Area Calculator
Find the area and perimeter of a square, rectangle, triangle, parallelogram, trapezoid, circle, semicircle, sector, ellipse, regular polygon, rhombus or ring, exact in terms of π where it applies, with a labelled drawing and the area in other units.
How to Use
- Choose the shape. The boxes change to the measurements that shape needs.
- Choose a unit (optional) and type the dimensions. Decimals and fractions such as 3/8 or 1 1/2 are fine.
- Read the area, the perimeter and the exact area in terms of π or √ where there is one.
- The table gives extra measurements (diagonal, arc length, angles …) and, with a unit, the same area in square metres, square feet, acres, hectares and more.
- The drawing labels each dimension on the shape; Show Work below has every step.
Worked Example
A room. 12 ft × 10 ft = 120 ft² of floor, with a perimeter of 2(12 + 10) = 44 ft. One square foot is 0.3048² = 0.09290304 m², so the room is 120 × 0.09290304 = 11.15 m².
Two pizzas or one? A 16-inch pizza has radius 8: π × 8² = 64π ≈ 201.06 in². Two 12-inch pizzas have 2 × π × 6² = 72π ≈ 226.19 in², so two 12-inch pizzas are more food than one 16-inch.
A triangle from three sides. Sides 13, 14 and 15: s = 42 ÷ 2 = 21, and Heron’s formula gives √(21 × 8 × 7 × 6) = √7056 = 84.
The common mistake: using the diameter as the radius. A 12-inch pizza is 12 inches across, so r = 6 and the area is π × 6² ≈ 113.10 in², not π × 12² ≈ 452.39 in², which is four times too big.
Show Work
Formulas
From Field Surveys to Heron
Area began with land. The Egyptian Rhind Papyrus (copied by the scribe Ahmes around 1550 BC) finds the area of a round field of diameter 9 by squaring 8, eight ninths of the diameter. That works out to π ≈ 256/81 ≈ 3.1605, within 1% of the true value.
Archimedes, in Measurement of a Circle (3rd century BC), proved that a circle has the same area as a right triangle whose two short sides are the radius and the circumference, which is ½ × 2πr × r = πr². Using 96-sided polygons he pinned π between 223/71 and 22/7. Heron of Alexandria wrote down the three-sides formula in his Metrica in the 1st century AD, though Arab writers later credited it to Archimedes.
About This Calculator
This calculator finds the area and perimeter of twelve flat shapes, including a triangle from three sides by Heron’s formula. It keeps whole numbers, decimals and fractions exact, so a circle’s area comes out as 25π and a hexagon’s as 6√3, and gives the extra measurements each shape has: diagonals, arc lengths, angles, the apothem. With a unit chosen it converts the area to square metres, square feet, acres, hectares and the other common units.
Everything runs in your browser; nothing is sent anywhere.
Related calculators: Circle Calculator, Triangle Calculator, and Square Footage Calculator.
Frequently Asked Questions
What are the area formulas for common shapes?
Rectangle: length × width. Triangle: ½ × base × height. Parallelogram: base × height. Trapezoid: ½(a + b) × height. Circle: πr². Ellipse: πab. A 12 × 10 ft room is 120 ft², a triangle with base 4 and height 3 is 6, and a circle of radius 5 is 25π ≈ 78.54.
How do I find the area of a triangle from its three sides?
Use Heron’s formula. Halve the perimeter to get s, then the area is √(s(s − a)(s − b)(s − c)). For sides 13, 14 and 15, s = 21 and the area is √(21 × 8 × 7 × 6) = √7056 = 84. If the two shorter sides don’t add up to more than the longest, there is no triangle.
Why is the area given in terms of π?
Because it is exact. A circle of radius 5 has an area of exactly 25π, about 78.5398. Rounding π to 3.14 first gives 78.5, already wrong in the first decimal place. Square roots are kept the same way: a regular hexagon with side 2 has an area of exactly 6√3 ≈ 10.3923.
How do I convert square feet to square metres?
Square the length factor. One foot is 0.3048 m, so one square foot is 0.3048² = 0.09290304 m², and one square metre is 10.7639 ft². A 120 ft² room is 11.15 m². Multiplying by 0.3048 only once gives 36.58, which is wrong. An acre is 43,560 ft².
Does doubling the size double the area?
No: it multiplies it by 4, because area grows with the square of length. A 16-inch pizza (64π ≈ 201 in²) is only a third wider than a 12-inch one (36π ≈ 113 in²) but has 1.78 times the area.
How do I use the Area Calculator?
Simply type your numbers and read the result, which refreshes the instant you change something. There is nothing to submit and nothing to wait for.
Do I need to install or sign up for anything?
Not at all — it runs in the browser with nothing to install and no account. After it loads once, it even works without an internet connection.
Is my information private?
Yes. Everything happens in your browser. Nothing you type is sent to a server or saved anywhere.
Common Use Cases
Flooring and paint
A 12 × 10 ft room is 120 ft² (11.15 m²) of floor and 44 ft of skirting.
Pizza value
A 16-inch pizza is 201 in², 1.78 times a 12-inch at 113 in².
Gardens
A round bed of radius 1.5 m covers 2.25π ≈ 7.07 m².
Washers and rings
Outer radius 8 mm, inner 5 mm: 39π ≈ 122.5 mm² of bearing face.
Tiles
A hexagonal tile with 2 cm sides covers 6√3 ≈ 10.39 cm².
Land
An acre is 43,560 ft², or 4,046.86 m².
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