Free Area of Rectangle Calculator – Instant, Accurate & Ad-Free
Calculate the area, perimeter, and diagonal of a rectangle with step-by-step solutions
Rectangle Formulas:
- Area: A = length × width
- Perimeter: P = 2(length + width)
- Diagonal: d = √(length² + width²)
Examples:
- Length = 10, Width = 8 → Area = 80 sq units
- Length = 5, Width = 5 → Area = 25 sq units (square)
- Length = 12, Width = 5 → Area = 60 sq units
Applications:
- Room floor area calculations
- Land area measurements
- Wall and fence planning
- Carpet or tile requirements
Calculate the area of any rectangle instantly with our Free Area of Rectangle Calculator. Whether you’re a student learning geometry, a builder working on dimensions, or a designer estimating space, this easy tool gives you fast and accurate results every time.
At Digital Calculator, we make math simple, visual, and practical. Our Area of Rectangle Calculator helps you find the surface area of a rectangle in just a few clicks — using length, width, diagonal, or even perimeter. No formulas to memorize, no manual errors — just quick, reliable geometry at your fingertips.
What Is the Area of a Rectangle?
The area of a rectangle is the total space covered within its four sides. It’s one of the most fundamental concepts in geometry and real-world measurements.
A rectangle is a quadrilateral with four right angles and opposite sides equal in length. Its area is measured in square units (like cm², m², ft², or in²).
In simple terms: the area tells us how much surface the rectangle occupies.
Formula:
Area = Length × Width
Example:
If a rectangle is 10 meters long and 5 meters wide,
Area = 10 × 5 = 50 m²
Our calculator uses this and other formulas automatically, depending on the data you enter.
Area of Rectangle Formula
There are several ways to find the area depending on what information you have — whether you know length and width, diagonal, or perimeter. Here are the main formulas our calculator uses:
1) Using Length and Width
Formula: Area = Length × Width
Example: Length = 12 cm, Width = 8 cm → Area = 96 cm²
Result: The area is 96 cm²
2) Using Diagonal and One Side
If you know the diagonal (d) and one side (l or w), use the Pythagorean theorem:
d² = l² + w² → w = √(d² – l²)
Then, Area = l × w
Example: Diagonal = 13 cm, Length = 12 cm → Width = √(169 – 144) = 5 cm → Area = 60 cm²
Result: The area is 60 cm²
3) Using Perimeter and Length
Perimeter (P) of a rectangle: P = 2 × (l + w) → w = (P / 2) – l
Then, Area = l × w
Example: P = 50 cm, l = 15 cm → w = 10 cm → Area = 150 cm²
Result: The area is 150 cm²
4) Using Diagonal and Perimeter (Advanced Geometry)
Sometimes, diagonal and perimeter are known, but not sides. Use:
l² + w² = d² and l + w = P/2
Solve simultaneously to get sides, then the area. Our calculator automates this.
How to Use the Free Area of Rectangle Calculator
Select your method: length & width, diagonal, or perimeter.
Enter your values in any preferred unit.
Click “Calculate.”
Instantly view the area with step-by-step details.
Switch methods or reset the inputs to start again.
Try the Free Area of Rectangle Calculator on Digital Calculator — fast, accurate, and ad-free.
Step-by-Step Examples
Example 1: Using Length and Width
Length = 20 cm, Width = 10 cm → Area = 200 cm²
Answer: 200 cm²
Example 2: Using Diagonal
Diagonal = 10 m, Length = 8 m → Width = √(100 – 64) = 6 m → Area = 48 m²
Answer: 48 m²
Example 3: Using Perimeter
Perimeter = 60 cm, Length = 20 cm → Width = 10 cm → Area = 200 cm²
Answer: 200 cm²
Example 4: Converting Units
If the area is 2 m², and 1 m² = 10,000 cm² → 2 m² = 20,000 cm²
Result: 20,000 cm²
Our calculator can display results in any standard unit — including square meters, square feet, square inches, and more.
Area of Rectangle Formula Table
| Known Parameters | Formula | Example | Result |
|---|---|---|---|
| Length & Width | A = l × w | 10 × 8 | 80 |
| Diagonal & Length | A = l × √(d² – l²) | l = 12, d = 13 | 60 |
| Perimeter & Length | A = l × ((P / 2) – l) | P = 50, l = 15 | 150 |
| Square (special case) | A = side² | side = 6 | 36 |
| Unit Conversion | 1 m² = 10,000 cm² | 2 m² | 20,000 cm² |
This table highlights how flexible area calculations can be based on different data inputs.
Understanding Rectangle Geometry
Length (l): The longer side of the rectangle.
Width (w): The shorter side perpendicular to the length.
Perimeter (P): Total distance around the rectangle — P = 2(l + w).
Diagonal (d): Line connecting opposite corners — d = √(l² + w²).
Area (A): Total surface enclosed — A = l × w.
These relationships form the foundation for most 2D shape calculations, making rectangles fundamental in geometry, architecture, and measurement.
Real-Life Applications of Rectangle Area
Construction & Architecture: Walls, floors, tiles, land plots.
Interior Design: Carpet area, paint coverage, flooring.
Education: Foundational 2D measurements and spatial reasoning.
Agriculture: Rectangular plots for yield estimates and irrigation.
Manufacturing: Panels, sheets, boards, packaging.
In short, any field involving measurement and design relies on accurate area calculations — and our tool ensures just that.
Comparing Rectangles and Squares
| Shape | Formula | Unique Property | Example |
|---|---|---|---|
| Rectangle | Area = l × w | Opposite sides equal, angles 90° | 10 × 8 = 80 |
| Square | Area = side² | All sides equal | 6² = 36 |
| Parallelogram | Area = base × height | No right angles | 10 × 5 = 50 |
Our calculator also handles square inputs automatically — simply enter equal values for length and width.
Benefits of Using Digital Calculator’s Area of Rectangle Tool
Completely Free & Ad-Free
Multiple Input Methods (length, width, diagonal, perimeter)
Automatic Unit Conversion (cm², m², ft², in²)
Step-by-Step Solution Display
Fast & Mobile-Friendly
At Digital Calculator, we prioritize both accuracy and learning. You get reliable results and a deeper understanding of geometry with every use.
Calculate instantly with the Free Area of Rectangle Calculator — accuracy made simple and always free.
Common Mistakes to Avoid
Confusing units (keep all inputs in the same unit).
Incorrect side labeling (multiply length by width, not diagonal or perimeter).
Ignoring conversions (stick to metric or imperial consistently).
Mixing up square vs. rectangle formulas (square: side²; rectangle: l × w).
Our calculator automatically handles these conversions and provides precise results every time.
Why Choose Digital Calculator
At Digital Calculator, our mission is to combine accuracy, education, and convenience in one place. We design tools that are:
Precise and easy to use
Free of ads and distractions
Perfect for students, engineers, and everyday users
Visually clear and mobile-optimized
From simple geometry to advanced equations, we help you calculate smarter — not harder.
Try the Free Area of Rectangle Calculator now — fast, accurate, and ad-free on Digital Calculator.