Rhombus Formulas (Area, Perimeter)

A rhombus is a quadrilateral with four equal sides whose diagonals meet at right angles. Its area is A = ½·d₁·d₂, half the product of the diagonals. Each side is √((d₁/2)² + (d₂/2)²), so the perimeter is P = 4s.

Rhombus formulas

Area: $A = \tfrac{1}{2} d_1 d_2$
Side: $s = \sqrt{(d_1/2)^2 + (d_2/2)^2}$
Perimeter: $P = 4s$

where d₁, d₂ = the two diagonals, s = side length, A = area

Area

A = \tfrac{1}{2} d_1 d_2

Worked example

A rhombus with diagonals 6 and 8 has area 24 and side length 5.

A = \tfrac12 d_1 d_2 = \tfrac12\cdot 6\cdot 8 = 24

Side

s = \sqrt{(d_1/2)^2 + (d_2/2)^2}

Perimeter

P = 4s

Interactive rhombus explorer

Drag a slider (or type a value, or use the arrow keys) and watch the diagram, the results, and the full step-by-step substitution update live.

Diagonal d₁ d₁

Diagonal d₂ d₂

Area A 24units²

Side s 5units

Perimeter P 20units

Step-by-step substitution

A = ½ · d₁ · d₂ = ½ · 6 · 8 = 24
side = √((d₁/2)² + (d₂/2)²) = 5
P = 4 · side = 4 · 5 = 20

Classroom use: rhombus formulas

Who it's for: Grades 6–10 · Middle and high-school students studying quadrilateral classification and the diagonal area rule.

Learning objectives

After using this page, students will be able to:

Compute rhombus area from its two diagonals using A = ½d₁d₂.
Explain why a rhombus is also a parallelogram but not always a square.
Choose between the diagonal rule and the base-height rule given the data available.

Suggested classroom activity

Give students a rhombus described two ways — by diagonals and by base and height — and have them verify both routes agree in the explorer. It is a compact argument that the two formulas are the same claim in different clothes.

Standards alignment

Aligned to the Common Core State Standards for Mathematics. Codes are given exactly as published so they can be matched against state crosswalks.
Code	Standard
`6.G.A.1`	Find the area of triangles, special quadrilaterals, and polygons by composing or decomposing shapes.
`7.G.B.6`	Solve real-world problems involving area, volume, and surface area of 2-D and 3-D objects.
`HSG.CO.C.11`	Prove theorems about parallelograms.

Free to use and adapt in class under the terms on our license page — no account, no sign-up, no ads. Content last reviewed August 2026.

Related & next steps

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Frequently asked questions

How do you find the area of a rhombus?

The area of a rhombus is A = ½·d₁·d₂, half the product of its diagonals. With diagonals 6 and 8, the area is ½ × 6 × 8 = 24 square units.

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