Perimeter Calculator

Perimeter Calculator — Find the Distance Around Shapes

Calculate the perimeter of common geometric shapes with step-by-step explanation. Learn formulas for rectangles, squares, triangles, circles, trapezoids, and parallelograms. For related geometry tools, see our area calculator.

Table of Contents

1. 1What Is Perimeter?
2. 2Perimeter of a Rectangle
3. 3Perimeter of a Square
4. 4Perimeter of a Triangle
5. 5Circumference of a Circle
6. 6Perimeter of a Trapezoid
7. 7Perimeter of a Parallelogram
8. 8Common Mistakes to Avoid
9. 9Real-World Applications
10. 10Practice Problems with Solutions
11. 11Tips for Mastering Perimeter
12. 12Final Thoughts
13. 13FAQ: Common Questions

Calculate Perimeter

Select a shape, enter its dimensions, and click Calculate for step-by-step working.

Select Shape Rectangle Square Triangle Circle (Circumference) Trapezoid Parallelogram

Length (l)

Width (w)

Perimeter will appear here.

Note: Perimeter measures the total distance around a shape in linear units. For circles, it's called circumference (C = 2πr).

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Perimeter – Complete Explanation

Perimeter is the total distance around a two-dimensional shape. It's measured in linear units (m, cm, ft, in). For circles, it's called circumference.

What Is Perimeter?

Perimeter = sum of all side lengths
Units = linear (m, cm, ft, in)

Circle perimeter = CIRCUMFERENCE = 2πr

1. What Is Perimeter?

Perimeter answers: "How long is the boundary of this shape?"

Key concepts:

• Linear units: Not squared.
• Additive: Sum of all sides.
• Perimeter vs Area: Different measures.
• Always positive.

2. Perimeter of a Rectangle

Rectangle Formula

P = 2l + 2w = 2(l + w)

Example: l=10, w=5 → P = 2(15) = 30 units

3. Perimeter of a Square

Square Formula

P = 4s

Example: s=7 → P = 28 units

4. Perimeter of a Triangle

Triangle Formula

P = a + b + c

Example: 8, 6, 10 → P = 24 units

5. Circumference of a Circle

Circumference Formula

C = 2πr = πd

Example: r=5 → C = 10π ≈ 31.42 units

6. Perimeter of a Trapezoid

Trapezoid Formula

P = a + b + c + d

7. Perimeter of a Parallelogram

Parallelogram Formula

P = 2(a + b)

8. Common Mistakes to Avoid

• Confusing perimeter with area.
• Forgetting to double both dimensions.
• Using slant height for perimeter (use actual side lengths).
• Confusing radius with diameter.
• Mixing units.

9. Real-World Applications

• Fencing: Enclosing yards.
• Framing: Picture frames, window frames.
• Baseboards: Room trim.
• Running tracks: Lap distance.
• Land surveying: Property boundaries.

10. Practice Problems with Solutions

Problem 1: Rectangle l=12, w=7 → P = 38 cm

Problem 2: Circle r=3 → C = 6π ≈ 18.85 m

Problem 3: Triangle 5,12,13 → P = 30 units

Problem 4: Square P=36 → s = 9 units

11. Tips for Mastering Perimeter

• Polygon perimeter = sum of sides.
• Rectangles/parallelograms: P = 2(a+b).
• Circle is special: C = 2πr.
• Consistent units.
• Draw diagrams for irregular shapes.

12. Final Thoughts

Perimeter is intuitive and practical. Use this calculator to verify your work, but practice until perimeter calculations become automatic.

13. Frequently Asked Questions

Perimeter measures the distance around a shape (linear units). Area measures the space inside (square units). A fence uses perimeter; carpet uses area.

Circumference is the circle's perimeter: C = 2πr = πd. For radius 5, C = 10π ≈ 31.42 units.

Use P = 2(l + w). Add length and width, then double. For l=10, w=5: P = 2(15) = 30.

Add all three sides: P = a + b + c. For sides 5, 12, 13: P = 30.

Perimeter uses linear units — meters, centimeters, feet, inches. Never square units.

Yes. A 1×9 rectangle has P=20, A=9. A 5×5 square has P=20, A=25. Same perimeter, very different areas.

Add up all the side lengths. Draw a diagram and verify you've included every side exactly once.

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 — Find the space inside shapes.
• 🔹 Rectangle Calculator — Calculate rectangle properties.
• 🔹 Square Calculator — Calculate square properties.
• 🔹 Circle Circumference Calculator — Dedicated circumference tool.
• 🔹 Trapezoid Calculator — Calculate trapezoid properties.
• 🔹 Triangle Area Calculator — Dedicated triangle area tool.

Conclusion

Perimeter is intuitive and practical. Use this calculator to verify your work, but practice until perimeter calculations become automatic.

Readers who wish to continue practicing and reinforce what they've learned can explore the companion learning resource for guided exercises.