Rectangle Area Calculator: Calculate Area, Perimeter & Diagonal
A rectangle area calculator computes the area, perimeter, diagonal, and dimensions of a rectangle using geometric formulas, where area equals length times width (A = l × w), perimeter equals twice the sum of length and width (P = 2(l + w)), and diagonal follows the Pythagorean theorem (d = √(l² + w²)). This comprehensive geometric tool performs bidirectional calculations including finding area from dimensions, determining dimensions from area and one side, calculating diagonal from length and width, finding perimeter from any known values, and converting between different units of measurement (square meters, square feet, acres, hectares) essential for students, architects, engineers, contractors, designers, real estate professionals, and anyone requiring accurate rectangular measurements for mathematics education, construction planning, room layout, flooring estimation, land surveying, garden design, window sizing, or geometric problem-solving in education, architecture, construction, interior design, landscaping, and property development.
📏 Rectangle Area Calculator
Calculate all properties of a rectangle
Calculate Area from Length and Width
Find area, perimeter, and diagonal
Find Dimensions from Area
Calculate width from area and length, or vice versa
Complete Rectangle Analysis
Calculate all properties with unit conversions
Understanding Rectangle Area
A rectangle is a quadrilateral with four right angles (90°) and opposite sides that are equal in length. The area of a rectangle represents the amount of two-dimensional space enclosed within its boundaries. Unlike a square, a rectangle has two pairs of sides with different lengths—commonly called length (the longer side) and width (the shorter side).
Rectangle Formulas
Basic Area Formula
Area of a Rectangle:
\[ A = l \times w \]
Where:
\( A \) = area
\( l \) = length
\( w \) = width
Related Formulas
Perimeter:
\[ P = 2(l + w) = 2l + 2w \]
Diagonal (Pythagorean Theorem):
\[ d = \sqrt{l^2 + w^2} \]
Reverse Formulas
Width from Area and Length:
\[ w = \frac{A}{l} \]
Length from Area and Width:
\[ l = \frac{A}{w} \]
Length from Perimeter and Width:
\[ l = \frac{P - 2w}{2} \]
Step-by-Step Examples
Example 1: Calculate Area from Dimensions
Problem: Find the area of a rectangle with length 12 meters and width 5 meters.
Step 1: Identify the formula
Area = length × width
\[ A = l \times w \]
Step 2: Substitute values
\[ A = 12 \times 5 \]
Step 3: Calculate
\[ A = 60 \text{ m}^2 \]
Answer: The area is 60 square meters.
Example 2: Find Width from Area
Problem: A rectangle has an area of 48 square feet and a length of 8 feet. Find the width.
Step 1: Use the reverse formula
\[ w = \frac{A}{l} \]
Step 2: Substitute values
\[ w = \frac{48}{8} \]
Step 3: Calculate
\[ w = 6 \text{ ft} \]
Answer: The width is 6 feet.
Example 3: Calculate Perimeter and Diagonal
Problem: Find perimeter and diagonal of a rectangle: length 9 cm, width 4 cm.
Perimeter:
\[ P = 2(l + w) = 2(9 + 4) = 2(13) = 26 \text{ cm} \]
Diagonal:
\[ d = \sqrt{l^2 + w^2} = \sqrt{9^2 + 4^2} = \sqrt{81 + 16} = \sqrt{97} \approx 9.85 \text{ cm} \]
Summary:
Perimeter = 26 cm, Diagonal ≈ 9.85 cm
Rectangle Measurements Reference Table
| Length | Width | Area | Perimeter | Diagonal |
|---|---|---|---|---|
| 10 | 5 | 50 | 30 | 11.18 |
| 12 | 6 | 72 | 36 | 13.42 |
| 15 | 8 | 120 | 46 | 17.00 |
| 20 | 10 | 200 | 60 | 22.36 |
| 25 | 15 | 375 | 80 | 29.15 |
| 30 | 20 | 600 | 100 | 36.06 |
Common Rectangle Dimensions
| Application | Typical Dimensions | Area | Notes |
|---|---|---|---|
| A4 Paper | 297 mm × 210 mm | 623.7 cm² | Standard document size |
| US Letter | 11 in × 8.5 in | 93.5 in² | North American standard |
| King Bed | 80 in × 76 in | 6,080 in² (42 ft²) | Mattress size |
| Parking Space | 18 ft × 9 ft | 162 ft² | Standard parking |
| Tennis Court | 78 ft × 36 ft | 2,808 ft² | Regulation size |
| Basketball Court | 94 ft × 50 ft | 4,700 ft² | NBA regulation |
Area Unit Conversions
| Unit | Square Meters (m²) | Square Feet (ft²) | Acres |
|---|---|---|---|
| 1 m² | 1 | 10.764 | 0.000247 |
| 1 ft² | 0.0929 | 1 | 0.0000229 |
| 1 yd² | 0.836 | 9 | 0.000206 |
| 1 acre | 4,047 | 43,560 | 1 |
| 1 hectare | 10,000 | 107,639 | 2.471 |
Real-World Applications
Construction & Architecture
- Room planning: Calculate floor area for material estimation
- Wall area: Determine paint and wallpaper requirements
- Flooring installation: Calculate tiles, carpet, or hardwood needed
- Window sizing: Determine appropriate window dimensions
Interior Design
- Furniture placement: Ensure proper fit in rectangular rooms
- Rug selection: Choose appropriately sized area rugs
- Wall art: Plan artwork arrangements
- Space optimization: Maximize usable area
Landscaping & Gardening
- Garden beds: Calculate soil and mulch requirements
- Lawn area: Determine grass seed or sod needed
- Patio design: Plan paver quantities
- Irrigation planning: Design sprinkler coverage
Real Estate & Property
- Property measurement: Calculate lot sizes
- Pricing calculations: Price per square foot/meter
- Space comparison: Compare property sizes
- Zoning compliance: Verify building footprints
Tips for Rectangle Calculations
Best Practices:
- Identify dimensions correctly: Length typically longer than width
- Use consistent units: Convert all measurements to same unit
- Double-check measurements: Verify accuracy before calculating
- Include units: Always specify square units for area
- Consider precision: Round appropriately for application
- Verify right angles: Confirm shape is truly rectangular
- Account for waste: Add 10% for flooring/tile projects
Common Mistakes to Avoid
⚠️ Calculation Errors
- Confusing perimeter and area: Area = l×w, Perimeter = 2(l+w)
- Adding instead of multiplying: Area requires multiplication
- Missing square units: Area in m², not m
- Wrong order of operations: Calculate parentheses first in perimeter
- Incorrect diagonal formula: Use Pythagorean theorem, not addition
- Mixed units: Convert to same unit before calculating
- Assuming square: Don't use square formulas for rectangles
- Forgetting to square in diagonal: d = √(l² + w²), not √(l + w)
Frequently Asked Questions
How do you calculate the area of a rectangle?
Multiply length by width. Formula: Area = length × width. Example: rectangle 12 feet long and 7 feet wide has area = 12 × 7 = 84 square feet. Simple multiplication—no exponents or complex operations. Works for any rectangle regardless of size. Length usually refers to longer side, width to shorter side, though order doesn't affect area calculation. Result always in square units (m², ft², cm²). Most fundamental area calculation after square. For 15 m × 8 m rectangle: area = 120 m².
What's the difference between area and perimeter of a rectangle?
Area measures space inside (length × width), perimeter measures distance around (2 × length + 2 × width). Area in square units (m², ft²), perimeter in linear units (m, ft). Example: 10×6 rectangle has area 60 units² and perimeter 32 units. Area shows coverage (flooring, paint), perimeter shows border (fencing, trim). Area uses multiplication, perimeter uses addition. Both essential but serve different purposes. Area for two-dimensional coverage, perimeter for one-dimensional boundary measurement.
How do you find the diagonal of a rectangle?
Use Pythagorean theorem: diagonal = √(length² + width²). Rectangle diagonal forms right triangle hypotenuse. Example: 8×6 rectangle has diagonal = √(8² + 6²) = √(64 + 36) = √100 = 10 units. Calculator needed for non-perfect squares. For 12×5: diagonal = √(144 + 25) = √169 = 13 units. Diagonal always longer than either dimension. Useful for fitting objects diagonally through doorways or determining TV size fit. Essential for construction and design verification.
How do you find width if you know area and length?
Divide area by length. Formula: width = area ÷ length. Reverse of area calculation. Example: area 60 ft² with length 12 ft means width = 60 ÷ 12 = 5 ft. Simple division. Works because area = length × width, so width = area/length. Useful when one dimension and area known but other dimension missing. For 100 m² area with 20 m length: width = 100 ÷ 20 = 5 m. Common in construction planning and space layout.
Can a rectangle have equal length and width?
Yes—that's a square! Square is special case of rectangle where all sides equal. All squares are rectangles, but not all rectangles are squares. Rectangle defined as quadrilateral with four right angles; doesn't require different side lengths. Square has additional property of equal sides. Same area formula works: A = side × side = side². Example: 5×5 shape is both square and rectangle with area 25 units². Technically correct to call square a rectangle, though usually specified as square for clarity.
How many square feet in a 10×12 room?
120 square feet. Calculation: 10 × 12 = 120 ft². Dimensions assumed in feet. "10×12" means 10 feet by 12 feet. Standard way to describe room size. For flooring, need 120 sq ft plus 10% waste (132 total recommended). Common bedroom size. If dimensions in different units (10 m × 12 m), that's 120 m² or approximately 1,292 ft². Always verify units—huge difference between feet and meters. Length × width = area, simple multiplication gives result.
Key Takeaways
Understanding rectangle area calculations is essential for countless practical applications in construction, design, real estate, and everyday problem-solving. The simple formula A = l × w provides the foundation for material estimation, space planning, and geometric problem-solving across numerous fields.
Essential principles to remember:
- Rectangle area formula: A = length × width
- Perimeter formula: P = 2(length + width)
- Diagonal formula: d = √(length² + width²)
- Reverse calculation: width = area ÷ length
- Opposite sides equal in rectangles
- All angles are 90 degrees (right angles)
- Area always in square units
- Use consistent units throughout calculations
- Square is special case where length = width
- Add waste factor for real-world material estimates
Getting Started: Use the interactive calculator at the top of this page to calculate rectangle area, dimensions, perimeter, and diagonal. Enter your known values, select units, and receive instant results with step-by-step solutions and unit conversions. Perfect for students, contractors, designers, and anyone needing accurate rectangular measurements for education, construction, or planning projects.