Rectangle Calculator
Calculate area, perimeter, diagonal, and aspect ratio of a rectangle or square.
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How to use this calculator
Basic rectangle formulas derived from its length and width.
- 1
Enter the length and width of the rectangle.
- 2
For a square, enter the same value for both.
- 3
The calculator shows area, perimeter, diagonal length, and aspect ratio.
Frequently asked questions
What units does the rectangle calculator use?
None are built in. Whatever unit you type for length and width is the unit of the perimeter and diagonal, and the area is in that unit squared. Use the same unit for both sides: entering 297 and 210 (millimetres) gives an area of 62,370 mm², not square metres.
What input produces an error?
Length or width of zero or less returns “Dimensions must be positive”. There is no upper limit, and decimals are fine. Clearing a box counts as 0, so an emptied field gives the same error.
How is the aspect ratio worked out?
It divides length and width by their greatest common divisor, then prints length : width in that order. 1920 by 1080 gives 16 : 9, and 12 by 8 gives 3 : 2. Swapping the inputs swaps the ratio, so 3 by 4 reads 3 : 4.
Why is my aspect ratio such an odd pair of numbers?
Reduction only simplifies cleanly when the sides share a neat common divisor. A4 paper at 297 × 210 reduces only to 99 : 70, and 12.34 by 5.67 gives 1234 : 567. For a familiar ratio, divide length by width yourself and compare it with the shape you expect.
How does “Is Square?” decide?
It says Yes only when length and width are exactly equal as typed. 5 and 5 is a square; 5 and 5.0001 is not. For a square the diagonal is the side times √2, so a 5 × 5 square has a diagonal of 7.071068.
Can I work backwards from the area or diagonal?
No. The calculator takes both sides and returns area, perimeter, diagonal and ratio. If you know the area and one side, divide to get the other side first. A perimeter alone does not fix a rectangle, since many shapes share it.
Does a bigger perimeter mean a bigger area?
Not necessarily. At a fixed area of 36, a 6 × 6 square has a perimeter of 24, a 9 × 4 rectangle has 26, 18 × 2 has 40 and 36 × 1 has 74. The long thin shapes need much more edge for the same area.
Does it handle tilted rectangles or rectangles with cut-outs?
It only uses the two side lengths, so rotation does not matter, but notches, L-shapes and rounded corners are outside what it computes. Split such shapes into plain rectangles, run each, and add or subtract the areas.
Rectangle measurements from two sides
What the calculator returns
From a length and a width it gives the area (length × width), the perimeter (2 × (length + width)), the diagonal (the square root of length² + width²) and the reduced length : width ratio. Because the diagonal splits the rectangle into two right triangles, it is the hypotenuse of a triangle whose legs are the two sides. The 3 × 4 rectangle is the classic case: its diagonal comes out at exactly 5.
| Length × width | Area | Perimeter | Diagonal | Ratio |
|---|---|---|---|---|
| 12 × 8 | 96 | 40 | 14.422205 | 3 : 2 |
| 3 × 4 | 12 | 14 | 5 | 3 : 4 |
| 1920 × 1080 | 2073600 | 6000 | 2202.90717 | 16 : 9 |
| 297 × 210 | 62370 | 1014 | 363.743041 | 99 : 70 |
Worked example: a screen resolution
Entering 1920 and 1080 returns an area of 2,073,600, the pixel count of a full-HD display, and a ratio of 16 : 9. The diagonal of 2202.90717 is measured in pixels, not inches, so it says nothing about physical screen size unless you know the pixel density. Use the same logic for any image: area gives total pixels, and the ratio tells you whether it will fit a given frame without cropping.
Worked example: a sheet of A4
An A4 sheet is 297 mm by 210 mm. The calculator gives an area of 62,370 mm², a perimeter of 1,014 mm and a diagonal of 363.743041 mm. The ratio reduces only to 99 : 70, which shows how an exact-looking pair of numbers can still produce an awkward fraction. Divide 297 by 210 and you get about 1.414, the figure the paper size is designed around.
Same area, different perimeter
Area and perimeter do not move together. Four rectangles with area 36 have perimeters of 24 (6 × 6), 26 (9 × 4), 40 (18 × 2) and 74 (36 × 1). Among all rectangles of equal area, the square has the shortest perimeter, which is why fencing a fixed plot costs least when the plot is as square as possible.
Practical checks before you rely on the numbers
Keep both sides in one unit, convert afterwards, and remember that area units are squared: 1 m equals 100 cm, but 1 m² equals 10,000 cm². For flooring, paint or fabric, add an allowance for waste yourself, since the calculator returns the exact geometric area only. When measuring a room that is not perfectly square, compare the two diagonals; equal diagonals confirm the corners are right angles.
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Results are estimates for informational purposes only and do not constitute professional financial, medical, legal, or technical advice. Read full disclaimer →