Tube notching template generator: a printable coping template for any tube, angle and offset

A tube that meets another tube has to be notched, coped or fishmouthed to sit tight before it is welded: every roll cage, chassis, trailer frame, handrail and go-kart is full of these joints. The cut is a curve that depends on both tube sizes, the angle between them and how far one is offset from the other, and the reliable way to get it right is a paper template wrapped round the tube. This page draws that template for any combination and prints it at full size.

Everything runs in your browser: nothing to install, no account, and the template prints on ordinary A4 or Letter paper, tiled when it is wider than one sheet.

Tube notching template generator

Type the outside diameter of the tube you are cutting, the outside diameter of the tube it meets, the angle between them and the offset between their centre lines (0 when they are centred). The depth of the notch and the table of heights come out at once, and Print gives the template at 1:1.

Embed this calculator on your site

Free, and it works on any site: paste the code where you want the calculator. It links back to this guide.

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How to use the template

1. Print at actual size, 100 %, with no fit-to-page. Measure the check bar on the sheet: it must read 100 mm or 4 in. If it does not, the printer scaled the page.
2. Cut out the template along the curve. When it took more than one sheet, glue the sheets on the repeated strip at the edge, matching the curve.
3. Wrap it round the end of the tube with the straight edge square to the tube, and tape it. The wrap is exactly the circumference of the tube, so the two ends meet.
4. Put the 0° station on the line of the tube that lies in the plane of both tubes, on the side of the acute angle; 180° is the heel, where the cut is deepest on an angled joint. For a 90° joint without offset, any of the four quarter marks works.
5. Mark along the curve with a scriber or a fine marker, take the template off and cut: grinder, band saw, hole-saw notcher or plasma. Leave the line, then dress the notch to fit on the other tube.

The formula

Take r as the outside radius of the tube you cut, R as the outside radius of the tube it meets, α as the angle between the two centre lines and e as the offset between them. The generator of the cut tube at angle φ round its circumference reaches the other tube at

Notch line

ℓ(φ) = [ r × cos φ × cos α − √(R² − (r × sin φ + e)²) ] / sin α The template height at each station is ℓ(φ) minus the lowest ℓ, plus the margin to the straight edge. The wrap is π × d, the outside circumference of the cut tube.

It is the same geometry as the pipe branch and the offset pipe branch, worked on the outside of both tubes because that is where the paper sits. Two equal tubes at 90° give the deepest centred notch: half the diameter, 0.875 in on 1-3/4 in tube. At 45° the same pair notches 2.112 in deep at the heel.

The offset has to keep the cut tube within the other one: r + e cannot exceed R. Beyond that the tubes no longer meet all round, and the joint is a different cut.

Tube sizes and wraps

The wrap of the template is the outside circumference of the tube you are cutting. For the round tube sizes used in cages, chassis and frames:

For standard pipe sizes, from 1/2 in to 12 in, there are ready-made templates for the 90° tee, the 45° lateral and the mitre cut, as printable PDFs: start with the 2 inch pipe saddle template.

Wall thickness and plate

The template is drawn on the outside of both tubes, which is right for tube and thin-wall pipe: the notch is cut to the outside and the joint closes on the outside of the other tube. On heavy-wall pipe the inside edge of the cut also touches the other tube near the flanks; cut to the line and dress the inside with a grinder until it seats.

A branch rolled from flat plate is a different job: its pattern is worked on the mid-thickness of the plate, and the pipe branch calculator does that one, with the flat pattern, the 1:1 template and the DXF.

Frequently asked questions

How do I make a tube notching template?

Type the two tube outside diameters, the angle and the offset in the generator above and print the template at 100 %. Wrap it round the tube end with the straight edge square, mark the curve and cut to the line.

What is the difference between notching, coping and fishmouthing?

None: they are three names for the same saddle-shaped cut on the end of a tube that lets it sit on another tube.

Which way round does the template go?

0° on the line of the tube in the plane of both tubes, on the acute side; 180° is the heel, where an angled notch is deepest. On a 90° joint without offset the template is symmetric and any quarter mark lines up.

Does the wall thickness change the template?

Not for a template wrapped round the tube: it is drawn on the outside, where the paper sits. On heavy-wall pipe, dress the inside edge of the notch after cutting.

Why does the printed template not fit round my tube?

The printer scaled it. Print at actual size, 100 %, and check the bar on the sheet: 100 mm or 4 in. Also check the tube with a calliper: a 1-3/4 in tube is 1.750 in outside, and the wrap is 5.498 in.