Perimeter Calculator

Calculate the perimeter for various geometric shapes

Select a shape and enter its dimensions to compute the perimeter. The perimeter is the total length of the boundary of a two-dimensional shape.

Examples

Click on an example to load it into the calculator.

Perimeter of a Square

Square

Calculate the perimeter of a square with a side length of 15.

Side: 15

Perimeter of a Rectangle

Rectangle

Calculate the perimeter of a rectangle with length 12 and width 8.

Length: 12

Width: 8

Circumference of a Circle

Circle

Calculate the circumference (perimeter) of a circle with a radius of 7.

Radius: 7

Perimeter of a Triangle

Triangle

Calculate the perimeter of a triangle with sides 5, 12, and 13.

Side A: 5

Side B: 12

Side C: 13

Other Titles
Understanding Perimeter: A Comprehensive Guide
Explore the concept of perimeter, learn how to calculate it for different shapes, and discover its real-world applications.

What is Perimeter? Core Concepts

  • Defining the boundary of a shape
  • Distinguishing perimeter from area
  • The importance of units in perimeter calculations
Perimeter is a fundamental concept in geometry that refers to the total distance around the boundary of a closed two-dimensional figure. Imagine walking along the edge of a park; the total distance you cover is its perimeter. It's a measure of length, and as such, it's expressed in linear units like meters, centimeters, feet, or inches.
Perimeter vs. Area
It's crucial not to confuse perimeter with area. While perimeter is the length of the outline, area is the measure of the space enclosed within that outline. For a rectangular field, the perimeter is the length of the fence needed to enclose it, while the area is the amount of grass inside it.

Conceptual Examples

  • The perimeter of a rectangular garden determines the length of fencing required.
  • The circumference of a circular running track is the distance an athlete runs in one lap.

Step-by-Step Guide to Using the Perimeter Calculator

  • Selecting the correct shape for your calculation
  • Entering dimensions accurately
  • Interpreting the calculated results and formula
Our calculator simplifies finding the perimeter for a variety of common shapes. Follow these steps for an accurate calculation.
1. Select the Shape
Start by choosing the geometric shape you're interested in from the dropdown menu. We support squares, rectangles, triangles, circles, and regular polygons.
2. Enter the Dimensions
Once you select a shape, specific input fields for its dimensions will appear. For a square, you'll need the side length. For a circle, you'll need the radius. Ensure you enter positive numerical values.
3. Calculate and Review
Click the 'Calculate Perimeter' button. The result will be displayed, showing the calculated perimeter and the mathematical formula used. This helps you understand how the answer was derived.

Usage Examples

  • To find a square's perimeter: Select 'Square', enter side length '10', click calculate.
  • For a circle's circumference: Select 'Circle', enter radius '5', click calculate.

Perimeter Formulas for Common Shapes

  • Calculating the perimeter of rectilinear shapes
  • Finding the circumference of a circle
  • Formulas for triangles and regular polygons
Understanding the formula for each shape is key to manual calculation and for appreciating the calculator's logic.
Square and Rectangle
For a square with side length 'a', the formula is P = 4a. For a rectangle with length 'l' and width 'w', the formula is P = 2(l + w).
Circle
The perimeter of a circle is called its circumference. With radius 'r', the formula is C = 2πr. The constant π (pi) is approximately 3.14159.
Triangle
For a triangle with side lengths a, b, and c, the perimeter is simply the sum of its sides: P = a + b + c.
Regular Polygon
For a regular polygon with 'n' sides of equal length 's', the formula is P = n × s.

Formula Applications

  • Square (a=5): P = 4 * 5 = 20
  • Rectangle (l=6, w=4): P = 2 * (6 + 4) = 20
  • Circle (r=3): C = 2 * π * 3 ≈ 18.85
  • Equilateral Triangle (a=b=c=7): P = 7 + 7 + 7 = 21

Real-World Applications of Perimeter

  • Construction and home improvement projects
  • Urban planning and landscaping
  • Sports and recreational activities
Perimeter calculations are essential in many practical scenarios.
Home and Construction
When you're fencing a yard, installing baseboards in a room, or putting a decorative border around a garden, you need to calculate the perimeter to determine the amount of material required.
Event Planning and Safety
Organizers use perimeter calculations to set up barriers for festivals, parades, or marathons. It's also used to determine safety zones around a hazard.

Practical Scenarios

  • Calculating the length of Christmas lights needed to frame a window.
  • Determining the amount of tape needed to mark a boundary for a sports field.

Common Questions and Advanced Topics

  • Handling irregular shapes
  • The relationship between perimeter and area
  • Perimeter in three-dimensional space
Let's address some common questions and explore more advanced concepts related to perimeter.
What About Irregular Shapes?
For irregular polygons, the perimeter is found by summing the lengths of all its individual sides. For shapes with curved edges, calculus (specifically, arc length integration) is often required, which is beyond the scope of this basic calculator.
The Isoperimetric Problem
This is a classic mathematical question: of all shapes with a given perimeter, which one encloses the largest area? The answer is the circle. This principle is seen in nature, such as how soap bubbles form spheres to minimize surface area for a given volume.

Further Insights

  • An L-shaped room's perimeter is the sum of all its wall lengths.
  • A farmer wanting to enclose the maximum area with a fixed length of fence should make a circular pen.