Octagon Layout Calculator

Octagon Layout Calculator

Side Length Width (Distance Across Flats) Diameter (Distance Across Corners)

Octagon Dimensions:

Side Length:

–

Perimeter:

–

Width (Across Flats):

–

Diameter (Across Corners):

–

Total Area:

–

Internal Angle:

135°

function calculateOctagon() { var method = document.getElementById("calcMethod").value; var val = parseFloat(document.getElementById("inputValue").value); var resDiv = document.getElementById("octagonResults"); if (isNaN(val) || val <= 0) { alert("Please enter a valid positive number."); return; } var s, w, d, area, perimeter; var sqrt2 = Math.sqrt(2); if (method === "side") { s = val; w = s * (1 + sqrt2); d = s * Math.sqrt(4 + 2 * sqrt2); } else if (method === "width") { w = val; s = w / (1 + sqrt2); d = w / Math.cos(Math.PI / 8); } else if (method === "diameter") { d = val; s = d * Math.sin(Math.PI / 8); w = d * Math.cos(Math.PI / 8); } perimeter = 8 * s; area = 2 * (1 + sqrt2) * Math.pow(s, 2); document.getElementById("resSide").innerText = s.toFixed(4); document.getElementById("resPerimeter").innerText = perimeter.toFixed(4); document.getElementById("resWidth").innerText = w.toFixed(4); document.getElementById("resDiameter").innerText = d.toFixed(4); document.getElementById("resArea").innerText = area.toFixed(4); resDiv.style.display = "block"; }

How to Use the Octagon Layout Calculator

Whether you are building a gazebo, laying out a deck, or cutting tile, calculating the exact dimensions of a regular octagon is crucial for a professional finish. Our octagon layout calculator handles the complex trigonometry for you.

Understanding Octagon Geometry

A regular octagon is a polygon with 8 equal sides and 8 equal angles. To lay one out, you typically need to know one of three primary measurements:

• Side Length: The length of any single outer edge.
• Width (Across Flats): The shortest distance from one flat side to the opposite flat side. This is often used when fitting an octagon inside a square box.
• Diameter (Across Corners): The longest distance from one corner to the opposite corner. This is the diameter of the "circumcircle" that would perfectly enclose the octagon.

Practical Example: Building a Gazebo

Imagine you want to build an octagon-shaped gazebo that is 10 feet wide (from flat side to flat side). Here is how you would determine your layout:

1. Select Width (Distance Across Flats) in the calculator.
2. Enter 10 in the value field.
3. The calculator will reveal that your Side Length is approximately 4.14 feet.
4. The Perimeter (total length of all railing) is 33.14 feet.
5. The Diameter (corner-to-corner) is 10.82 feet, which is useful for marking out your foundation posts.

The Math Behind the Octagon

For those interested in the manual formulas, the relationship between the width (W) and side (S) is defined by the silver ratio:

W = S × (1 + √2)

Every internal angle of a regular octagon is 135°, meaning the external "miter" cut for your wood joints will be 22.5° (since 135 / 2 = 67.5, and 90 – 67.5 = 22.5).

Quick Reference Table

Desired Width	Required Side Length
12 inches	4.97 inches
24 inches	9.94 inches
48 inches	19.88 inches