Rectangle Calculator
Enter any two known properties of a rectangle and this calculator finds the rest, including area, perimeter, diagonal, circumradius, and inradius. Choose to solve from length and width, from area, from perimeter, or from the diagonal. Switch between metric (metres) and imperial (feet) units; results update as you type.
Formula
Worked example
A rectangle 8 m long and 5 m wide: Area = 8 x 5 = 40 m^2; Perimeter = 2(8+5) = 26 m; Diagonal = sqrt(64+25) = sqrt(89) = 9.434 m; Circumradius = 9.434/2 = 4.717 m; Inradius = 5/2 = 2.5 m.
Rectangle formulas
A rectangle has four right angles and two pairs of equal parallel sides, called the length (l) and the width (w). Its area is A = l x w, which measures the flat surface enclosed. Its perimeter is P = 2(l + w), the total distance around the outside. The diagonal d connects opposite corners and is found using the Pythagorean theorem: d = sqrt(l^2 + w^2). Because every rectangle can be inscribed in a circle, the circumradius (radius of the smallest enclosing circle) equals half the diagonal: R = d/2. The inradius is the radius of the largest circle that fits inside and equals half the shorter side: r = w/2.
Solve from any two known values
Most rectangle problems give you length and width, but sometimes you know the area or perimeter and only one side. This calculator covers seven solve modes. If you know the area (A) and one side, the other side is simply A divided by the known side. If you know the perimeter (P) and one side, the missing side is P/2 minus the known side. If you know the diagonal (d) and one side, the missing side is sqrt(d^2 - known^2). Use the "Known values" dropdown above to pick the right mode; the calculator fills in all remaining properties.
Area and perimeter in practice
Area tells you how much surface is inside the shape: useful for flooring, painting, lawns, and screens. Perimeter tells you how much material goes around the edge: useful for fencing, skirting boards, picture frames, and trim. The diagonal is critical when you need to fit a rectangle through a doorway or check that a frame is truly square (the two diagonals of a rectangle are always equal). The inradius matters when fitting a circular object inside a rectangular space.
Aspect ratio and common formats
The aspect ratio is the length divided by the width. A ratio of 1:1 is a square; 1.414:1 is the ISO A-series paper standard; 1.618:1 is the golden ratio; 1.778:1 is the 16:9 widescreen standard. Recognising the ratio of your rectangle helps identify whether it matches a standard format for printing, screens, or construction. The reference table below lists the most common ratios and their names.
Common rectangle aspect ratios
| Ratio (l:w) | Name / Standard | Common use |
|---|---|---|
| 1:1 | Square | Instagram photos, floor tiles |
| 1.414:1 | ISO 216 (root-2) | A4, A3, Letter-sized paper |
| 1.5:1 | 3:2 | Classic film frames, DSLR sensors |
| 1.618:1 | Golden ratio | Architecture, design, art |
| 1.778:1 | 16:9 | Widescreen TVs, YouTube, monitors |
| 2:1 | 2:1 Banner | Web banners, sports fields |
| 2.39:1 | Anamorphic | Cinematic widescreen film |
Recognising the ratio of length to width helps identify standard formats.
Frequently asked questions
How do I find the area of a rectangle?
Multiply the length by the width: A = l x w. If your rectangle is 8 metres long and 5 metres wide, the area is 40 square metres. The units of area are always the square of the length units, so feet give square feet and metres give square metres.
How do I find the perimeter of a rectangle?
Add the length and width, then multiply by two: P = 2(l + w). For an 8 m by 5 m rectangle, P = 2(8 + 5) = 26 m. This is the total distance around all four sides.
How do I calculate the diagonal of a rectangle?
The diagonal is the hypotenuse of the right triangle formed by the two sides. Use the Pythagorean theorem: d = sqrt(l^2 + w^2). For 8 m and 5 m: d = sqrt(64 + 25) = sqrt(89) = 9.43 m. Both diagonals of a rectangle are equal in length.
Can I find the sides if I only know the area and one side?
Yes. Divide the area by the known side: missing side = A divided by known side. For example, if the area is 40 m^2 and the length is 8 m, the width is 40 / 8 = 5 m. Select "Area and Length" or "Area and Width" in the Known values dropdown above.
What is the circumradius of a rectangle?
The circumradius (R) is the radius of the smallest circle that completely contains the rectangle. All four corners of the rectangle lie on this circle. It equals half the diagonal: R = d/2. For a diagonal of 9.43 m, the circumradius is 4.72 m.
What is the inradius of a rectangle?
The inradius (r) is the radius of the largest circle that fits entirely inside the rectangle, touching the two longer sides. It equals half the shorter side: r = w/2. For a width of 5 m the inradius is 2.5 m. Note: the inscribed circle only touches all four sides when the rectangle is a square.
What is the difference between area and perimeter?
Area is the amount of flat space inside the rectangle, measured in square units (m^2, ft^2). Perimeter is the total length of the boundary around it, measured in linear units (m, ft). Doubling both sides quadruples the area but only doubles the perimeter, so large shapes are much more area-efficient than small ones with the same proportions.