45 degree pipe offset
For a 45° offset, the travel is the offset times 1.4142 and the run is equal to the offset. That is all of it; the rest of this page is why, and a calculator.
Fitting angle
Travel · diagonal pipe length
14-1/8″
14.14″ · 1′ 2-1/8″
Run · advance along the line
10″
10.00″
travel = offset ÷ sin(angle) · run = offset ÷ tan(angle) · rounded to the nearest 1/16″ · the same engine as the app.
Where 1.4142 comes from
With 45° fittings the triangle has two 45° corners, so the offset and the run are the same length. The travel is the diagonal of a square of that side, which is the side times the square root of 2. The square root of 2 is 1.41421356…, and 1.4142 is that rounded to four places. You get the same number from the formula: 1 ÷ sin 45° = 1.4142.
So the run needs no arithmetic at all: run = offset. The travel is offset × 1.4142.
Three sizes
| Offset | Travel (× 1.4142) | Run |
|---|---|---|
| 6″ | 8-1/2″ (8.4853″) | 6″ |
| 10″ | 14-1/8″ (14.1421″, 1′ 2-1/8″) | 10″ |
| 18″ | 25-7/16″ (25.4558″, 2′ 1-7/16″) | 18″ |
Travel is rounded to the nearest 1/16 inch. The decimal beside it is the value to four places.
Other angles
The multiplier chart has the same two numbers for 11.25°, 22.5°, 30°, 60° and 90°, and the calculator takes any angle from 1° to 90°.
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 ). 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.