Rhombus Calculator - Area from Diagonals, Side

The Rhombus Calculator finds area from the two diagonals or from base and height, computes side length from diagonals when they are perpendicular, and reports perimeter from the side. All four sides are equal, so one side length times four gives the perimeter.

Diagonals of a rhombus cross at right angles and bisect each other, splitting the figure into four congruent right triangles. That geometry is why half of each diagonal appears inside the Pythagorean theorem for side length.

Calculate a rhombus from its diagonals

When both diagonals are known, area follows from half their product because the diagonals divide the rhombus into four triangles whose combined area simplifies to d1 * d2 / 2. Enter diagonal lengths along the crossing axes shown on the diagram. The tool labels d1 and d2 on the figure.

Side length and perimeter can follow from the same diagonals when they are perpendicular, which holds for every rhombus. The result panel orders area first, then side and perimeter when computable.

Calculate the area two ways

Diagonal area and base-height area must agree when the same rhombus is described two ways. Base in the second form is any side, and height is the perpendicular distance between opposite sides. Pick the inputs available on the worksheet.

A = (d1 * d2) / 2
A = base * height

For diagonals 6 and 8:

A = (6 * 8) / 2 = 24

Calculate the side from the diagonals

Each side is the hypotenuse of a right triangle with legs half of d1 and half of d2 because diagonals bisect each other at right angles. Take the positive square root for side length. Perimeter is four times that side.

side = sqrt((d1/2)^2 + (d2/2)^2)

For d1 = 6 and d2 = 8:

side = sqrt(3^2 + 4^2) = sqrt(9 + 16) = 5

Solve a rhombus with diagonals 6 and 8

Use d1 = 6 and d2 = 8 as the reference rhombus. Area is an integer. Side length falls into a 3-4-5 triangle scaled on the half-diagonals. 1. Area

A = (6 * 8) / 2 = 24

2. Side

side = sqrt(3^2 + 4^2) = 5

3. Perimeter

P = 4 * 5 = 20

Understand how a rhombus differs from a parallelogram

Every rhombus is a parallelogram with four equal sides. Not every parallelogram is a rhombus unless the adjacent sides match. A square is both a rhombus and a rectangle when diagonals are equal as well as perpendicular. The parallelogram page keeps general opposite-side equality.

The rhombus page adds equal sides and the diagonal product area shortcut. The square case also fits the rectangle calculator in square mode.

Frequently asked questions

Summary

Rhombus Calculator returns the measures named in the sections above, with substituted arithmetic for every formula and a labelled figure drawn to the entered dimensions. Worked numbers on this page match the geometry reference fixtures.