Perimeter Calculator

Calculate the perimeter of common geometric shapes with step-by-step explanation. Learn the formulas for rectangles, squares, triangles, circles (circumference), trapezoids, and parallelograms with worked examples.

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

Calculate Perimeter

Select a shape, enter its dimensions, and click Calculate for the perimeter with 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 the outside of a two-dimensional shape. It's measured in linear units (e.g., m, cm, ft). For circles, the perimeter is called the circumference and is calculated using π (pi ≈ 3.14159).

---

Perimeter – Complete Explanation

Perimeter is the total distance around the outside of a two-dimensional shape. Think of it as the length of a fence needed to enclose a yard, or the distance you'd walk if you traced the boundary of the shape. Perimeter is measured in linear units — such as meters (m), centimeters (cm), feet (ft), or inches (in).

What Is Perimeter?

Perimeter = the sum of all side lengths of a shape.

Measured in linear units (m, cm, ft, in, etc.)

For a circle, perimeter is called CIRCUMFERENCE.

1. What Is Perimeter?

Perimeter answers the question: "How long is the boundary of this shape?" It's the one-dimensional measurement of the shape's outline. Unlike area (which measures the space inside), perimeter measures the edge itself.

Key concepts:

• Linear units: Perimeter is measured in regular units (not squared) — meters, feet, inches, etc.
• Additive: The perimeter of any polygon is simply the sum of its side lengths.
• Perimeter vs. Area: Two shapes with the same perimeter can have very different areas. A 1×9 rectangle has perimeter 20 but area 9; a 5×5 square also has perimeter 20 but area 25.
• Always positive: Perimeter is a distance — it's always positive.

2. Perimeter of a Rectangle

Rectangle Perimeter Formula

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

Where l = length and w = width.

A rectangle has two pairs of equal sides. The perimeter formula accounts for both lengths and both widths.

Example: Rectangle with length 10 and width 5.

P = 2(10 + 5) = 2(15) = 30 units

This is the total distance around: 10 + 5 + 10 + 5 = 30.

3. Perimeter of a Square

Square Perimeter Formula

P = 4s

Where s = side length.

A square has four equal sides, so its perimeter is simply four times one side.

Example: Square with side length 7.

P = 4 × 7 = 28 units

4. Perimeter of a Triangle

Triangle Perimeter Formula

P = a + b + c

Where a, b, and c are the three side lengths.

A triangle's perimeter is the sum of its three sides — no special formula needed beyond addition.

Example: Triangle with sides 8, 6, and 10.

P = 8 + 6 + 10 = 24 units

(This is the famous 6-8-10 right triangle!)

5. Circumference of a Circle

Circumference Formula

C = 2πr = πd

Where r = radius and d = diameter (d = 2r). π ≈ 3.14159.

A circle's perimeter is called its circumference. The constant π (pi) appears because the ratio of a circle's circumference to its diameter is always π, regardless of the circle's size.

Example: Circle with radius 5.

C = 2π × 5 = 10π ≈ 10 × 3.14159 ≈ 31.416 units

Exact form: 10π units

6. Perimeter of a Trapezoid

Trapezoid Perimeter Formula

P = a + b + c + d

Where a, b, c, and d are the four side lengths.

A trapezoid has four sides — two parallel bases and two non-parallel legs. The perimeter is simply the sum of all four.

Example: Trapezoid with sides 8, 6, 10, and 7.

P = 8 + 6 + 10 + 7 = 31 units

7. Perimeter of a Parallelogram

Parallelogram Perimeter Formula

P = 2a + 2b = 2(a + b)

Where a and b are the lengths of the two different sides.

A parallelogram has two pairs of equal, parallel sides — same as a rectangle, so the perimeter formula is identical.

Example: Parallelogram with sides 10 and 6.

P = 2(10 + 6) = 2(16) = 32 units

8. Common Mistakes to Avoid

• Confusing perimeter with area: Perimeter is the distance around (units); area is the space inside (square units). Don't use area formulas when you need perimeter.
• Forgetting to double both dimensions: For rectangles and parallelograms, P = 2(l + w), not l + w. Both dimensions contribute twice.
• Using slant height for perimeter: Perimeter uses actual side lengths, not perpendicular heights. Measure along the edges.
• Confusing radius with diameter in circles: C = 2πr uses the radius. If you have the diameter, C = πd or divide d by 2 first.
• Mixing units: All side lengths must be in the same unit before adding.

9. Real-World Applications

• Fencing: Calculating how much fencing material is needed to enclose a yard or garden.
• Framing: Determining the length of wood or metal needed for picture frames, window frames, or door frames.
• Baseboards and Trim: Measuring the perimeter of rooms for baseboard installation.
• Running Tracks: The perimeter of an oval track is the distance of one lap.
• Walls: The perimeter of a room determines how much wallpaper border or chair rail is needed.
• Land Surveying: Property boundaries are measured by perimeter.
• Sewing: Hem lengths and border trims use perimeter measurements.

10. Practice Problems with Solutions

Problem 1: Find the perimeter of a rectangle with length 12 cm and width 7 cm.

Solution: P = 2(12 + 7) = 2(19) = 38 cm

Problem 2: Find the circumference of a circle with radius 3 m.

Solution: C = 2π × 3 = 6π ≈ 18.85 m

Problem 3: Find the perimeter of a triangle with sides 5, 12, and 13.

Solution: P = 5 + 12 + 13 = 30 units (5-12-13 right triangle)

Problem 4: A square has a perimeter of 36. What is the side length?

Solution: 4s = 36 → s = 9 units

11. Tips for Mastering Perimeter

• For any polygon, perimeter is simply the sum of all side lengths — no complex formulas needed.
• Rectangles and parallelograms use the same perimeter formula: P = 2(a + b).
• The circle is the special case — its perimeter is called circumference and uses π.
• Always use consistent units — convert everything to the same unit before adding.
• Draw a diagram when working with irregular shapes to make sure you account for every side.
• For regular polygons (all sides equal), perimeter = number of sides × side length.

12. Final Thoughts

Perimeter is one of the most intuitive and practical geometric concepts — it's simply the distance around a shape. From fencing a yard to framing a picture, perimeter calculations are part of everyday life. Unlike area, which requires different formulas for different shapes, the perimeter of any polygon follows a single principle: add up all the side lengths.

Master the basic perimeter formulas — especially the circle's circumference (the only one involving π) — and you'll be equipped to handle a wide range of practical measurement problems. Use this calculator to verify your manual calculations, but practice until finding perimeters becomes quick and automatic.