Pie Cut Calculator – Loan calculator

Pie Cut Fabrication Calculator

Calculate precise dimensions for custom exhaust and tube bends

Total Bend Angle (°)

Number of Pie Cuts

Tube Outside Diameter (mm/in)

Desired Bend Radius (CLR)

Fabrication Results

Miter Angle (Per Side):

Total Degree per Cut:

Outside (Long) Length:

Inside (Short) Length:

Centerline Length per Cut:

Understanding Pie Cut Calculations

A pie cut calculator is an essential tool for fabricators, welders, and automotive enthusiasts who need to create custom bends in metal tubing—most commonly for exhaust systems, intercooler piping, or roll cages. Instead of using a mandrel bender, which can be expensive and limited by specific radii, pie cuts allow you to achieve any bend angle and radius using straight sections of pipe.

How to Calculate Pie Cuts

To use this calculator, you need four primary measurements:

Total Bend Angle: The final angle you want the pipe to turn (e.g., a 90-degree elbow).
Number of Pie Cuts: How many individual "wedges" you want to use. More cuts result in a smoother, more gradual flow but require more welding.
Tube Outside Diameter (OD): The measurement across the widest part of your tubing.
Bend Radius (CLR): The "Center Line Radius." This determines how tight or wide the curve is.

The Math Behind the Cut

The calculation involves trigonometry to determine the miter angle of each cut. The formula for the miter angle is:

            Miter Angle = Total Angle / (Number of Cuts * 2)
        

Once the miter angle is found, we calculate the lengths of the long and short sides of each wedge to ensure the radius is perfectly maintained throughout the bend.

Example Calculation

If you want to build a 90° bend using 5 pie cuts with a 3-inch diameter pipe and a 4.5-inch radius:

Miter Angle: 90 / (5 * 2) = 9° per side.
Total Cut Angle: 18° per wedge.
Outside Length: Approx 1.90 inches.
Inside Length: Approx 0.95 inches.

By marking these lengths on your tube and cutting at the 9° miter angle, the pieces will fit together to form a perfect 90° curve.

function calculatePieCuts() { var totalAngle = parseFloat(document.getElementById('totalAngle').value); var numCuts = parseFloat(document.getElementById('numCuts').value); var diameter = parseFloat(document.getElementById('tubeDiameter').value); var radius = parseFloat(document.getElementById('bendRadius').value); if (isNaN(totalAngle) || isNaN(numCuts) || isNaN(diameter) || isNaN(radius) || numCuts <= 0) { alert("Please enter valid positive numbers in all fields."); return; } // Calculation Logic // Each pie cut has two mitered faces. // Total number of miter interfaces = numCuts * 2 var miterAngle = totalAngle / (numCuts * 2); var totalDegreePerCut = totalAngle / numCuts; // Convert miter angle to radians for Math functions var miterRad = (miterAngle * Math.PI) / 180; // Lengths are based on the tangent of the miter angle // Length = 2 * Radius * tan(MiterAngle) var centerLength = 2 * radius * Math.tan(miterRad); var longSide = 2 * (radius + (diameter / 2)) * Math.tan(miterRad); var shortSide = 2 * (radius – (diameter / 2)) * Math.tan(miterRad); // Display Results document.getElementById('resMiterAngle').innerText = miterAngle.toFixed(2) + "°"; document.getElementById('resTotalDegree').innerText = totalDegreePerCut.toFixed(2) + "°"; document.getElementById('resLongSide').innerText = longSide.toFixed(3); document.getElementById('resShortSide').innerText = shortSide.toFixed(3); document.getElementById('resCenterLength').innerText = centerLength.toFixed(3); document.getElementById('results-area').style.display = 'block'; }