How do you lay out the elliptical hole where a pipe passes through a plate at an angle?
A round pipe through a slanted plate makes an oval hole. Cut a circle instead and you get one of two things: a gap you could post a letter through, or a plate that won't slide on at all. Adam Fleisch lays out the elliptical hole for an angled pipe with one line of trig and a strip of sheet metal, a method he credits to W.V. Graves' The Pipe Fabricator's Blue Book.
Applies to
- Process
- Sheet metal, pipefitting, HVAC
- Materials
- Sheet metal or plate; card for a template
- Setup
- Calculator with sin (degree mode), straight strip of metal or card, marker, straightedge, snips or plasma
- Best for
- Escutcheon plates, roof and flashing penetrations, flanges
- Orientation
- Long axis runs the way the pipe leans; short axis across it
Why it matters
Slice a cylinder at an angle and the cut face is an ellipse. Across the lean, the hole is exactly as wide as the pipe. Along the lean, it stretches, and the shallower the angle, the longer it gets.
That stretch is the whole formula. At 90° the sine is 1 and you get a plain circle. At 30° the sine is 0.5 and the long axis is twice the diameter. At 44° the sine is 0.695, so a 4 1/2 in pipe needs 4.5 ÷ 0.695 = 6.48 in.
The strip is the clever bit.
A paper-strip trammel draws a true ellipse from nothing but the two half-axes. No compass, no string and two nails, no CAD. Sheet metal, a marker and two lines.
What good looks like
- The plate slides over the pipe at the set angle with an even gap all round
- The ellipse is symmetric on both centerlines
- The long axis points the way the pipe tilts
- A card template fits before any metal gets cut
How to apply it
- Measure the pipe's outside diameter and the angle between the pipe and the plate surface.
- Work out the long axis: OD ÷ sin(angle), with the calculator in degree mode.
- Draw two perpendicular centerlines on the plate, the long one running the way the pipe leans.
- On a straight strip, measure from one end and mark half the OD and half the long axis. For the 4 1/2 in pipe: 2 1/4 in and 3 1/4 in.
- Lay the strip so the half-long-axis mark sits on the short centerline and the half-OD mark sits on the long centerline. Mark at the end of the strip.
- Slide the strip around, keeping both marks on their lines, and dot the end every inch or so. Join the dots.
- Cut, deburr, and slide the plate over the pipe.
Test it on your setup
- Card first: cut the ellipse out of cardboard and drop it over the pipe at the real angle before you cut metal.
- Check the math: 90° should give a circle, and 30° a long axis exactly twice the OD.
- Check the trammel: with the strip lying along the long centerline, its end should land on the tip of the long axis; along the short centerline, on the tip of the short axis.
Exceptions & tradeoffs
The formula gives the cut line at the plate surface with zero clearance. For a slip fit or room for sealant, add your clearance to the diameter before you run the math.
On thick plate the hole on the far face shifts along the long axis by about the thickness ÷ tan(angle). On 1/4 in (6.4 mm) plate at 44°, that's about 1/4 in (6.6 mm). Bevel the hole or open it up in that direction.
Mind you, if you measured the angle from the plate's normal (straight up off the plate) instead of from its surface, use cos instead of sin. Same answer, other side of the triangle.
Common mistakes
- Measuring the angle from vertical instead of from the plateUse the angle between pipe and plate surface, or swap sin for cos
- Running the math on nominal pipe sizeMeasure the outside diameter; 4 in steel pipe is 4 1/2 in OD
- Calculator left in radiansSet degree mode — sin(44) in radians is about 0.017 and turns a 6 1/2 in hole into a 22 ft one
- Turning the long axis across the leanIt runs in the direction the pipe tilts
Frequently asked questions
- What shape is a hole for a pipe at an angle?An ellipse. Its short axis equals the pipe's outside diameter, and its long axis equals that diameter divided by the sine of the angle between the pipe and the plate.
- How do you calculate the long axis of the ellipse?Divide the pipe OD by the sine of the angle between pipe and plate. A 4 1/2 in OD pipe at 44° gives 4.5 ÷ 0.695 = 6.48 in (165 mm).
- How do you draw an ellipse with a strip of paper?Draw the two centerlines. From one end of a strip, mark half the short axis and half the long axis. Keep the half-long mark on the short centerline and the half-short mark on the long centerline, slide the strip around, and dot its end. Join the dots.
- What is an escutcheon plate?A cover plate that slides over a pipe where it passes through a wall, floor, roof or panel, hiding the rough hole. When the pipe passes through at an angle, the plate's hole has to be an ellipse.
The long-axis formula 1 ÷ sin(angle) × diameter and drawing the ellipse with a marked strip; credits the method to W.V. Graves, The Pipe Fabricator's Blue Book — How to Lay Out an Ellipse for an Escutcheon Plate (pipe fitter blue book method) ↗ at 0:30–1:06.
Summarized and independently edited by Start Here from Adam Fleisch's Facebook clip, read off the frames, burned-in captions and caption text with no audio. The formula card and the strip marked "1/2 diameter = 2 1/4, 1/2 answer = 3 1/4" are his, and he credits the method to W.V. Graves' The Pipe Fabricator's Blue Book. His phone screen only shows the entry part-typed, so the 4 1/2 in pipe size is worked back from that strip (a 2 1/4 in half-diameter is 4 1/2 in OD, which is 4 in steel pipe). I checked it against his numbers: 4.5 ÷ sin 44° = 6.48 in, half of that rounds to his 3 1/4. The sampled frames don't make clear which tick rides which line, so the trammel step is the standard paper-strip arrangement, checked against the geometry. The clearance, thick-plate offset, degree-mode and test notes are mine.