Area Polygon Calculator
Fast, accurate and free online area polygon calculator tool running directly in your browser.
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Other tools you may find usefulPolygon Area Calculator - Area and Perimeter of Geometric Figures
Polygon Area Calculatorcalculates the area and perimeter of regular (triangle, square, hexagon, octagon) and irregular polygons (by vertex coordinates). Patterns with explanations for students and professionals.
Formulas for the area of basic polygons
Triangle— P = (a × h) / 2, where a = base, h = height. Or by Heron's formula: P = √(s(s-a)(s-b)(s-c)), where s = (a+b+c)/2.Square— P = a², where a = side length.Rectangle— P = a × b, where a, b = side lengths.Parallelogram- P = a × h, where a = base, h = perpendicular height.Trapezoid— P = (a + c) / 2 × h, where a, c = parallel bases, h = height.Rhombus— P = (d₁ × d₂) / 2, where d₁, d₂ = lengths of the diagonals.Regular hexagon— P = (3√3 / 2) × a², where a = side length.
Area of an irregular polygon - methods
For a polygon with arbitrary vertices, the following applies:Gauss's formula (Shoelace Formula)- P = |½ × Σ(xᵢ × yᵢ₊₁ - xᵢ₊₁ × yᵢ)|. Enter the coordinates of the vertices in the order (x₁,y₁), (x₂,y₂)... - the calculator will apply the string formula.Triangulation- divide the polygon into triangles and sum their areas. This method is visual and useful for manual calculations.Coordinate method- identical to Gauss's formula, implemented in the calculator.
Applications of the polygon area calculator
Calculations of polygon areas are necessary in: construction and architecture (calculation of plot area, rooms with irregular shapes), geodesy and cartography (calculation of plot areas from GPS measurements), cutting of materials (fabrics, sheet metal, wood), planning of gardens and green areas, graphic design (layouts, grids), geometry school tasks.
Perimeter of a polygon
The perimeter is the sum of the lengths of all sides. For a regular n-sided polygon: O = n × a, where a = side length. For irregular: O = Σ √((xᵢ₊₁-xᵢ)² + (yᵢ₊₁-yᵢ)²). The calculator calculates both area and perimeter based on the same input.
Area of regular polygons - table
Area of regular n-gons with side a=1: Triangle (n=3): P ≈ 0.433. Square (n=4): P = 1.000. Pentagon (n=5): P ≈ 1.720. Hexagon (n=6): P ≈ 2.598. Octagon (n=8): P ≈ 4.828. Dodecagon (n=12): P ≈ 11.196. General formula: P = (n × a²) / (4 × tan(π/n)).
Frequently asked questions
How to calculate the area of an irregularly shaped plot?
Get the GPS coordinates of the corners of the plot (GPS app or Google Maps map with ruler) or measure the distances between the corners. Enter the coordinates in the calculator (or side distances and angles) - it will apply the Gauss formula. For cadastral plots, reliable data can be found at geoportal.gov.pl - the cadastral map contains the area of each plot.
What is Heron's formula and when to use it?
Heron's formula calculates the area of a triangle knowing only the lengths of three sides (without the need to know the height): s = (a+b+c)/2, P = √(s×(s-a)×(s-b)×(s-c)). Use when: you know the lengths of all three sides, but you can't easily measure the height. The formula works for any triangle (acute, right-angled and obtuse).
How to calculate the area of a regular hexagon?
Regular hexagon with side a: P = (3√3/2) × a². For a = 5 cm: P = (3 × 1.732 / 2) × 25 = 2.598 × 25 ≈ 64.95 cm². Or calculator - enter the number of sides (6) and the length of the side. The regular hexagon is especially popular in honeycombs and board game design (hexagonal grids).
What is the difference between area and perimeter?
Area (P) = a measure of the area inside a figure, expressed in square units (cm², m², km²). Perimeter (O) = the length of the figure's border (the sum of the lengths of all sides), expressed in linear units (cm, m, km). Metonymy: area is "how much paint you need to paint the floor", perimeter is "how much molding you need along the walls".
How to calculate the area of a polygon from coordinates in code?
function polygonArea(points) { let area = 0; const n = points.length; for (let i = 0; i < n; i++) { const j = (i + 1) % n; area += points[i].x * points[j].y; area -= points[j].x * points[i].y; } return Math.abs(area) / 2; }. Input: array of objects {x, y}. Result: area of the polygon. The Gaussian algorithm works for any simple polygon (without self-intersections).