What is the formula for arc length on a pipe?

Arc length = outside diameter × π × angle ÷ 360. The circumference is diameter × π, and an angle takes the same fraction of it as it does of 360°. Per degree, that's the OD × 0.00873.

How far around a pipe is 90 degrees?

A quarter of the circumference, which is OD × π ÷ 4. On a 2 in (50.8 mm) OD tube that's 1.571 in (39.9 mm). On 2 in nominal pipe, which is 2.375 in (60.3 mm) OD, it's 1.865 in (47.4 mm).

Should I use the inside or outside diameter?

The outside diameter, because you're marking the outside surface. Measure it with calipers, since nominal pipe size and actual OD are different numbers.

How do you draw a straight line along a pipe?

Lay a length of angle iron on the pipe with the V facing down. It settles parallel to the pipe's axis, and its edge gives you a straight line to draw along. A door jamb or a flat bar held against the pipe also works for short runs.

Cutting, Not HackingMetal & PipeMark an angle on a pipe

How do you mark an exact angle around a pipe?

The drawing says the hole goes 25° around from the seam. A protractor won't sit on a round surface, so most people eyeball it, drill, and find out at assembly. Adam Fleisch's fix is to stop thinking in degrees at all. An angle around a pipe is just a distance along the outside of it. And a distance is something a ruler can read.

⚡ Rule of thumb

Turn the angle into a distance around the pipe: arc length = outside diameter × π × degrees ÷ 360. Mark that distance on a thin paper strip, wrap the strip around the pipe from a 0° reference line, and transfer the mark. On a 2 in (50.8 mm) OD pipe, 25° is 0.436 in (11.1 mm).

Starting point

Arc = OD × π × degrees ÷ 360 · per degree = OD × 0.00873

Measured

Along the outside surface from the 0° line, on a strip wrapped tight, never straight across the curve

Confidence

Widely accepted

▶ Source video — Need to mark an exact angle on a pipe? — Adam Fleischwatch on Facebook ↗

Applies to

Process: Pipe fitting, tube fabrication, welding layout, drilling holes at set angles around a tube
Materials: Round pipe and tube, any size
Setup: Calipers or tape for the OD, calculator, rule, thin paper strip, marker or soapstone, a length of angle iron
Measure: Outside diameter (OD), not the nominal pipe size

Why it matters

A hole or branch that's a few degrees off looks fine on the bench. Then the mating part goes on, and the bolt won't drop, or the brace runs crooked for its whole length.

The math is one line. The circumference is the diameter × π, and an angle is that same fraction of the trip round. 25° is 25/360 of the circumference. Once it's a length, it's a ruler measurement, and a ruler doesn't care how round the pipe is.

Worked through on a 2 in (50.8 mm) OD tube: 2 × 3.1416 = 6.283 in (159.6 mm) around. Divide by 360 and every degree is 0.01745 in (0.443 mm). Times 25 is 0.436 in (11.1 mm), just under 7/16 in.

The paper strip is what makes it work. Flat, you measure it. Wrapped, it carries the measurement round the curve for you.

What good looks like

The 0° reference line runs dead straight along the pipe
The mark sits at the calculated distance from it, measured round the surface
A strip marked at the full circumference meets itself exactly when wrapped
The finished hole or branch lines up with the mating part first try

How to apply it

Draw a straight 0° reference line along the pipe. Lay a length of angle iron on the pipe, V down, and it sits parallel to the axis and gives you a straight edge to draw against.
Measure the outside diameter with calipers.
Work out the distance: OD × 3.1416 × your angle ÷ 360.
On a strip of thin paper, draw a start line, then measure your distance from it and mark it.
Wrap the strip tight around the pipe with the start line on the 0° line, and transfer the mark onto the pipe.
Pull the new line along the pipe with the angle iron and work from it.

Test it on your setup

Full-wrap check: wrap the strip once round the pipe and mark where it overlaps. That length should match OD × π. If it doesn't, re-measure the OD. Or skip the OD entirely and work from the wrapped length: arc = wrap length × degrees ÷ 360.
Opposites check: a 180° mark should sit directly across from 0°, and 90° and 270° should sit across from each other. On a 2 in (50.8 mm) OD tube, 90° is 1.571 in (39.9 mm) round from the line.

Exceptions & tradeoffs

Nominal pipe size is not the OD. 2 in nominal steel pipe is 2.375 in (60.3 mm) outside, and 25° on that is 0.518 in (13.2 mm), not 0.436 in. Measure, don't assume.

Thick strips read a little short once wrapped, because they sit outside the surface. Printer paper on a 2 in pipe is about 0.2% off, which is nothing. A 0.020 in (0.5 mm) metal strip is about 1%, and the error grows as the tube gets smaller. Thin paper, or use the full-wrap length.

For lots of even divisions (4, 6, 8, 12) don't calculate each one. Mark the full wrap on the strip, fold or divide it flat, then wrap it back on.

Common mistakes

Plugging the nominal pipe size into the formulaCaliper the OD, or use the wrapped length instead
Measuring the arc straight across the curve with a ruleMeasure flat on the strip, then wrap the strip to the surface
Measuring each angle from the last markMeasure every angle from the 0° line so errors don't stack up
No reference line, just a mark near the seamDraw the 0° line along the pipe first and measure everything from it

Frequently asked questions

How do you mark degrees on a pipe?Convert the angle to a distance: outside diameter × π × degrees ÷ 360. Measure that distance on a thin paper strip, wrap the strip around the pipe from a straight 0° line drawn along it, and mark the pipe at the strip mark.
What is the formula for arc length on a pipe?Arc length = outside diameter × π × angle ÷ 360. The circumference is diameter × π, and an angle takes the same fraction of it as it does of 360°. Per degree, that's the OD × 0.00873.
How far around a pipe is 90 degrees?A quarter of the circumference, which is OD × π ÷ 4. On a 2 in (50.8 mm) OD tube that's 1.571 in (39.9 mm). On 2 in nominal pipe, which is 2.375 in (60.3 mm) OD, it's 1.865 in (47.4 mm).
Should I use the inside or outside diameter?The outside diameter, because you're marking the outside surface. Measure it with calipers, since nominal pipe size and actual OD are different numbers.
How do you draw a straight line along a pipe?Lay a length of angle iron on the pipe with the V facing down. It settles parallel to the pipe's axis, and its edge gives you a straight line to draw along. A door jamb or a flat bar held against the pipe also works for short runs.

Adam FleischSource & visual reference

The OD × π ÷ 360 × degrees conversion (stated in his caption) and wrapping a marked strip to transfer the angle onto the pipe — Need to mark an exact angle on a pipe? ↗ at 0:04–1:28.

Summarized and independently edited by Start Here from Adam Fleisch's Facebook reel: sampled frames and his caption, no audio. The formula and the paper-wrap transfer are his, spelled out in the caption. His pipe size wasn't readable on screen, so the worked examples (2 in OD, 2 in nominal, the 90° figures) are my own arithmetic, along with the angle-iron tip, the nominal-vs-OD warning, the strip-thickness note and the test steps.