What this calculator does
This calculator answers the length and width question that comes up when you already know one side of a rectangle and its area or its perimeter, and need the other side. Enter the side you have, choose whether the second number you know is an area or a perimeter, and it solves for the missing dimension.
It is the reverse of the usual rectangle calculation. Working forward from length and width to area or perimeter is straightforward multiplication; working backward from area or perimeter to a missing side means rearranging the formula, which is where people get stuck.
The formula
From an area, the missing side is the area divided by the known side, since area = length × width. From a perimeter, the missing side is half the perimeter minus the known side, since perimeter = 2 × (length + width), so half the perimeter equals length + width.
| Term | Meaning |
|---|---|
| Known side | The one dimension of the rectangle you already have, entered as the length. |
| Area | Length × width, in square units matching whatever unit the sides are measured in. |
| Perimeter | The total distance around the rectangle: 2 × (length + width). |
The inputs explained
| Field | What to enter |
|---|---|
| Solve using | Choose from Area and one known side, Perimeter and one known side. |
| Known side (length) | The one side you already know, always treated as the length in the working shown. |
| Area (if solving by area) or perimeter (if solving by perimeter) | The area if solving by area, or the perimeter if solving by perimeter, matching the mode selected above. |
When to use it
Buying flooring or turf for a fixed-area space
A supplier or planning document sometimes states the total area and one wall length, without giving the other wall length directly; this backs out the missing measurement.
Working from a fence or edging quote
A perimeter figure and one known side, such as a boundary that runs along a known-length property line, gives the missing side of a rectangular plot the same way.
Checking a plan against a stated area
If a floor plan states a room’s area and shows only one dimension clearly, this confirms what the other dimension should be before measuring on site.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
What is the missing width for a range of areas, at a fixed 12-unit length?
A 12-unit length held fixed, against a range of stated areas.
| Area | Missing side (width) | Resulting perimeter |
|---|---|---|
| 48 | 4.000 | 32.000 |
| 72 | 6.000 | 36.000 |
| 96 | 8.000 | 40.000 |
| 120 | 10.000 | 44.000 |
| 180 | 15.000 | 54.000 |
| 240 | 20.000 | 64.000 |
What is the missing width for a range of perimeters, at a fixed 12-unit length?
The same 12-unit length, against a range of stated perimeters.
| Perimeter | Missing side (width) | Resulting area |
|---|---|---|
| 30 | 3.000 | 36.000 |
| 36 | 6.000 | 72.000 |
| 40 | 8.000 | 96.000 |
| 48 | 12.000 | 144.000 |
| 60 | 18.000 | 216.000 |
| 80 | 28.000 | 336.000 |
Questions
What if the perimeter is too small for the known side?
Half the perimeter has to be larger than the known side, otherwise the missing side would come out at zero or negative, which is not a valid rectangle. The calculator flags this rather than showing a nonsense result.
Does this work for a square?
A square is just a rectangle where both sides are equal, so it works the same way, though if you already know it is a square there is no missing side to solve for.
Can I use this with an area measured in different units to the side length?
No, convert everything to the same length unit first. If the side is in metres, the area needs to be in square metres, not square feet or square centimetres, or the missing side will be wrong.
What is the difference between this and a plain rectangle calculator?
A standard rectangle calculator goes forward from length and width to area and perimeter. This one goes backward, starting from an area or perimeter and one known side, to find the side that is missing.
To go the other way, from both sides to area and perimeter directly, see the rectangle and square calculator. For area across several shapes at once, see the area of common shapes calculator.