Guide · Offsets

60 degree offset formula: travel, run, and cut length

Short answer

For a 60 degree offset, travel = offset × 1.155 and run = offset × 0.577. Then subtract the take-out of each fitting and the root gap at each butt weld to get the cut. A 10 inch offset has a travel of 11.547 inches and a run of only 5.774 inches. On 2 inch pipe with 90 LR elbows cut down to 60 and 1/8 inch gaps, the cut is 7 13/16.

Travel = offset × 1.155   (1 ÷ sin 60°)
Run    = offset × 0.577   (1 ÷ tan 60°)
Cut    = travel − 2 × take-out − 2 × gap

A 60 degree offset makes a steep jog: the angled piece is only a little longer than the offset, and the second fitting lands close to the first. That is the reason to choose 60s over 45s, when the line has no room to run along before it has to move over.

Why the 60 degree multipliers are 1.155 and 0.577

An offset with 60 degree fittings is a 30-60-90 triangle, half of an equilateral triangle. Its sides always stand in the ratio 1 : 1.732 : 2. The offset is opposite the 60 degree angle, so it is the 1.732 side; the travel is the long side, 2; and the run is the short side, 1.

Travel ÷ offset = 2 ÷ 1.732 = 1.1547, the travel multiplier.
Run ÷ offset = 1 ÷ 1.732 = 0.5774, the run multiplier.

The same numbers come out of the general pipe offset formula: sin 60° is 0.8660, and 1 ÷ 0.8660 = 1.155; tan 60° is 1.732, and 1 ÷ 1.732 = 0.577.

Copper: travel, fitting center to fitting center. Green: the piece you cut, shorter by a take-out and a gap at each end. Dots: fitting centers.

How to calculate a 60 degree offset

Measure the offset center to center
Square to the two runs, centerline to centerline.
Multiply by 1.155 for the travel
10 × 1.1547 = 11.547 inches, fitting center to fitting center.
Multiply by 0.577 for the run
10 × 0.5774 = 5.774 inches. Mark the second fitting that far along the line from the first.
Subtract two take-outs
Use your fittings' center-to-end. A butt-weld 90 cut down to 60 takes out its center-to-end × 0.577 (tan 30°); see cutting down a 90.
Subtract two gaps, then round once
For butt welds, two root gaps. Round the final decimal to the nearest 1/16.

60 degree offset chart

Travel and run for common offsets with 60 degree fittings, before take-outs and gaps:

60 degree offsets: travel and run center to center (travel × 1.1547, run × 0.5774), marked to the nearest 1/16 inch, before take-outs and gaps
Offset	Travel, decimal	Travel, mark	Run, decimal	Run, mark
4"	4.619	4 5/8"	2.309	2 5/16"
6"	6.928	6 15/16"	3.464	3 7/16"
8"	9.238	9 1/4"	4.619	4 5/8"
10"	11.547	11 9/16"	5.774	5 3/4"
12"	13.856	13 7/8"	6.928	6 15/16"
16"	18.475	18 1/2"	9.238	9 1/4"
18"	20.785	20 13/16"	10.392	10 3/8"
20"	23.094	23 1/8"	11.547	11 9/16"
24"	27.713	27 11/16"	13.856	13 7/8"
30"	34.641	34 5/8"	17.321	17 5/16"
36"	41.569	41 9/16"	20.785	20 13/16"
48"	55.426	55 7/16"	27.713	27 11/16"

Worked examples on 2, 4, and 6 inch pipe

60 degree offsets with 90 LR butt-weld elbows cut down to 60 (take-out = 90 LR center-to-end × tan 30°) and a 1/8 inch gap per joint
Pipe	Offset	Travel	Run	Take-outs	Gaps	Cut
2 in	10"	11.547	5.774	2 × 1.732	2 × 1/8	7 13/16"
4 in	18"	20.785	10.392	2 × 3.464	2 × 1/8	13 5/8"
6 in	24"	27.713	13.856	2 × 5.196	2 × 1/8	17 1/16"

Line by line, the 2 inch example: 10 × 1.1547 = 11.547. A 2 inch 90 LR has a 3 inch center-to-end, and cut to 60 it takes out 3 × 0.5774 = 1.732. Take off 2 × 1.732 = 3.464 and 2 × 0.125 = 0.25, leaving 7.833, which marks as 7 13/16.

In plumbing, a 60 is a 1/6 bend, and the joint has no root gap. If your 60s allow 1 1/4 inch each from center to the socket shoulder (measure yours), a 10 inch offset cuts at 11.547 − 2.5 = 9.047, marked 9 1/16.

60 degree offsets compared with 45 and 30

The same 12 inch offset made with three fitting angles, center to center
Fitting angle	Travel ×	Run ×	Travel, 12" offset	Run, 12" offset
60°	1.155	0.577	13 7/8"	6 15/16"
45°	1.414	1.000	17"	12"
30°	2.000	1.732	24"	20 13/16"

The 60 uses the least pipe and the least room along the line. The trade-off is a sharper change of direction at each fitting. For 45s, the 1.414 rule covers the details; for 22.5 and 11.25, see the offset multiplier chart.

A 60 degree rolling offset

For an offset that moves both up and over, find the true offset first, √(rise² + roll²), then use the 60 degree multipliers on it. An 8 inch rise and a 16 inch roll give a true offset of 17.889; the travel is 17.889 × 1.1547 = 20.656 (20 5/8) and the run 17.889 × 0.5774 = 10.328 (10 5/16). The rolling offset formula guide explains how to measure rise and roll.

Common mistakes

Swapping 30 and 60. At 30 degrees the travel is 2.000 × and the run 1.732 ×. At 60 it is 1.155 × and 0.577 ×. Using the 30 degree run on a 60 offset puts the second fitting three times too far away.
Using a conduit chart's 1.2. Bender charts round 1.155 up to 1.2. On a 20 inch pipe offset that makes the travel about 29/32 inch long.
Using a 45's take-out. A fitting cut or made for 60 degrees has its own center-to-end. For a 90 cut to 60 it is 0.577 of the 90's.
Cutting the travel. The travel is center to center; the pipe is shorter by both take-outs and both gaps.
Measuring the angle from the wrong side. The fitting angle is between the travel and the run. A 60 degree offset is the steep one, with a short run.

Questions about 60 degree offsets

What is the formula for a 60 degree offset?

Travel = offset × 1.155 and run = offset × 0.577. The first number is 1 ÷ sin 60°, the second is 1 ÷ tan 60°. A 10 inch offset with 60s has a travel of 11.547 inches and a run of 5.774 inches, center to center.

Why is the 60 degree offset multiplier 1.155?

A 60 degree offset is a 30-60-90 triangle, whose sides are always in the ratio 1 : 1.732 : 2. The offset is the 1.732 side and the travel is the 2 side, so the travel is 2 ÷ 1.732 = 1.155 times the offset. The run is the 1 side, so it is 1 ÷ 1.732 = 0.577 times the offset.

How much run does a 60 degree offset take?

A little over half the offset: run = offset × 0.577. A 10 inch offset with 60s moves only 5 3/4 inches along the line, against 10 inches with 45s and 24 1/8 inches with 22.5s. That short run is the reason to pick 60s.

What is the difference between a 30 and a 60 degree offset?

The multipliers trade places. At 30 degrees the travel is 2.000 × the offset and the run 1.732 ×. At 60 degrees the travel is 1.155 × and the run 0.577 ×. A 12 inch offset needs 20 13/16 inches of run with 30s but only 6 15/16 with 60s. Mixing up the two is the most common 60 degree mistake.

Is a 60 degree fitting the same as a 1/6 bend?

Yes. In drain, waste, and vent fittings the bends are named by the fraction of a full circle they turn: a 1/4 bend is 90 degrees, a 1/6 bend is 60, a 1/8 bend is 45, and a 1/16 bend is 22.5. A 1/6 bend offset uses the 1.155 and 0.577 multipliers. Whether a 60 is allowed in a given drain line is a code question for your area.

What take-out do I use for a 60 degree offset?

The center-to-end of the fittings you have, from the maker's chart. For a butt-weld 90 cut down to 60 degrees, the take-out is the 90's center-to-end × tan 30°, or 0.577 of it: a 2 inch 90 LR (3 inch center-to-end) cut to 60 takes out 1.732 inches, marked 1 3/4. See cutting down a 90.

Why do conduit charts say 1.2 for 60 degree bends?

Bender charts round 1.155 up to 1.2 because a one-piece conduit bend only needs a mark on the tube. For a pipe offset made with fittings, keep 1.155: on a 20 inch offset, 1.2 gives a travel of 24 inches against the true 23.094, about 29/32 inch long.

Can I use 60s in a rolling offset?

Yes. Find the true offset first, the square root of rise² + roll², then apply the 60 degree multipliers to it. An 8 inch rise and a 16 inch roll give a true offset of 17.889, a travel of 20.656 (20 5/8), and a run of 10.328 (10 5/16).

Related guides

Check one now

Pick 60 in the pipe offset calculator, type your offset, and it shows the travel, the run, the take-outs of 90s cut to 60, and the cut. In the FitUp app, 60 degree offsets are part of Pro; 45 degree offsets are free with no limit.

Verify measurements before cutting.