How to Calculate Area of an Octagon

Octagon Area Calculator

An octagon is a polygon with eight sides and eight angles. A regular octagon is a special type where all eight sides are equal in length, and all eight interior angles are equal, each measuring 135 degrees. These symmetrical shapes are frequently encountered in architecture, design, and various everyday objects, such as stop signs or certain types of flooring patterns.

Calculating the area of an octagon is a fundamental task in many fields, including construction, engineering, graphic design, and mathematics. Whether you're planning a landscape feature, designing a unique piece of furniture, or solving a geometric problem, accurately determining the area is crucial for material estimation and spatial planning.

Formula for the Area of a Regular Octagon

The most straightforward method to calculate the area of a regular octagon involves using its side length. If 's' represents the length of one side of a regular octagon, the formula for its area (A) is:

A = 2 × (1 + √2) × s²

Where:

  • A is the total Area of the octagon.
  • s is the length of one side of the regular octagon.
  • √2 represents the square root of 2, which is approximately 1.41421356.

This formula is derived by dissecting the octagon into eight congruent isosceles triangles or by conceptualizing it as a square with its corners precisely cut off.

How to Use the Octagon Area Calculator

Our Octagon Area Calculator simplifies this calculation, providing quick and accurate results. Follow these simple steps:

  1. Enter Side Length: Input the length of one side of your regular octagon into the designated "Side Length (s)" field below. Ensure your measurement is accurate and in your preferred unit (e.g., meters, feet, inches).
  2. Calculate: Click the "Calculate Area" button.
  3. View Result: The calculated area will be displayed instantly in the "Calculated Area" section, presented with the appropriate squared unit.

Example Calculation

Let's consider a regular octagon with a side length of 7 units.

Using the formula:

A = 2 × (1 + √2) × s²
A = 2 × (1 + 1.41421356) × 7²
A = 2 × (2.41421356) × 49
A = 4.82842712 × 49
A ≈ 236.5929

Therefore, the area of this octagon would be approximately 236.59 square units.

Enter side length and click 'Calculate Area'.
function calculateOctagonArea() { var sideLengthInput = document.getElementById("sideLength"); var sideLength = parseFloat(sideLengthInput.value); var resultDiv = document.getElementById("result"); if (isNaN(sideLength) || sideLength <= 0) { resultDiv.innerHTML = "Please enter a valid positive number for the side length."; resultDiv.style.backgroundColor = "#f8d7da"; resultDiv.style.borderColor = "#f5c6cb"; return; } // Formula for the area of a regular octagon given side length 's': // A = 2 * (1 + sqrt(2)) * s^2 var area = 2 * (1 + Math.sqrt(2)) * Math.pow(sideLength, 2); resultDiv.innerHTML = "The area of the octagon is: " + area.toFixed(4) + " square units."; resultDiv.style.backgroundColor = "#e9f7ef"; resultDiv.style.borderColor = "#c3e6cb"; resultDiv.style.color = "#218838"; }

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