Rectangle Calculator

Rectangle Calculator — Area, Perimeter & Diagonal

Calculate the area, perimeter, and diagonal of a rectangle with step-by-step explanation. Learn A = l × w, P = 2(l + w), and d = √(l² + w²). For related tools, see our area calculator.

Table of Contents

1. 1What Is a Rectangle?
2. 2Area of a Rectangle
3. 3Perimeter of a Rectangle
4. 4Diagonal of a Rectangle
5. 5Step-by-Step Examples
6. 6More Rectangle Examples
7. 7Special Case: The Square
8. 8The Golden Rectangle
9. 9Common Mistakes
10. 10Real-World Applications
11. 11Practice Problems
12. 12Tips for Mastery
13. 13Final Thoughts
14. 14FAQ: Common Questions

Calculate Rectangle Properties

Enter length and width. Click Calculate for step-by-step working.

Length (l)

Width (w)

Results will appear here.

Note: A rectangle has four right angles. Area = space inside, Perimeter = distance around, Diagonal = corner-to-corner (Pythagorean theorem).

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Rectangle – Complete Explanation

A rectangle is a four-sided polygon with four right angles and opposite sides equal and parallel.

Rectangle Formulas

A = l × w
P = 2(l + w)
d = √(l² + w²)

1. What Is a Rectangle?

A rectangle has four right angles, equal opposite sides, and equal diagonals.

2. Area of a Rectangle

A = l × w

3. Perimeter of a Rectangle

P = 2(l + w)

4. Diagonal of a Rectangle

d = √(l² + w²)

This is the Pythagorean theorem — the diagonal is the hypotenuse.

5. Step-by-Step Examples

10 × 6 Rectangle

A = 60 | P = 32 | d = √136 = 2√34 ≈ 11.662

12 × 5 Rectangle

A = 60 | P = 34 | d = √169 = 13 (5-12-13!)

6. More Rectangle Examples

8×6: d=10 (6-8-10)

15×8: d=17 (8-15-17)

7×24: d=25 (7-24-25)

5×5: d=5√2 (square)

7. Special Case: The Square

A = s² | P = 4s | d = s√2

8. The Golden Rectangle

l/w = φ ≈ 1.618

9. Common Mistakes

• Confusing area (square units) with perimeter (linear units).
• Forgetting the 2 in perimeter formula.
• Diagonal ≠ l + w — use the Pythagorean theorem.
• Mixing units.

10. Real-World Applications

• Flooring/Carpeting: Area.
• Baseboards/Fencing: Perimeter.
• Checking squareness: Equal diagonals.
• Screen sizes: Diagonal measurement.

11. Practice Problems

P1: 15×8 → A=120, P=46, d=17

P2: A=48, w=6 → l=8, P=28, d=10

P3: P=30, l=10 → w=5, A=50, d=5√5

P4: Square d=8 → s=4√2, A=32

12. Tips for Mastery

• Memorize all three formulas.
• Recognize Pythagorean triples for diagonals.
• Area = product; Perimeter = sum doubled.
• Use equal diagonals to check squareness.

13. Final Thoughts

The rectangle is foundational geometry. Master its three formulas and you'll handle countless practical problems.

14. Frequently Asked Questions

A = l × w. Multiply length by width.

P = 2(l + w). Add length and width, then double.

d = √(l² + w²) using the Pythagorean theorem.

A rectangle with all sides equal. A = s², P = 4s, d = s√2.

Measure both diagonals. If they're equal, the frame is a perfect rectangle.

A rectangle with aspect ratio φ ≈ 1.618. Aesthetically pleasing proportions.

The diagonal is the longest dimension and gives a single number representing size.

Explore Math Topics

Continue your learning journey with our other math guides

🔢Basic Arithmetic 📐Pre-Algebra 📊Algebra 📏Geometry 📈Statistics

Related Calculators

Explore these other geometry tools:

• 🔹 Area Calculator — Area of common shapes.
• 🔹 Perimeter Calculator — Distance around shapes.
• 🔹 Square Calculator — Square properties.
• 🔹 Triangle Area Calculator — Triangle area.
• 🔹 Circle Area Calculator — Circle area.
• 🔹 Trapezoid Calculator — Trapezoid properties.

Conclusion

The rectangle is foundational geometry. Master its three formulas and you'll handle countless practical problems.

Readers who wish to continue practicing can explore the companion learning resource for guided exercises.