Math
Rectangle Calculator
The rectangle calculator solves the whole rectangle from any two known properties.
Give it length and width, or length and diagonal, or even area and perimeter, and it finds the other measurements, shows the diagonal as an exact radical when possible, and explains when a combination is impossible.
Area is in square units; everything else is a length.
Pick a different property from the first.
Pick the unit your measurements use. Area is reported in square units and volume in cubic units.
Try an example
Result
Area
—
- Length
- —
- Width
- —
- Diagonal
- —
- Perimeter
- —
- Diagonal angle to the length
- —
Student quick launch
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Study path
Use this calculator with
Follow these when you want the formula behind the answer, a short lesson, or nearby tools in the same topic.
What the rectangle calculator solves
The rectangle calculator solves the whole rectangle from any two known properties. Give it length and width, or length and diagonal, or even area and perimeter, and it finds the other measurements, shows the diagonal as an exact A root expression written with the √ symbol, such as a square root. when possible, and explains when a combination is impossible.
Formula
How to use it
- Choose the two properties you know (for example area and perimeter) and enter their values.
- Pick the unit; area is labeled in square units automatically.
- Read length, width, diagonal, area, perimeter, and the angle the diagonal makes with the length.
How to read the answer
Length and width are the two side lengths (length is shown as the longer one when solved from area or perimeter). The diagonal comes from the Pythagorean theorem and is shown as an exact radical like 13 or 5√5 when the sides are nice numbers.
Common mistakes and edge cases
- Picking the same property twice gives no new information; choose two different ones.
- A diagonal shorter than a side is impossible — the diagonal is the The longest side of a right triangle, always opposite the right angle. of the side triangle.
- For a fixed perimeter the largest possible area is a square; asking for more area than P²/16 has no solution.
- Area and perimeter together lead to a quadratic; when the The b² − 4ac part of the quadratic formula; its sign tells you how many real solutions exist. is negative no real rectangle exists.
- Zero or negative values cannot form a rectangle.
Worked examples
Length 12 and width 5
Area
60
Length 12 and diagonal 13
Area
60
Area 60 and perimeter 34
Area
60
Diagonal 13 and perimeter 34
Area
60
Width 2.5 and area 11.25 (decimal)
Area
11.25
Area 25 and perimeter 20 (a square)
Area
25
Area 100 with perimeter 20 (impossible)
Area
Error
Same property twice
Area
Error
Frequently asked questions
How do I find the width of a rectangle from the area and length?+
Divide: w = A / l. A rectangle with area 60 and length 12 has width 5.
How do I find the diagonal of a rectangle?+
Use the Pythagorean theorem: d = sqrt(l² + w²). For 12 by 5 the diagonal is sqrt(144 + 25) = 13.
Can I find a rectangle from its area and perimeter?+
Yes. With l + w = P/2 and l·w = A, the sides are the roots of x² − (P/2)x + A = 0. Area 60 and perimeter 34 give 12 and 5. If the discriminant is negative, no such rectangle exists.
What is the angle of the diagonal?+
The angle between the diagonal and the length is arctan(w / l). For 12 by 5 it is about 22.62°; the other angle is 90° minus that.
Is a square a rectangle?+
Yes — a square is a rectangle whose sides are all equal. This calculator reports when the solved length and width are equal.
Why does length come out larger than width?+
When the sides are solved from area, perimeter, or diagonal, the calculator cannot know which you call length, so it assigns the larger root to length.
About this calculator
- Written by
- mathcheck editorial team
- Last reviewed
- September 4, 2026
Method
- Uses the values entered by the user and stable formulas documented on the page.
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Last updated: September 4, 2026