formulas for trapezoids, parallelograms, and L-shaped rooms.

Jump to the Area Calculator above to enter your dimensions and calculate immediately.

What Is Area?

Area is the measure of how much two-dimensional flat space lies inside a closed geometric boundary. Geometrically, if you cover a flat surface with 1-by-1 unit squares—such as 1 meter by 1 meter tiles—without leaving gaps or overlapping edges, the total count of squares equals the shape's area.

Understanding area is essential across everyday projects, academic geometry, and engineering:

• Home renovation & construction: Estimating hardwood flooring, ceramic tile, carpet, drywall sheets, wall paint coverage, and roof shingles.
• Landscaping & agriculture: Sizing lawn sod, garden beds, patio pavers, irrigation zones, and farmland parcels in square meters, acres, or hectares.
• Architecture & real estate: Comparing gross floor area (square footage or square meterage) of rooms, apartments, warehouses, and building lots.
• Mathematics & manufacturing: Solving plane geometry problems and calculating sheet-metal, glass, or fabric material requirements.

Note on 2D area vs. 3D surface area: In plane geometry, area measures a single flat two-dimensional figure. When working with a three-dimensional solid (such as a rectangular box or cylinder), total surface area equals the sum of the 2D areas of each outer face—which you can compute by finding the area of each rectangular or circular face individually and adding them together.

Difference Between Area, Perimeter, and Volume

Students and DIY planners frequently confuse boundary length, surface coverage, and three-dimensional capacity. Keeping their dimensions and units distinct prevents costly ordering errors:

How to Calculate Area

Regardless of whether you are measuring a small tabletop in square centimeters or a commercial lot in square feet, calculating area follows four consistent mathematical principles:

1. Identify the shape geometry: Determine whether the surface is a rectangle, square, triangle, circle, trapezoid, parallelogram, or a composite layout that needs to be split into simpler parts.
2. Measure the required linear dimensions: Depending on the figure, measure length and width, base and perpendicular height, three side edges, or radius (distance from the center of a circle to its rim).
3. Standardize all units before multiplying: Every measurement fed into a manual formula must share the same linear unit. For instance, convert 6 inches to 0.5 feet before multiplying by a length in feet (or let the calculator above convert mixed units automatically).
4. Apply the formula and write square units: Multiplying two linear measurements multiplies both the numbers and the units—for example, 8 m × 5 m = 40 m² (read as "40 square meters").

Quadratic scaling behavior: Because area multiplies two perpendicular dimensions, scaling every linear side of a shape by a factor of k multiplies its area by k². Doubling a 3 ft × 3 ft square (9 ft²) to 6 ft × 6 ft produces 36 ft²—four times the surface area, not twice.

How to Use the Area Calculator

1. Select a shape in the dropdown menu: Choose Rectangle (also used for squares), Triangle, or Circle at the top of the calculator card.
2. Enter your measurements:
   • Rectangle / Square: Enter Length and Width (enter identical values for a square).
   • Triangle: Enter all three boundary lengths—Edge a, Edge b, and Edge c.
   • Circle: Enter the Radius (if you measured diameter across the center, divide it by 2 first).
3. Pick your measurement units: Select meters, centimeters, kilometers, inches, feet, yards, or miles for each input. If your inputs use different units, the calculator automatically standardizes all values into the unit selected for the first input field.
4. Read the result and step-by-step solution: Results update automatically as you type or when you click Calculate. The output shows the exact area in square units (rounded up to 4 decimal places) followed by unit conversion steps (Step 0, when mixed units are used), the formula (Step 1), and the substituted calculation (Step 2).

Tip for tape-measure fractions: If your measurements include imperial fractions such as 5/8 in or mixed numbers like 12 3/4 ft, convert them quickly into decimal values first using our Fraction to Decimal Calculator or Mixed Numbers Calculator.

Area Formulas for Different Shapes

The table below summarizes the core plane geometry area formulas, the dimensions required, and how each shape relates to the interactive calculator above:

1. Rectangle Area Formula

A rectangle has four right angles (90°) and two pairs of equal opposite sides. Multiply its length by its perpendicular width:

Practical example: A rectangular deck measures 6 m long by 4.5 m wide. Entering 6 and 4.5 meters in the Rectangle mode gives 6 × 4.5 = 27 m².

2. Square Area Formula

A square is a special case of a rectangle in which all four sides share the exact same length s. Multiply one side length by itself:

Practical example: A square courtyard tile zone with side s = 6.5 m covers 6.5 × 6.5 = 42.25 m². To compute this directly in the calculator above, keep Rectangle selected and type 6.5 for both Length and Width. Conversely, if you already know a square's area and need its side length (s = √A), evaluate the root with our Square Root Calculator.

3. Triangle Area Formula (Base-Height & Heron's Formula)

Depending on which measurements you can take on site or read from a geometry diagram, two primary formulas find the area of any triangle:

• Base and Perpendicular Height Formula (Reference): When you know one base b and the perpendicular altitude h dropped at 90° to that base:
  Area = ½ × base × height
  Example: A roof gable with a 10 m horizontal base and a 3.2 m vertical peak height has an area of 0.5 × 10 × 3.2 = 16 m².
• Heron's Three-Side Formula (Used in This Calculator): Measuring a true 90° interior height across a lawn or land parcel is often impractical, whereas measuring the three outer boundary edges (a, b, c) with a tape or laser meter is straightforward. The Triangle mode of our calculator applies Heron's formula in two steps:
  Step 1: s = (a + b + c) ÷ 2  (semi-perimeter)
  Step 2: Area = √[s(s − a)(s − b)(s − c)]
  Example: For sides a = 13 m, b = 14 m, and c = 15 m, the semi-perimeter is s = (13 + 14 + 15) ÷ 2 = 21 m, giving Area = √(21 × 8 × 7 × 6) = √7,056 = 84 m².

Triangle Inequality check: Three lengths form a closed triangle only if the sum of every pair of sides exceeds the remaining side (a + b > c, a + c > b, and b + c > a). If you enter edges such as 4 ft, 5 ft, and 12 ft, the two shorter edges cannot meet, and the calculator alerts you that the edges do not form a valid triangle.

4. Circle Area Formula (Radius & Diameter)

Every point on a circle sits at a constant distance—the radius (r)—from the center. Multiply the mathematical constant Pi (π ≈ 3.14159265) by the square of the radius:

Practical example: Suppose a round above-ground pool has a measured diameter of 18 ft across the middle. Divide by 2 to get radius r = 9 ft, then enter 9 feet in Circle mode: Area = π × 9² = 81π ≈ 254.4690 ft². For a semicircle (half-circle), compute the full circle area first and divide the result by 2.

5. Trapezoid Area Formula (Reference)

A trapezoid (called a trapezium in British English) is a four-sided polygon with one pair of parallel bases (a and b) separated by a perpendicular height (h). While trapezoids are not an interactive tab in the widget above, you can calculate trapezoid area manually or with our Simple Calculator by averaging the two parallel bases and multiplying by the height:

Practical example: A sloped retaining-wall section has a top width a = 6 m, a bottom width b = 10 m, and a vertical height h = 4 m. Its area is 0.5 × (6 + 10) × 4 = 0.5 × 16 × 4 = 32 m².

6. Parallelogram Area Formula (Reference)

A parallelogram has two pairs of parallel, equal-length opposite sides, with angles that are not necessarily 90°. Like rectangles, its area equals base times height—provided you measure the perpendicular height (h) at a right angle to the base rather than along the slanted side:

Practical example: An angled paving stone has a base b = 18 cm, a slanted side of 13 cm, and a perpendicular height h = 11 cm. Ignore the slanted edge and multiply 18 cm × 11 cm = 198 cm². (Note: Parallelogram is provided here as a reference formula rather than a separate calculator dropdown option.)

How to Calculate the Area of Irregular or L-Shaped Surfaces

Real-world floor plans, gardens, and property lots rarely form a single textbook polygon. To measure an L-shaped room, T-shaped hallway, or room with a curved bay window:

1. Sketch the outline and split it with straight dividing lines into non-overlapping rectangles, triangles, or semicircles.
2. Calculate each sub-shape's area in the same unit using the Rectangle, Triangle, or Circle modes above.
3. Add the sub-areas together (and subtract any unfloored cutouts such as a kitchen island or fireplace hearth) using the Simple Calculator.

Understanding Area Measurement Units

Because area is two-dimensional, every linear unit has a squared counterpart, and land surveying adds dedicated surface units that do not use the word "square." When converting between area units, you must square the linear conversion factor: because 1 m = 100 cm, one square meter equals 100 × 100 = 10,000 cm², and because 1 yd = 3 ft, one square yard equals 3 × 3 = 9 ft².

• Square millimeters (mm²): Used in mechanical engineering, wire gauge cross-sections, and precision CAD drawings. 100 mm² = 1 cm² and 1,000,000 mm² = 1 m². (Reference unit; enter millimeter measurements divided by 10 as centimeters in the calculator.)
• Square centimeters (cm²): Ideal for small objects, craft materials, paper sizes, and laboratory surfaces. 10,000 cm² = 1 m². (Supported directly via centimeters.)
• Square meters (m²): The standard SI derived unit worldwide for apartment floor plans, wall painting, tiling, and residential plots. 1 m² ≈ 10.7639 ft². (Supported directly via meters.)
• Square kilometers (km²): Used for city districts, watersheds, forests, and geographic regions. 1 km² = 1,000,000 m² = 100 hectares. (Supported directly via kilometers.)
• Square inches (in²): Common in US woodworking, tile sizing, and pipe or duct cross-sections. 144 in² = 1 ft² and 1 in² = 6.4516 cm². (Supported directly via inches.)
• Square feet (ft²): The primary unit in the United States, Canada, and UK commercial real estate for room sizes, house square footage, drywall, and roofing. 1 ft² = 0.092903 m². (Supported directly via feet.)
• Square yards (yd²) & Square miles (mi²): Square yards (1 yd² = 9 ft² ≈ 0.8361 m²) are widely used for carpet, turf, and fabric, while square miles (1 mi² = 640 acres ≈ 2.5900 km²) measure large regional territories. (Both supported directly via yards and miles.)
• Acres (ac): Traditional imperial and US customary land-area unit for residential lots, farms, and parks. Exactly 1 acre = 43,560 ft² = 4,840 yd² ≈ 4,046.86 m². (Reference conversion: divide calculator output in ft² by 43,560, or output in m² by 4,046.86.)
• Hectares (ha): Metric land-measurement unit equal to a 100 m × 100 m square: 1 hectare = 10,000 m² = 0.01 km² ≈ 2.4711 acres. (Reference conversion: divide calculator output in m² by 10,000.)

Examples of Area Calculations

The step-by-step worked examples below illustrate how to move from raw measurements to final square-unit answers across residential, landscaping, and land-measurement scenarios.

Example 1: Rectangular Living Room Flooring (Square Feet)

• Given measurements: Length = 15 ft, Width = 12 ft, plus a 10% cutting-waste allowance.
• Formula: Area = Length × Width
• Calculation: Area = 15 ft × 12 ft = 180 ft². Adding 10% waste (you can verify waste margins with our Percentage Calculator): 180 ft² × 1.10 = 198 ft².
• Final answer: Exact floor area = 180 ft² (order 198 ft² of flooring material).

Example 2: Mixed-Unit Concrete Patio (Feet and Inches)

• Given measurements: Length = 10 ft, Width = 90 in.
• Unit conversion & formula: Standardize width to feet: 90 in ÷ 12 in/ft = 7.5 ft, then apply Area = Length × Width. (Selecting feet for Length and inches for Width in the calculator performs this conversion automatically as Step 0.)
• Calculation: Area = 10 ft × 7.5 ft = 75
• Final answer: 75 ft² (square feet).

Example 3: Triangular Land Parcel Using Three Sides (Heron's Formula)

• Given measurements: Boundary edges a = 30 m, b = 45 m, and c = 50 m.
• Formula: Semi-perimeter s = (a + b + c) ÷ 2; Area = √[s(s − a)(s − b)(s − c)]
• Calculation: s = (30 + 45 + 50) ÷ 2 = 62.5 m
Area = √[62.5 × (62.5 − 30) × (62.5 − 45) × (62.5 − 50)] = √[62.5 × 32.5 × 17.5 × 12.5] = √444,335.9375 ≈ 666.5853
• Final answer: 666.5853 m² (approximately 0.0667 hectares when divided by 10,000).

Example 4: Circular Garden Bed Measured Across the Diameter

• Given measurements: Measured diameter across the center d = 4 m.
• Formula: Radius r = d ÷ 2; Area = π × r²
• Calculation: r = 4 m ÷ 2 = 2 m → Area = π × 2² = 4π ≈ 12.5664
• Final answer: 12.5664 m² (square meters).

Example 5: L-Shaped Studio Floor Plan (Composite Subdivision)

• Given measurements: Main living zone = 14 ft × 10 ft; adjoining alcove = 8 ft × 6 ft.
• Formula: Total Area = (l₁ × w₁) + (l₂ × w₂)
• Calculation: Section 1 = 14 × 10 = 140 ft²; Section 2 = 8 × 6 = 48 ft²; Total = 140 + 48 = 188
• Final answer: 188 ft² (square feet). When scaling dimensions from architectural blueprints first, use our Ratio Calculator.

Common Area Calculation Mistakes

• Mixing linear units before multiplying: Multiplying a length of 4 meters directly by a width of 80 centimeters gives 320—which is neither square meters nor square centimeters. Always convert to one unit first (4 m × 0.8 m = 3.2 m²) or select the exact unit for each field in the calculator above so it converts them automatically.
• Plugging diameter into the circle radius formula: Entering a 10 ft diameter directly as r in π × r² yields 314.16 ft² instead of the true 78.54 ft²—an error of 300% (4× too large). Always halve the diameter first.
• Measuring slanted edges instead of perpendicular height: For triangles (base-height method), parallelograms, and trapezoids, height h must meet the base at a 90° right angle. Using a diagonal side length overstates the true surface area.
• Confusing area with perimeter: Perimeter adds side lengths to measure outer border distance (m or ft), whereas area multiplies dimensions to measure interior coverage (m² or ft²). Two rooms with identical 20 m perimeters can have very different areas (for example, a 5 m × 5 m room covers 25 m², while a 9 m × 1 m hallway covers only 9 m²).
• Forgetting to square conversion factors—or omitting square units: Converting 5 m² to cm² requires multiplying by 100² = 10,000 (giving 50,000 cm²), not 100. Likewise, always label final answers in squared units (m², ft²) so contractors and suppliers know the figure represents surface area rather than linear run.
• Rounding intermediate measurements too early: Rounding a room width from 3.46 m to 3.5 m over a 12 m length adds nearly half a square meter of error (you can check relative impact with the Percentage Change Calculator). Keep full precision during calculation and round only the final purchase quantity.

Frequently Asked Questions

Related Calculators and Tools

• Square Root Calculator – evaluate square roots in Heron's formula or find a square's side length from its area
• Fraction to Decimal Calculator – convert fractional inch or foot tape-measure readings into decimals
• Mixed Numbers Calculator – add, subtract, and multiply mixed imperial dimensions such as 12 3/4 ft
• Fraction Calculator – solve exact arithmetic with proper and improper fractional measurements
• Ratio Calculator – convert architectural blueprint scales and solve geometric proportions
• Percentage Calculator – add 10% to 15% material waste allowances for flooring, tiles, and paint
• Percentage Change Calculator – compare percentage area increases or decreases when resizing plans
• Simple Calculator – sum multiple room sections for composite floor plans and cost totals
• All English Calculators – browse our complete collection of math, fraction, finance, and statistics tools

Last updated: October 2026