The quick tee

The method is intended for soft materials such as PVC and paper insulation. Confirm that your tee piece is either at exactly 45 degrees or another specific angle — if the angle is not a clean 45°, you must use the tangent method instead of the Pythagoras shortcut.

Multiply the pipe diameter by π (3.14) to find the circumference. If the diameter is, for example, 120 mm, that gives 120 × 3.14 = 376.8 mm. This figure is the width of the piece of cardboard you need to cut.

Use the line method: find the nearest round number above your calculated circumference (for 376.8 mm this is 400), and divide this number by four to find the field width (here 100 mm per field). Mark the lines on the card so you get four exactly equal fields corresponding to the circumference.

For a T-piece of equal diameter at 45 degrees, the distance from the top of the main pipe down to the tip equals the radius (for Ø120 mm it is 60 mm). As the T-piece runs at an angle, you need Pythagoras: A² + B² = C². With A = 60 and B = 60, 3600 + 3600 = 7200, and the square root of 7200 is 84.85 mm. This value is C.

Place a measuring piece corresponding to the pipe diameter (120 mm) on the cardboard and mark a dotted line across it. The remaining length above the dotted line forms the short side, and the line marks the top edge of your main pipe. Join the shortest and the longest side with a line — that is the top edge of your finished tee piece.

Set the compasses to the C value (84.85 mm). Start from the top-edge line and mark down at right angles to find the position of the point on the front. On the back (the joint side) the point is marked in two places — one on each side of the centre line.

Use the round template to draw a curved line connecting the two apex points and forming the T-piece's opening. Adjust the curve so it has a natural, neat shape. It is essential that you hit both end points precisely, otherwise the angle will not be a correct 45 degrees.

Cut along the lines that fit best. You now have a quick tee piece of equal diameter at 45 degrees, which can easily be used in PVC. If needed, add lamellas/flaps at the edges of the opening so that the tee piece can be hidden and held in place under the jacket pipe — this is particularly useful for condensation insulation.

When the tee piece joins a larger diameter (e.g. 120 on 175 mm), the centre line does not reach all the way down to the centre of the main pipe. The vertical distance from the tee's centre line to the point is 28 mm in this example. This distance is laid at an angle of 45°, and Pythagoras gives: √(28² + 28²) ≈ 40 mm. Remember this measurement for the next step.

Calculate the circumference of the T-piece's pipe (diameter × 3.14) and divide the card into four fields as before. Mark the starting point on the card and mark the dotted line. If you subtract a distance equal to the main pipe's diameter from the starting point, this forms the line that gives 45° when the sheet is rolled.

From the top-edge line, measure the ≈ 40 mm perpendicularly out to both sides and make a mark. Then draw a fine freehand curve joining the two marks, matching the shape of a 45° T-piece on unequal diameters.

If the angle is not 45° (example: 48°), subtract the angle from 90°: 90 − 48 = 42°. Calculate the tangent of 42° = 0.90. Multiply by the diameter: 0.90 × 120 = 108.04 mm. This is the Y distance, which replaces the dimension you would otherwise have found with Pythagoras.

Choose X yourself (the starting point's length) and mark it on the card. Mark Y (108.04 mm) down from the dotted line. Draw a line from the starting point to the Y mark — this corresponds to the top edge and replaces C from the Pythagoras calculation.

Z corresponds to C in the previous calculations: measure it at right angles from the Y mark and transfer it to both sides. Then draw a neat arc freehand, cut out and make the necessary small adjustments. The tee is now ready for fitting.