Formula and Method for the Width of a Rectangle
A rectangle has two pairs of equal, parallel sides: the length (the longer side, by convention) and the width (the shorter side). You often know the length plus one other measurement — the area, the perimeter, or the diagonal — and need to back out the width. This calculator solves for width using whichever of those three relationships matches what you already know, then reports the width alongside the full set of area, perimeter, and diagonal.
How the calculation works
Each method rearranges a standard rectangle formula to isolate width (w), given the length (l):
- From area: since A = l × w, width is w = A / l.
- From perimeter: since P = 2(l + w), half the perimeter is l + w, so width is w = P / 2 - l.
- From diagonal: the diagonal splits a rectangle into two right triangles with legs l and w, so by the Pythagorean theorem l² + w² = d², giving width w = √(d² - l²).
Once the width is known, the calculator fills in the remaining values: area (l × w), perimeter (2(l + w)), and diagonal (√(l² + w²)). Enter the length and known quantity in the same unit system — mixing feet and inches, or centimeters and meters, produces incorrect results.
Common mistakes
- Entering area in the wrong units: if the length is in feet, the area must be in square feet (ft²), not square inches or square meters.
- Perimeter smaller than twice the length: since w = P/2 - l must be positive, the perimeter has to be greater than 2 × length, otherwise the shape is not a valid rectangle.
- Diagonal shorter than the length: the diagonal is always the longest measurement in a rectangle, so it must be greater than the length — if it is not, the inputs are inconsistent.
Real-world applications
- Construction and carpentry, where you know a room's length and its floor area from a permit or blueprint and need the missing wall width.
- Framing and fencing, where you know the total perimeter of material available and one side, and need the other.
- Furniture and screen sizing, where you know a diagonal (a TV's advertised size) and one side, and need the other.
- Land surveying and landscaping, converting between area, perimeter, and side lengths for irregular-shaped lots approximated as rectangles.
Frequently Asked Questions
How do you find the width of a rectangle if you know the area and length?
How do you find the width if you know the perimeter and length?
How do you find the width if you know the diagonal and length?
What is the difference between length and width?
Common Tip Percentages
| Service | Typical Tip Range | Notes |
|---|---|---|
| Restaurant (sit-down) | 15–20% | 20%+ for exceptional service |
| Food delivery | 10–20% | Consider extra for long distances |
| Taxi / rideshare | 10–20% | More for assistance with luggage |
| Hotel housekeeping | $2–5/night | Leave daily, not just at checkout |
| Barber / hair salon | 15–20% | On pre-discount total |
| Pizza delivery | 10–15% or $3–5 minimum | Higher in bad weather |
General Household Budget Ratios (50/30/20 Rule)
| Category | % of Net Income | Examples |
|---|---|---|
| Needs | 50% | Rent, groceries, utilities, insurance |
| Wants | 30% | Dining out, entertainment, hobbies |
| Savings / Debt | 20% | Emergency fund, retirement, extra payments |
Common Measurement Conversions for Everyday Use
| Quantity | US / Imperial | Metric Equivalent |
|---|---|---|
| 1 cup | 8 fl oz | 237 mL |
| 1 pint | 16 fl oz | 473 mL |
| 1 quart | 32 fl oz | 946 mL |
| 1 gallon | 128 fl oz | 3.785 L |
| 1 lb | 16 oz | 453.6 g |
| 1 ft | 12 in | 30.48 cm |