How to Calculate Perimeter

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Perimeter Calculator

Rectangle Square Circle (Circumference) Triangle Regular Polygon (Equal Sides)
The Perimeter is: 0

How to Calculate Perimeter: A Comprehensive Guide

The perimeter is the total distance around the outside of a two-dimensional shape. Understanding how to calculate the perimeter is a fundamental skill in geometry, architecture, and daily tasks like measuring a room for baseboards or fencing a yard.

Perimeter Formulas for Common Shapes

Depending on the geometry of the object, the formula for perimeter changes. Here are the most common equations used by our calculator:

  • Rectangle: The formula is P = 2(l + w), where l is length and w is width. Because opposite sides are equal, you simply add one length and one width and double the result.
  • Square: Since all four sides are equal, the formula is P = 4s, where s is the length of one side.
  • Circle (Circumference): The "perimeter" of a circle is called the circumference. It is calculated using C = 2πr (where π ≈ 3.14159) or C = πd (using diameter).
  • Triangle: For any triangle, you simply add the lengths of the three sides: P = a + b + c.
  • Regular Polygon: If a shape has equal sides (like a regular hexagon or pentagon), the formula is P = n × s, where n is the number of sides and s is the side length.

Practical Example

Suppose you have a rectangular garden that is 10 meters long and 5 meters wide. To find out how much fencing you need:

1. Identify the formula: P = 2(Length + Width)
2. Substitute the values: P = 2(10 + 5)
3. Solve: P = 2(15) = 30 meters.

Why Calculating Perimeter Matters

Beyond math homework, perimeter calculations are vital for:

  • Construction: Estimating materials for framing, molding, and foundations.
  • Agriculture: Determining the amount of wire needed for livestock enclosures.
  • Graphic Design: Creating borders and defining stroke paths in vector art.
  • Sports: Measuring track lengths or field boundaries.
function updateFields() { var selectedShape = document.getElementById("shapeSelector").value; var groups = document.getElementsByClassName("shape-input-group"); // Hide all groups for (var i = 0; i < groups.length; i++) { groups[i].style.display = "none"; } // Show selected group document.getElementById(selectedShape + "Inputs").style.display = "block"; document.getElementById("perimeterResult").style.display = "none"; } function calculatePerimeter() { var shape = document.getElementById("shapeSelector").value; var result = 0; var resultDiv = document.getElementById("perimeterResult"); var resultText = document.getElementById("resultValue"); if (shape === "rectangle") { var l = parseFloat(document.getElementById("rectLength").value); var w = parseFloat(document.getElementById("rectWidth").value); if (!isNaN(l) && !isNaN(w)) { result = 2 * (l + w); } else { alert("Please enter valid numbers for length and width."); return; } } else if (shape === "square") { var s = parseFloat(document.getElementById("squareSide").value); if (!isNaN(s)) { result = 4 * s; } else { alert("Please enter a valid side length."); return; } } else if (shape === "circle") { var r = parseFloat(document.getElementById("circleRadius").value); if (!isNaN(r)) { result = 2 * Math.PI * r; } else { alert("Please enter a valid radius."); return; } } else if (shape === "triangle") { var a = parseFloat(document.getElementById("triA").value); var b = parseFloat(document.getElementById("triB").value); var c = parseFloat(document.getElementById("triC").value); if (!isNaN(a) && !isNaN(b) && !isNaN(c)) { result = a + b + c; } else { alert("Please enter valid lengths for all three sides."); return; } } else if (shape === "polygon") { var n = parseFloat(document.getElementById("polySides").value); var sVal = parseFloat(document.getElementById("polyLength").value); if (!isNaN(n) && !isNaN(sVal)) { result = n * sVal; } else { alert("Please enter valid numbers for sides and length."); return; } } resultText.innerHTML = result.toLocaleString(undefined, {maximumFractionDigits: 2}); resultDiv.style.display = "block"; }

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