Perimeter of a Quadrilateral Calculator
Enter the four side lengths or the x/y coordinates of each corner to find the perimeter of any quadrilateral - square, rectangle, rhombus, parallelogram, trapezoid, kite, or an irregular four-sided shape. Switch between metric and imperial at any time. The step-by-step panel shows exactly how each side contributes to the total.
Formula
Worked example
A rectangle has sides 8 cm and 5 cm. P = 8 + 5 + 8 + 5 = 26 cm. Using coordinates (0,0), (8,0), (8,5), (0,5): each side = sqrt((8-0)^2 + 0^2) = 8 and sqrt(0 + (5-0)^2) = 5, giving the same 26 cm.
What is the perimeter of a quadrilateral?
The perimeter of any polygon is simply the total distance around its outside edge. For a quadrilateral - any flat, closed shape with exactly four sides - that means adding the lengths of all four sides together: P = a + b + c + d. The result is always in the same unit as the sides you enter. Perimeter is a one-dimensional measure (length), not area, so doubling all four sides doubles the perimeter but quadruples the area.
How to use this calculator
Choose "Four side lengths" if you already know how long each side is. Enter a, b, c, and d and pick metric (centimetres) or imperial (inches). The perimeter appears instantly alongside a bar chart showing how each side contributes. Choose "Four vertex coordinates" if you have the corner positions from a graph, a map, or a CAD drawing. Enter the x and y coordinates of each corner in order (either clockwise or counter-clockwise). The calculator uses the distance formula to compute each side length, then sums them for the perimeter.
Coordinate mode and the distance formula
When you enter corner coordinates, each side length is found with the Euclidean distance formula: d = sqrt((x2 - x1)^2 + (y2 - y1)^2). For example, if one corner is at (0, 0) and the next is at (8, 0), the side length is sqrt(64 + 0) = 8. The four sides are computed in the order you enter the vertices (1 to 2, 2 to 3, 3 to 4, 4 back to 1), and then summed. The coordinates can be any real numbers, including negative values, and the unit of the perimeter is the same as the unit of the coordinate grid.
Perimeter of specific quadrilateral types
Most named quadrilaterals have simplified formulas because their sides are related by symmetry. A square has four equal sides, so P = 4a. A rectangle with length l and width w has P = 2(l + w), because opposite sides are equal. A rhombus is like a square without right angles - all four sides equal, so P = 4a again. A parallelogram has two pairs of equal opposite sides, giving P = 2(a + b). A kite has two pairs of adjacent equal sides (the two "top" sides equal each other, and the two "bottom" sides equal each other), so P = 2(a + b) where a and b are the two distinct lengths. For a general trapezoid or any irregular quadrilateral, all four sides must be entered separately.
Perimeter formulas for common quadrilaterals
| Shape | Properties | Perimeter formula |
|---|---|---|
| Square | All sides equal, all angles 90 deg | P = 4a |
| Rectangle | Opposite sides equal, all angles 90 deg | P = 2(l + w) |
| Rhombus | All sides equal, opposite angles equal | P = 4a |
| Parallelogram | Opposite sides parallel and equal | P = 2(a + b) |
| Trapezoid (trapezium) | One pair of parallel sides | P = a + b + c + d |
| Kite | Two pairs of adjacent equal sides | P = 2(a + b) |
| Irregular quadrilateral | No special symmetry | P = a + b + c + d |
Simplified formulas apply when the shape has special symmetry. For irregular quadrilaterals always use P = a + b + c + d.
Frequently asked questions
What is the formula for the perimeter of a quadrilateral?
The general formula is P = a + b + c + d, where a, b, c, and d are the four side lengths. For shapes with equal sides the formula simplifies: a square uses P = 4a, a rectangle uses P = 2(l + w), a rhombus uses P = 4a, and a parallelogram or kite uses P = 2(a + b). For irregular quadrilaterals, you must add all four sides individually.
Can I calculate the perimeter from coordinates?
Yes. Switch the input mode to "Four vertex coordinates" and enter the x and y position of each corner. The calculator uses the distance formula d = sqrt((x2 - x1)^2 + (y2 - y1)^2) for each of the four sides, then sums them. This is useful for shapes drawn on a grid, a coordinate plane in a maths problem, or GPS-referenced land plots.
Is the perimeter the same as the area?
No. Perimeter is the total length of the boundary - a one-dimensional measurement in units such as cm or inches. Area is the amount of surface inside the boundary - a two-dimensional measurement in square units. Two quadrilaterals can have the same perimeter but very different areas (a long, thin rectangle and a nearly-square one, for example), and vice versa.
What is the difference between a convex and a concave quadrilateral?
A convex quadrilateral has all interior angles less than 180 degrees, so the shape bulges outward on every side (rectangle, rhombus, trapezoid). A concave quadrilateral has one interior angle greater than 180 degrees, creating a "dent" or re-entrant corner (sometimes called an arrowhead or dart shape). The perimeter formula P = a + b + c + d applies to both, as long as you measure each physical side length correctly.
How do I find the perimeter of an irregular quadrilateral?
Measure each of the four sides individually, then add them together. If you know the corner positions, enter them in coordinate mode and the calculator applies the distance formula to each side automatically. There is no shortcut based on angles or diagonals alone - you need the side lengths.
Does the order of vertices matter in coordinate mode?
Yes - enter the four corners in a consistent order, either all clockwise or all counter-clockwise around the shape. If you enter them in a "crossed" order the calculator will compute a self-intersecting figure whose perimeter does not match the visible outline.