Taper Angle Calculator

Calculate the angle of a taper for machining, woodworking, or engineering projects using the large diameter, small diameter, and length.

Large Diameter (D)

Small Diameter (d)

Taper Length (L)

Calculation Results

Angle Per Side (α): –

Total Included Angle (θ): –

Taper Ratio (1 in X): –

Taper Per Unit: –

Understanding Taper Angles

A taper is a gradual narrowing of a workpiece over a specific length. It is widely used in mechanical engineering for tool holders (like Morse tapers), plumbing fittings, and furniture legs. Calculating the correct angle is crucial for ensuring that two tapered parts fit together perfectly without slipping or jamming.

The Formula

The Taper Angle Calculator uses trigonometry to determine the precise slope. The main formula used to find the angle per side (half angle) is:

α = arctan((D – d) / (2 * L))

D: Large diameter
d: Small diameter
L: Length of the taper
α: Angle per side
2α: Total included angle

Practical Example

Imagine you are turning a piece of metal on a lathe. You need a large diameter of 40mm, a small diameter of 30mm, and a length of 50mm.

Subtract small diameter from large diameter: 40 – 30 = 10mm.
Divide by 2 times the length: 10 / (2 * 50) = 10 / 100 = 0.1.
Find the arctan of 0.1: This equals roughly 5.71°.
The total included angle would be 11.42°.

Common Taper Standards

Taper Type	Taper Per Foot (Approx)
Morse Taper #2	0.599 inches
Brown & Sharpe	0.500 inches
Jarno Taper	0.600 inches

function calculateTaperAngle() { var D = parseFloat(document.getElementById('largeDiameter').value); var d = parseFloat(document.getElementById('smallDiameter').value); var L = parseFloat(document.getElementById('taperLength').value); var resultDiv = document.getElementById('taperResult'); if (isNaN(D) || isNaN(d) || isNaN(L) || L = D) { alert("Large diameter must be greater than small diameter."); return; } // Logic: Angle per side (alpha) // tan(alpha) = (D – d) / (2 * L) var diff = D – d; var angleRad = Math.atan(diff / (2 * L)); var angleDeg = angleRad * (180 / Math.PI); var totalIncludedAngle = angleDeg * 2; // Taper Ratio (1 in X) // X = L / (D – d) var ratioX = L / diff; // Taper per unit var taperPerUnit = diff / L; // Formatting outputs document.getElementById('anglePerSide').innerText = angleDeg.toFixed(4) + "°"; document.getElementById('totalAngle').innerText = totalIncludedAngle.toFixed(4) + "°"; document.getElementById('taperRatio').innerText = "1 in " + ratioX.toFixed(4); document.getElementById('taperPerUnit').innerText = taperPerUnit.toFixed(6); resultDiv.style.display = "block"; }