The pipe offset formula

A simple pipe offset is a right triangle, so two lines of trigonometry give you everything. Here they are, where they come from, and how to run them backwards.

The three sides

Offset: the step between the two pipe runs. This is the side you measure.
Run: how far the line advances along its original direction.
Travel: the diagonal, the hypotenuse of the triangle.

The fitting angle is the angle between the travel and the original line, the angle at the corner where the run meets the travel.

Travel and run from the offset

travel = offset ÷ sin(angle)
run = offset ÷ tan(angle)

The offset is the side opposite the angle. The sine is opposite over hypotenuse, so dividing the offset by it gives the hypotenuse. The tangent is opposite over adjacent, so dividing by it gives the run. As a check, the three sides always satisfy travel² = offset² + run².

For a 10 inch offset through 45° fittings: travel = 10 ÷ sin 45° = 14.1421 inches, which the calculator prints as 14-1/8″, and run = 10 ÷ tan 45° = 10.0000 inches, 10″.

Going backwards

If you know the travel and the angle instead:

offset = travel × sin(angle)
run = travel × cos(angle)

Rolling offset

When the pipe has to move sideways and up or down at once, the two moves combine into one. In the app, the vertical move is the set and the sideways move is the roll. They form a right triangle of their own, and its hypotenuse is the offset you then use above:

true offset = √(set² + roll²), then travel = true offset ÷ sin(angle) and run = true offset ÷ tan(angle).

A set of 15 and a roll of 8 give a true offset of 17″; through 45° fittings the travel is 24-1/16″ and the run is 17″. The app’s Rolling Offset tab does this for you, and there is a free rolling offset calculator on the Pipe Offset Calculator page.

Two limits worth knowing

At 90° the sine is 1, so the travel equals the offset, and the run is 0. The calculator shows 0 for any angle of 89.99° or more.
The calculator rounds each result to the nearest 1/16 inch, like the app. The decimal value is shown beneath it, in inches.

Try it

Put your numbers into the pipe offset calculator, or read the multiplier chart to skip the trig: each angle’s sine and tangent, already divided out.

How this was checked

The numbers on this page come from the same formulas as the Pipe Offset Calculator iPhone app, and an automated test compares them with the app’s own code on a grid of inputs (last run October 21, 2026). This is trigonometry, not a code or standards reference, and it does not subtract fitting take-outs. If something here is wrong, tell us at a@noshu.net.