Input mode
Area—
Perimeter—
Vertices—
Step by step
Areas are in square units of whatever unit you enter — feed the calculator metres and you get square metres.
Find the area of any polygon — an irregular shape from its vertex coordinates (shoelace formula), a triangle from its three sides (Heron's formula), or a regular polygon from its side length. Every mode shows the worked steps.
Input mode
Step by step
Areas are in square units of whatever unit you enter — feed the calculator metres and you get square metres.
Pick the mode that matches what you know about the shape.
List the vertices as (x, y) coordinates in order around the polygon, clockwise or counter-clockwise. The shoelace formula, A = ½ |Σ (xᵢ·yᵢ₊₁ − xᵢ₊₁·yᵢ)|, then gives the exact area of any simple (non-self-crossing) polygon, no matter how irregular. This is the general method — it works for triangles, quadrilaterals, and shapes with dozens of sides.
Three side lengths pin a triangle to a single shape, so its area follows from Heron's formula: s = (a + b + c) / 2, then A = √(s(s−a)(s−b)(s−c)). The sides must obey the triangle inequality — each shorter than the other two added together — or no triangle exists.
A regular polygon has n equal sides of length s, so its area is A = (n · s²) / (4 · tan(π/n)). Enter the number of sides and one side length to get the area, perimeter, apothem, and interior angle. Working with a right triangle? The Pythagorean Theorem Calculator finds a missing side; the Circle Area Calculator covers circles.
A triangle is rigid: fix its three sides and the shape can't move, so the area is determined. Add a fourth side and the figure becomes a hinge — a square with sides of 4 has an area of 16, but push it over into a thin rhombus and the four sides are still 4 while the area shrinks toward zero. The same freedom exists for every polygon with four or more sides. That is why this calculator deliberately offers no "quadrilateral from four sides" mode: it would be ill-posed. To pin down an irregular shape you need its coordinates (use the shoelace mode), or a real-world measurement.