Rhombus Area Calculator
Rhombus area from diagonals, plus side and perimeter.
What it does
A rhombus is the tilted square of tiling floors and quilt blocks: four equal sides with diagonals crossing at right angles. Those diagonals unlock everything, since half their product is the area.
The tool above takes both diagonals in centimeters or inches. It returns area, side length, and perimeter. The default 8 and 6 gives 24 cm2 with side 5 cm and perimeter 20 cm.
The formula sits in standard prealgebra and contemporary mathematics texts as half the diagonal product, with the side from half diagonal Pythagoras. Checks agree: 10 and 24 give 120 cm2 with side 13, and 3.15 with 2.36 in gives 3.72 in2.
Diamonds in cards, tiles, and garden beds all follow the same half product. When diagonals match, the rhombus graduates to square; when only one pair of sides matches, the kite next door borrows half the method.
How to use
- Pick centimeters or inches.
- Type both diagonals.
- Read area first.
- Read side beside it.
- Read perimeter last.
- Cross check: area / side must look sane.
Formula
- d1, d2
- Diagonal lengths in the same units.
- side
- Edge from half diagonal Pythagoras.
- P
- Four equal edges added.
Imperial inputs convert to centimeters first (x 2.54), then square centimeters divide by 6.4516 for square inches, so both systems agree. OpenStax prealgebra and contemporary mathematics texts carry the diagonal formula with the same half product.
Worked example
Example: diagonals 8 and 6
Metric defaults: diagonals 8 cm and 6 cm.
- Diagonals: 8 cm and 6 cm.
- Area: 8 x 6 / 2 = 24 cm2.
- Half diagonals: 4 and 3 cm.
- Side: root(16 + 9) = 5 cm.
- Perimeter: 4 x 5 = 20 cm.
- Tool shows 24 cm2, 5 cm, 20 cm.
Reference table
| Diagonals | Side | Area |
|---|---|---|
| 8 and 6 cm | 5 cm | 24 cm2 |
| 10 and 24 cm | 13 cm | 120 cm2 |
| 3.15 and 2.36 in | 1.97 in | 3.72 in2 |
| 12 and 5 cm | 6.5 cm | 30 cm2 |
Limits
- Straight edges assumed; curved tiles differ.
- Diagonals must cross at right angles.
- Single plane figures only.
- Units must match across inputs.
Common mistakes
- Multiplying diagonals without halving.
- Using a side as a diagonal.
- Mixing cm and inches in one run.
- Reporting length units for an area.
- Assuming all diamonds are squares.
Try it yourself
Quick checks. Answers sit tucked under each question.
Diagonals 10 and 24?
Area 120 cm2, side 13 cm, perimeter 52 cm.
Diagonals 3.15 and 2.36 in?
Area 3.72 in2, side 1.97 in, perimeter 7.87 in.
Why is the side 5?
Halves 4 and 3 give side 5: the 3-4-5 triangle hides inside.
Questions
What is the rhombus formula?
Half the product of the diagonals: A = d1 x d2 / 2. A square is the special case with equal diagonals.
Side from diagonals?
Root of the half diagonal squares: root((d1/2)2 + (d2/2)2). Here root(16+9) = 5.
Perimeter?
Four times the side. Equal sides make it a parallelogram with flair.
No base needed?
Yes, by diagonals alone. Base times height needs the altitude instead.
Rhombus or kite?
A kite shares perpendicular diagonals but adjacent sides differ, so the side math splits.
Unit conversion?
50 / 6.4516: 24 cm2 reads 3.72 in2, matching the imperial inputs.