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Numbers · geometry · rhombusArea of a rhombus — formula and calculator

Work out the area of a rhombus with the formula S = d₁ × d₂ / 2 — your numbers substituted and a diagram drawn. The perimeter is calculated too. Units can be mixed, and the answer comes in the units you need, hectares and acres included.

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01Calculator02Formula03Example04Mistakes05Nearby06Related
01

Calculator

enter the sizes — the formula and diagram follow

Rhombus

area · perimeter
d₁ = 8 cmd₂ = 6 cm
diagram · not to scale
Result
Area
24cm²
= 0.0024 m²
Perimeter
20cm
= 0.2 m
How it was calculated
a = √((d₁ / 2)² + (d₂ / 2)²) = √((8 / 2)² + (6 / 2)²) = 5 cm
S = d₁ × d₂ / 2 = 8 × 6 / 2 = 24 cm²
P = 4a = 4 × 5 = 20 cm
← Other shapes and the composite shape
02

Formula

and what each letter means
Side
a = √((d₁ / 2)² + (d₂ / 2)²)
Area
S = d₁ × d₂ / 2
Perimeter
P = 4a
Notation
d₁, d₂
diagonals — they cross at a right angle
a
side of the rhombus
03

Worked example

with real numbers
Givend₁ = 8 cm, d₂ = 6 cm
Solution
a = √((d₁ / 2)² + (d₂ / 2)²) = √((8 / 2)² + (6 / 2)²) = 5 cm
S = d₁ × d₂ / 2 = 8 × 6 / 2 = 24 cm²
P = 4a = 4 × 5 = 20 cm
Answer: area — 24 cm², perimeter — 20 cm.
04

Common mistakes

The product of the diagonals must be halved — otherwise you get the area of the bounding rectangle.

The side is not half a diagonal: it is the hypotenuse of a triangle with legs d₁ / 2 and d₂ / 2.

05

Nearby shapes

SquareS = a²ParallelogramS = a × hRegular polygonS = n·a² / (4 tan(180° / n))CalculatorAll 19 shapes, the composite shape and hectares →
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