Rectangle Calculator
Calculate area, perimeter, diagonal and sides of rectangles instantly with precision.
Variable Definitions:
a = length side a
b = length side b
p = q = diagonals
P = perimeter
A = area
Formulas:
Area: A = a × b
Perimeter: P = 2(a + b)
Diagonal: p = √(a² + b²)
Key Rectangle Parameters
| Parameter | Symbol | Description | Unit of Measurement |
|---|---|---|---|
| Length | a or l | The longer side of the rectangle (though sometimes used for any side) | meters, feet, inches, etc. |
| Width | b or w | The shorter side of the rectangle (also called breadth) | meters, feet, inches, etc. |
| Area | A | The surface space enclosed within the rectangle | square units (m², ft², in²) |
| Perimeter | P | The total distance around the rectangle | linear units (m, ft, in) |
| Diagonal | p or d | The straight line connecting opposite corners |
How to Use the Rectangle Calculator
- Select Your Calculation Mode: Choose from multiple calculation options, eleven different modes including finding dimensions from area/perimeter, diagonal/area combinations, and even screen dimensions from diagonal and aspect ratio.
- Input Your Known Values: Enter the numerical values for your known parameters in the corresponding input fields.
- Choose Your Units: Select from comprehensive unit options including metric (km, m, cm, mm) and imperial (mi, yd, ft, in) systems.
- Set Significant Figures: Adjust the precision of your results by selecting the number of significant figures (3-9) or choose "auto" for default formatting.
- Calculate.
Formulas
Area Calculation
The area of a rectangle represents the surface space enclosed within its four sides and is calculated by multiplying its length by its width:
A = a × b
Where A is area, a is length, and b is width. For example, a rectangle with length 5 cm and width 6 cm has an area of 30 cm².
Perimeter Calculation
The perimeter represents the total distance around the rectangle and is calculated by summing all four sides:
P = 2(a + b)
Since opposite sides are equal, the formula simplifies to twice the sum of length and width. A rectangle with sides 5 cm and 6 cm would have a perimeter of 22 cm.
Diagonal Calculation
The diagonal connects opposite vertices, dividing the rectangle into two congruent right triangles. Its length derives from the Pythagorean theorem:
d = √(a² + b²)
This formula calculates the hypotenuse of the right triangle formed by the length, width, and diagonal. For a 5 cm by 6 cm rectangle, the diagonal equals √(25 + 36) = √61 ≈ 7.81 cm .
Advanced Calculations
The calculator also handles more complex scenarios:
- Finding sides from area and perimeter involves solving a quadratic equation derived from the standard formulas
- Calculating dimensions from diagonal and area requires simultaneous equation resolution
- Screen size calculations from diagonal and aspect ratio use trigonometric relationships.
These sophisticated mathematical operations occur instantly behind the intuitive interface, saving users from complex manual computations.
Troubleshooting Common Issues
Invalid Input Errors
If the calculator displays an error message, check that:
- All required fields contain numerical values
- Values are positive numbers
- For diagonal calculations, the diagonal is longer than either side length
- For area/perimeter combinations, the values can physically form a rectangle.
FAQ
Q1. Can I calculate rectangle sides if I only know the area and perimeter?
A: Yes, our calculator includes a specific mode for this exact scenario. The tool uses quadratic equation solving to determine possible side lengths from your area and perimeter values, providing both mathematical solutions (which may be the same values swapped).
Q2. How accurate are the calculator's results?
A: The calculator provides precision up to 9 significant figures, far exceeding most practical requirements. For most applications, 3-6 significant figures provides optimal readability without sacrificing precision.
Q3. Does the calculator work for squares?
A: Absolutely. Since a square is a special case of a rectangle with equal sides, all formulas and calculations work perfectly for squares. When equal sides are calculated or entered, the results automatically reflect square properties.
Q4. Can I use the calculator for metric and imperial units?
A: Yes, the calculator seamlessly handles both measurement systems and automatically converts between them. You can mix input values in different units, though for optimal clarity, maintaining consistent units throughout a calculation is recommended.
Q5. How does the screen size calculation work?
A: The screen size function uses the diagonal measurement combined with aspect ratio to calculate actual width and height. The calculator determines a scaling factor based on the Pythagorean theorem relationship between the diagonal and aspect ratio dimensions, then applies this factor to compute precise physical dimensions.