body {
font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Helvetica, Arial, sans-serif;
line-height: 1.6;
color: #333;
max-width: 800px;
margin: 0 auto;
padding: 20px;
}
.calculator-container {
background-color: #f9f9f9;
border: 1px solid #ddd;
border-radius: 8px;
padding: 25px;
margin-bottom: 30px;
box-shadow: 0 2px 5px rgba(0,0,0,0.05);
}
.calculator-title {
text-align: center;
color: #2c3e50;
margin-bottom: 20px;
font-size: 24px;
font-weight: bold;
}
.form-group {
margin-bottom: 15px;
}
.form-group label {
display: block;
margin-bottom: 5px;
font-weight: 600;
color: #555;
}
.form-group input {
width: 100%;
padding: 10px;
border: 1px solid #ccc;
border-radius: 4px;
font-size: 16px;
box-sizing: border-box;
}
.form-row {
display: flex;
gap: 15px;
flex-wrap: wrap;
}
.form-col {
flex: 1;
min-width: 200px;
}
.calc-btn {
display: block;
width: 100%;
background-color: #8b4513; /* Wood color */
color: white;
border: none;
padding: 12px;
font-size: 18px;
font-weight: bold;
border-radius: 4px;
cursor: pointer;
transition: background-color 0.3s;
margin-top: 10px;
}
.calc-btn:hover {
background-color: #6d360e;
}
#result-area {
margin-top: 25px;
padding: 20px;
background-color: #fff;
border: 1px solid #eee;
border-radius: 4px;
display: none;
}
.result-row {
display: flex;
justify-content: space-between;
border-bottom: 1px solid #eee;
padding: 10px 0;
}
.result-row:last-child {
border-bottom: none;
}
.result-label {
font-weight: 600;
color: #444;
}
.result-value {
font-weight: bold;
color: #8b4513;
}
.error-msg {
color: #d9534f;
text-align: center;
margin-top: 10px;
display: none;
}
.content-section h2 {
color: #2c3e50;
border-bottom: 2px solid #8b4513;
padding-bottom: 10px;
margin-top: 40px;
}
.content-section p {
margin-bottom: 15px;
}
.content-section ul {
margin-bottom: 20px;
padding-left: 20px;
}
.content-section li {
margin-bottom: 8px;
}
.diagram-note {
background-color: #fff3cd;
border-left: 5px solid #ffc107;
padding: 15px;
margin: 20px 0;
font-size: 0.95em;
}
Mastering Segmented Turning
Segmented woodturning is an art form that transforms flat boards into complex, patterned vessels. Unlike solid woodturning, which involves mounting a log or blank directly onto the lathe, segmented turning constructs a blank from many individual pieces of wood glued together to form rings.
By stacking these rings, woodturners can create bowls, vases, and platters with incredible geometric patterns and minimal wood waste. However, the success of a segmented project relies entirely on precision math. A fraction of a degree off in your cutting angle can result in gaps in your rings, compromising the structural integrity of the piece.
How to Use This Calculator
This tool eliminates the guesswork from the geometry required to build a perfect ring. Here is how to interpret the inputs:
- Target Outer Diameter (OD): The desired finished diameter of the ring. The calculator assumes this is the "flat-to-flat" diameter to ensures there is enough material to turn the ring perfectly round.
- Target Inner Diameter (ID): The diameter of the hollow center. The difference between the OD and ID determines the width of the board you need to cut.
- Number of Segments: How many pieces of wood will make up a single ring. Common numbers are 12, 16, 24, or 36.
Pro Tip: Always cut a test ring using scrap wood before cutting your expensive exotic hardwoods. This ensures your miter gauge or sled is set perfectly for the calculated angle.
Understanding the Geometry
The core of segmented turning math revolves around the Miter Angle and the Segment Edge Length.
The Miter Angle
To create a closed ring (a circle represents 360 degrees), the total degrees of all cut angles must equal 360. Since every segment has two cut sides, the formula for the cutting angle is:
Miter Angle = 360 / (Number of Segments × 2)
For example, a 12-segment ring requires a cutting angle of 15 degrees (360 / 24 = 15).
Segment Edge Length
The "Long Side" of your trapezoidal segment is the most critical dimension for setting stop blocks on your saw. This calculator uses the tangent formula to determine the side length based on the flat-to-flat diameter of the polygon. This ensures that when the segments are glued together, the resulting ring is large enough to encompass your target outer diameter.
Tips for Perfect Glue-Ups
Once you have calculated your dimensions and cut your segments, precision in assembly is key:
- Rub Joints: Ensure your glue surfaces are clean. A "rub joint" helps remove air pockets and creates an initial tack.
- Band Clamps: Hose clamps or specialized rubber band clamps are excellent for applying even pressure around the circumference of the ring.
- Flattening: After the glue dries, ensure one face of the ring is perfectly flat (using a drum sander or sanding board) before gluing it to the next ring in the stack.
function calculateSegments() {
// 1. Get input elements
var odInput = document.getElementById("outerDiameter");
var idInput = document.getElementById("innerDiameter");
var segInput = document.getElementById("numSegments");
var thickInput = document.getElementById("boardThickness");
var resultArea = document.getElementById("result-area");
var errorMsg = document.getElementById("error-message");
// 2. Parse values
var od = parseFloat(odInput.value);
var id = parseFloat(idInput.value);
var segments = parseInt(segInput.value);
var thickness = parseFloat(thickInput.value); // Optional, might be NaN
// 3. Validation
errorMsg.style.display = "none";
resultArea.style.display = "none";
if (isNaN(od) || isNaN(id) || isNaN(segments)) {
errorMsg.innerText = "Please enter valid numbers for Diameter and Segments.";
errorMsg.style.display = "block";
return;
}
if (od <= id) {
errorMsg.innerText = "Outer Diameter must be larger than Inner Diameter.";
errorMsg.style.display = "block";
return;
}
if (segments 180 / segments
var miterAngle = 180 / segments;
// Convert Angle to Radians for Math functions
var radians = miterAngle * (Math.PI / 180);
// Segment Outer Length (Long Side)
// We assume OD is the Flat-to-Flat distance (apothem * 2) so the circle fits inside.
// Formula: Side = Diameter * tan(180/N)
var segmentOuterLen = od * Math.tan(radians);
// Segment Inner Length (Short Side)
var segmentInnerLen = id * Math.tan(radians);
// Strip Width
var stripWidth = (od – id) / 2;
// Total Board Length Estimation
// (Long side + kerf) * segments. Assuming 1/8″ (0.125) kerf roughly.
var kerf = 0.125;
var totalLength = (segmentOuterLen + kerf) * segments;
// 5. Formatting Results (2 decimal places)
document.getElementById("res-miter-angle").innerText = miterAngle.toFixed(2) + "°";
document.getElementById("res-outer-length").innerText = segmentOuterLen.toFixed(3) + '"';
document.getElementById("res-inner-length").innerText = segmentInnerLen.toFixed(3) + '"';
document.getElementById("res-strip-width").innerText = stripWidth.toFixed(3) + '"';
// Add safety margin to total length (approx 10%)
var safeTotalLength = totalLength * 1.1;
document.getElementById("res-total-length").innerText = safeTotalLength.toFixed(1) + '" (approx)';
// 6. Display Results
resultArea.style.display = "block";
}