Perimeter of Polygon Calculator
Calculate Polygon Perimeter
Enter the lengths of the sides of your polygon below. If your polygon has fewer than 8 sides, leave the extra fields blank or set to 0. Also, specify the units used for the sides.
Results
Number of Sides Used: 3
Sum of Even-numbered Sides (2, 4, …): 4.00 cm
Sum of Odd-numbered Sides (1, 3, …): 8.00 cm
| Side Number | Length |
|---|---|
| 1 | 5.00 cm |
| 2 | 4.00 cm |
| 3 | 3.00 cm |
What is a Perimeter of Polygon Calculator?
A Perimeter of Polygon Calculator is a tool used to determine the total distance around the outside of a polygon. The perimeter is found by summing the lengths of all its sides. This calculator is useful for students, teachers, engineers, architects, and anyone needing to find the perimeter of a two-dimensional shape with straight sides. It simplifies the process, especially for polygons with many sides or irregular side lengths.
Anyone who works with geometric shapes might use a Perimeter of Polygon Calculator. This includes students learning geometry, builders estimating material lengths, or designers planning layouts. A common misconception is that you need a complex formula for every polygon; however, for the perimeter, it's always just the sum of the side lengths, regardless of the polygon's shape (convex, concave, regular, or irregular), as long as it's a simple polygon (doesn't intersect itself).
Perimeter of Polygon Formula and Mathematical Explanation
The formula to calculate the perimeter of any polygon is straightforward:
Perimeter (P) = s1 + s2 + s3 + … + sn
Where:
- P is the total perimeter of the polygon.
- s1, s2, s3, …, sn are the lengths of the individual sides of the polygon.
- n is the total number of sides of the polygon.
You simply add the lengths of all the sides together to get the perimeter. For example, if a triangle has sides of length 3 cm, 4 cm, and 5 cm, its perimeter is 3 + 4 + 5 = 12 cm. Our Perimeter of Polygon Calculator does this addition for you.
Variables Table
| Variable | Meaning | Unit | Typical Range |
|---|---|---|---|
| P | Perimeter | Length units (e.g., cm, m, inches, feet) | > 0 |
| si | Length of the i-th side | Length units (e.g., cm, m, inches, feet) | > 0 |
| n | Number of sides | Integer | ≥ 3 |
Practical Examples (Real-World Use Cases)
Example 1: Fencing a Triangular Garden
Imagine you have a triangular garden with sides measuring 5 meters, 7 meters, and 8 meters. To find out how much fencing you need, you calculate the perimeter:
Perimeter = 5 m + 7 m + 8 m = 20 meters.
Using the Perimeter of Polygon Calculator, you'd enter 5, 7, and 8 for the first three sides (and 0 for others), set the unit to "meters", and get a result of 20 meters.
Example 2: Framing a Pentagonal Window
An architect is designing a window shaped like an irregular pentagon with side lengths of 0.8 ft, 1.2 ft, 0.9 ft, 1.1 ft, and 1.0 ft. To determine the length of the frame material needed, they calculate the perimeter:
Perimeter = 0.8 + 1.2 + 0.9 + 1.1 + 1.0 = 5.0 feet.
The Perimeter of Polygon Calculator would give this result when these five side lengths are entered.
How to Use This Perimeter of Polygon Calculator
Using our Perimeter of Polygon Calculator is simple:
- Enter Unit: First, specify the unit of measurement (like cm, m, inches, ft) you are using for the sides in the "Unit of Measurement" field. This is for display purposes.
- Enter Side Lengths: Input the lengths of each side of your polygon into the respective "Side 1 Length", "Side 2 Length", …, "Side 8 Length" fields. If your polygon has fewer than 8 sides, enter the lengths for the sides it has and leave the remaining fields as 0 or blank.
- Calculate: The calculator automatically updates the perimeter and other details as you enter the side lengths. You can also click the "Calculate Perimeter" button.
- View Results: The "Results" section will display the total perimeter, the number of sides you entered lengths for, and the sums of even and odd-numbered sides.
- See Table & Chart: A table and a bar chart below the results will visualize the lengths of the sides you entered.
- Reset: Click the "Reset" button to clear all inputs and start over with default values.
- Copy: Click "Copy Results" to copy the main results and side lengths to your clipboard.
The Perimeter of Polygon Calculator provides immediate feedback, allowing you to quickly find the perimeter.
Key Factors That Affect Perimeter of Polygon Results
Several factors influence the calculated perimeter:
- Number of Sides: The more sides a polygon has (that have non-zero length), the more values you sum, affecting the total perimeter.
- Length of Each Side: The most direct factor. Longer sides result in a larger perimeter.
- Measurement Accuracy: The precision of your side length measurements will directly impact the accuracy of the calculated perimeter. Using precise tools for measurement is key.
- Units Used: While the numerical sum remains the same, the unit (cm, m, inches) determines the actual scale of the perimeter. Ensure all side lengths are in the same unit before using the Perimeter of Polygon Calculator.
- Polygon Type (for context, not calculation): Although the perimeter calculation is the same (sum of sides), knowing if it's regular (all sides equal) or irregular helps in how you might measure or input data. For a regular polygon with side 's' and 'n' sides, perimeter is simply n*s.
- Data Entry Errors: Incorrectly entering the side lengths will lead to an incorrect perimeter. Double-check your inputs in the Perimeter of Polygon Calculator.
Frequently Asked Questions (FAQ)
- What is a polygon?
- A polygon is a closed two-dimensional figure made up of straight line segments (sides) connected end-to-end. Examples include triangles, squares, pentagons, etc.
- Can I use the Perimeter of Polygon Calculator for a circle?
- No, a circle is not a polygon as it is curved. You need to calculate its circumference (2 * π * radius).
- What if my polygon has more than 8 sides?
- This specific Perimeter of Polygon Calculator is set up for up to 8 sides. For more sides, you would need a calculator that accommodates more inputs or sum them manually.
- What if I enter a negative side length?
- Side lengths cannot be negative. The calculator is set to handle non-negative inputs (min="0″). If you try to enter a negative number, it should be treated as invalid or reset to 0 by the browser or our validation.
- Does the Perimeter of Polygon Calculator work for irregular polygons?
- Yes, it works for any simple polygon, whether regular (all sides and angles equal) or irregular (sides and/or angles differ), as long as you input the length of each side.
- What units can I use?
- You can use any unit of length (cm, m, inches, feet, etc.), but you must be consistent and use the same unit for all side lengths. The unit field is for your reference and display in the results.
- Is the perimeter the same as the area?
- No, the perimeter is the distance around the outside of the polygon, while the area is the space enclosed within the polygon. The Perimeter of Polygon Calculator only calculates the perimeter.
- How do I find the perimeter of a regular polygon easily?
- For a regular polygon with 'n' sides each of length 's', the perimeter is P = n * s. You can still use the calculator by entering 's' for 'n' side inputs.
Related Tools and Internal Resources
- Area of Polygon Calculator: If you need to find the space inside a polygon, this tool can help (assuming {internal_links}[0] is about area).
- Right Triangle Calculator: Calculate sides, angles, and area of right-angled triangles ({internal_links}[1]).
- Circle Circumference and Area Calculator: For circles, find the circumference (perimeter) and area ({internal_links}[2]).
- Rectangle Perimeter and Area Calculator: A specialized calculator for rectangles ({internal_links}[3]).
- Basic Geometry Formulas: A reference page for common geometry formulas ({internal_links}[4]).
- Length Unit Converter: Convert between different units of length ({internal_links}[5]).
Our Perimeter of Polygon Calculator is one of many tools to assist with geometric calculations.