Geometry
How To Calculate The Perimeter Of A Rectangle
Perimeter is the fence, the skirting and the picture frame: the distance around the edge, which is always a plain length rather than a square measure.
Quick Answer
perimeter = 2 x (length + width)
- P
- Perimeter, the total distance around the edge
- l
- Length of the longer side
- w
- Width of the shorter side, in the same unit
Add the length and the width, then double the result. An eight by five metre room has a perimeter of 26 metres. Equivalently, add all four sides, but doubling the half sum is faster and leaves less room for error.
What Is The Perimeter Of A Rectangle?
The perimeter of a rectangle is the total distance around its outside edge. For a rectangle eight metres long and five metres wide it is twenty six metres, which is the length of skirting board, fence panel or picture frame moulding you would need.
The formula is twice the sum of the length and the width. The reasoning is simple: a rectangle has two long sides and two short sides, so walking the whole way round means covering the length twice and the width twice.
An equivalent form is to add all four sides one at a time. Both give the same answer, but the doubling form is shorter and less prone to a missed side. The only trap is doubling before adding rather than after, which gives a different and wrong result.
Perimeter is a plain length, measured in metres, feet or inches, never in square units. That is the clearest way to tell it apart from area, which is always square. If a question asks for square metres it wants the area, not the perimeter.
Perimeter and area are independent. A long thin strip can have a huge perimeter and a tiny area, while a square holds the most area for a given perimeter of any rectangle. This is why square pens enclose more ground than long narrow ones using the same amount of fencing.
Because the formula uses only addition and doubling, the units behave straightforwardly. Convert both measurements to the same unit before adding, and the answer comes out in that unit with no exponent attached.
A square is a rectangle with equal sides, so its perimeter is four times the side length. That is the same as two times the side plus the side, which confirms the general formula still holds.
Perimeter work in the real world is usually about materials. Skirting, guttering, edging, fencing and wallpaper borders are all bought by length, and each one needs the perimeter rather than the area. Measuring the wrong one is an expensive and very common mix up.
Sometimes the perimeter is known and a side is not. Rearranging the formula gives the width as the perimeter divided by two, minus the length. This is the usual shape of a school problem, and it is worth doing slowly because the division by two comes first.
The diagonal is not part of the perimeter. It is the corner to corner distance inside the shape, and adding it to the perimeter count is a frequent slip when a diagram shows all three measurements at once.
Finally, be careful with composite shapes. An L shaped room has a perimeter that is not the sum of the perimeters of its two rectangles, because the internal dividing line is not part of the outside edge. Only the outer boundary counts.
Formula
P = 2 x (l + w)
Add the two different sides, then double. Equivalent to adding all four sides individually.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| P | Perimeter | metres | Distance around the outside. |
| l | Length | metres | The longer side. |
| w | Width | metres | The shorter side. |
w = P / 2 - l
Divide the perimeter by two to get the half sum, then subtract the side you already know.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| w | Width | metres | The side being solved for. |
| P | Perimeter | metres | Known total distance around. |
| l | Length | metres | The known side. |
P = 4 x side
The rectangle formula with length and width equal, which collapses to four times one side.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| P | Perimeter | metres | Distance around the square. |
| side | Side length | metres | Any one of the four equal sides. |
How To Calculate The Perimeter Of A Rectangle
- 1
Measure one long side and one short side
You only need two measurements, not four. Opposite sides of a rectangle are equal by definition, so the other two are already known.
- 2
Convert both to the same unit
Addition is unforgiving about units. Two metres plus thirty centimetres has to become two metres plus 0.3 metres, or two hundred centimetres plus thirty centimetres, before anything else happens.
- 3
Add the length and the width
Eight plus five is thirteen. This half sum is the distance along one long side and one short side, a quarter of the way round.
- 4
Double the half sum
Two times thirteen is twenty six metres. Doubling at the end is safer than doubling each side first, because there is only one multiplication to get right.
- 5
Check against the area
The area of the same rectangle is forty square metres. A perimeter larger than the area in the same unit is not an error by itself, but a perimeter in square units certainly is.
Examples
Example 1: Skirting for an eight by five metre room
- Length
- 8 m
- Width
- 5 m
| Step | Calculation | Result |
|---|---|---|
| Half sum | 8 + 5 | 13 |
| Area | 8 x 5 | 40 |
| Perimeter | 2 x 13 | 26 |
Result: An eight by five metre room needs 26 metres of skirting, and the floor it surrounds has an area of 40 square metres.
Example 2: Fencing a twelve by three metre plot
- Length
- 12 m
- Width
- 3 m
| Step | Calculation | Result |
|---|---|---|
| Half sum | 12 + 3 | 15 |
| Area | 12 x 3 | 36 |
| Perimeter | 2 x 15 | 30 |
Result: A twelve by three metre plot takes 30 metres of fencing even though it only covers 36 square metres, which is why long thin land is expensive to enclose.
Example 3: Finding the width from a known perimeter
- Length
- 9 m
- Width
- unknown, perimeter 32 m
| Step | Calculation | Result |
|---|---|---|
| Half sum | 32 / 2 | 16 |
| Width | 16 - 9 | 7 |
| Perimeter check | 2 x (9 + 7) | 32 |
Result: A rectangle nine metres long with a perimeter of 32 metres must be 7 metres wide, and the check confirms the original figure.
Calculator
Perimeter
26
- Half sum (length + width)
- 13
- Area
- 40
- Diagonal
- 9.434
Values update as you type. This calculator covers the single scenario its formula assumes — see Common Mistakes for what it leaves out.
Prefer a full-width tool? Open the The Perimeter Of A Rectangle calculator page.
Common Mistakes
Doubling before adding
Twice the length plus twice the width is correct, but doubling only one of them is not. The safest order is to add first and double second, which makes the error impossible.
Measuring only two sides and guessing the rest
Opposite sides are equal in a rectangle, so two measurements are enough. In a room that is not truly rectangular, however, they are not, and the perimeter will be larger than the formula predicts.
Giving the answer in square units
Perimeter is a length. Writing twenty six square metres confuses it with area and is the most common marking error in school work on this topic.
Mixing units in the addition
Adding metres to centimetres without converting gives a meaningless number. Convert first, and keep both measurements in the same unit throughout.
Including the diagonal
The diagonal runs through the shape, not around it. It is longer than either side, so including it inflates the perimeter and is a natural slip when a diagram labels all three.
Adding the perimeters of an L shape
An L shaped room's perimeter is not the sum of two rectangles' perimeters, because the shared internal edge is not part of the boundary. Trace the outside once instead.
Forgetting a door or a gap
For skirting, subtract the width of each doorway. The formula gives the full boundary, and material is only needed along the parts of it that are actually wall.
FAQ
What is the formula for the perimeter of a rectangle?
Perimeter equals two times the sum of the length and the width. Add the two different sides together and double the result, which is quicker than adding all four sides one by one.
How is perimeter different from area?
Perimeter is the distance around the edge and is measured in plain units such as metres. Area is the surface inside and is measured in square units such as square metres.
Can you find the width if you know the perimeter and the length?
Yes. Divide the perimeter by two to get the half sum, then subtract the known length. A perimeter of thirty two with a length of nine gives a half sum of sixteen and a width of seven.
Does a square have a different perimeter formula?
It is the same formula simplified. With all four sides equal, two times the side plus the side becomes four times the side.
Why do you only need two measurements?
Because opposite sides of a rectangle are equal by definition. Once you know one long side and one short side, the other two are determined.
Does the perimeter change if the shape is rotated?
No. Rotating a rectangle swaps which sides are called length and width, but the sum and therefore the perimeter are unchanged.
References
- [1]Wikipedia, Perimeter — https://en.wikipedia.org/wiki/Perimeter
- [2]Wikipedia, Rectangle — https://en.wikipedia.org/wiki/Rectangle
- [3]Math is Fun, Perimeter of a rectangle — https://www.mathsisfun.com/geometry/perimeter.html
- [4]Wikipedia, Isoperimetric inequality — https://en.wikipedia.org/wiki/Isoperimetric_inequality