Area Calculator

Area is the amount of two-dimensional space enclosed within a shape, measured in square units (cm², m², in², etc.). Perimeter is the total length of the boundary of a shape, measured in linear units. Our area calculator computes both simultaneously for 9 common two-dimensional shapes — from simple squares and circles to complex regular polygons and ellipses — with the formula displayed for each shape so you always understand the calculation. All results are instant and run entirely in your browser.

1. 1. Select a Shape and Unit: Choose from 9 two-dimensional shapes using the shape selector. Select your unit of measurement (mm, cm, m, km, in, ft, or yd) — the area result will be labelled in square units and the perimeter in linear units.
2. 2. Enter the Dimensions: Fill in the required dimensions for your chosen shape. The formula is displayed above the inputs so you always know what each field represents. All inputs accept integers and decimals.
3. 3. Get Instant Results: Click Calculate Area and instantly see the area and perimeter (or circumference / arc length) side by side. All processing happens locally in your browser — your dimensions are never sent to any server.

• Square & Rectangle: Square area = a² where a is the side length; perimeter = 4a. Rectangle area = w × h; perimeter = 2(w + h). These are the most common shapes for floor plans, rooms, and rectangular plots.
• Circle & Circle Sector: Circle area = πr²; circumference = 2πr. A circle sector (pie slice) uses the central angle θ: area = (θ/360) × πr²; arc length = (θ/360) × 2πr. Useful for circular rooms, roundabouts, and pie chart segments.
• Triangle — Two Methods: If base and height are known: area = ½ × b × h. If all three sides are known but height is not, Heron's formula applies: area = √(s(s−a)(s−b)(s−c)) where s = (a+b+c)/2. The calculator validates the triangle inequality automatically.
• Trapezoid, Parallelogram & Ellipse: Trapezoid area = ½(a + b) × h where a and b are the parallel sides. Parallelogram area = base × height. Ellipse area = π × a × b where a and b are the semi-major and semi-minor axes.
• Regular Polygon: A regular polygon with n equal sides of length s: area = (n × s²) / (4 × tan(π/n)); perimeter = n × s. Works for any polygon with 3 or more sides — triangle, pentagon (5), hexagon (6), octagon (8), and beyond.

Our area calculator uses JavaScript's 64-bit floating-point arithmetic (IEEE 754 double precision), providing approximately 15–17 significant digits of precision — more than sufficient for all practical geometry work. Results are formatted to up to 6 decimal places, with scientific notation used for very large or very small values. For the triangle (three sides) mode, the calculator validates the triangle inequality (a + b > c for all combinations) and throws a clear error if the sides cannot form a valid triangle.