BYTETOOLS

Rhombus Calculator

Solve a rhombus from two diagonals, a side and an angle, a side and its height, or a side and one diagonal, with the formula behind every number shown.

24
Area
5
Side
73.74°
Acute angle
106.26°
Obtuse angle

Where each number came from

  • Side a = √((d₁/2)² + (d₂/2)²) = 5
  • Short diagonal d₁ = 6
  • Long diagonal d₂ = 8
  • Area = d₁·d₂/2 = 24
  • Cross-check: a²·sin θ = 24
  • Acute angle = 2·arctan(d₁/d₂) = 73.739795°
  • Height = Area / a = 4.8
  • Inradius = height / 2 = 2.4
  • Perimeter = 4a = 20

Solved from the diagonals you entered.

Shape

The diagonals bisect each other at right angles and bisect the interior angles.

What is the Rhombus Calculator?

The ByteTools Rhombus Calculator handles the four ways a rhombus is usually specified: both diagonals, a side plus an interior angle, a side plus the perpendicular height, or a side plus one diagonal.

  • Four input modes covering every common rhombus question
  • Area by d₁d₂/2 with an independent a²·sin θ cross-check displayed
  • Acute and obtuse angles from 2·arctan(d₁/d₂)
  • Height, inradius and perimeter included
  • Scale drawing with both diagonals, and a note when the rhombus is a square
  • 100% private — computed in your browser, never uploaded

How to use the Rhombus Calculator

  1. 1

    Choose what you know: both diagonals, side and angle, side and height, or side and one diagonal.

  2. 2

    Enter your two values in the fields that appear.

  3. 3

    Read the area, side and both angles in the summary tiles.

  4. 4

    Check the working panel to see which formula produced each result.

  5. 5

    Click Copy results to save the full solution.

About the Rhombus Calculator

The ByteTools Rhombus Calculator handles the four ways a rhombus is usually specified: both diagonals, a side plus an interior angle, a side plus the perpendicular height, or a side plus one diagonal. Whichever you pick, it recovers the missing measurements and prints the formula each one came from.

You get the side, both diagonals, area from d₁d₂/2 with an a²·sin θ cross-check, the acute and obtuse angles, the height, the inradius and the perimeter. A scale drawing shows the shape with both diagonals, which always bisect each other at right angles and bisect the interior angles.

All the trigonometry runs locally in your browser, so nothing is uploaded and the page works offline. Impossible combinations, such as a height larger than the side or a diagonal longer than twice the side, are rejected with an explanation.

Frequently asked questions

How do you find the area of a rhombus?

Multiply the two diagonals and halve the result: A = d₁d₂/2. Diagonals of 6 and 8 give an area of 24. If you know a side and an angle instead, use A = a²·sin θ — for a side of 5 at 73.74°, that also gives 24.

How do you find the side of a rhombus from its diagonals?

The diagonals bisect each other at right angles, so half of each diagonal forms a right triangle with the side. That makes the side √((d₁/2)² + (d₂/2)²). Diagonals of 6 and 8 give a side of √(9 + 16) = 5.

Is every rhombus a square?

No — a square is a special rhombus where all four angles are 90° and both diagonals are equal. Every square is a rhombus, but a rhombus only becomes a square when its diagonals match in length. The calculator points this out when it happens.

What is the height of a rhombus?

It is the perpendicular distance between two opposite sides, equal to the area divided by the side, or a·sin θ. Because the height can never exceed the side, entering a height larger than the side is impossible and the tool says so.

How do you find the angles of a rhombus from its diagonals?

The acute angle is 2·arctan(d₁/d₂), using the shorter diagonal on top, and the obtuse angle is whatever is left over from 180°. Diagonals of 6 and 8 give angles of about 73.74° and 106.26°.

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