Pipe Offset and Layout Math

A lead plumber's work is judged before the water goes on. Pipes that run straight, turn together, and clear every beam on the first try come from math done at the bench. A crew that cuts to fit burns hours and fittings. You already know how to measure a cut between two fittings. This level adds the angles: moving a pipe around an obstacle, turning several pipes together so they stay evenly spaced, and holding grade across a whole run. The math is a calculator and a short table, and it works on copper, plastic, and steel alike.

What You Will Be Able to Do

• Use the offset table to find travel and run for any common angle
• Deduct take-outs to get a true cut length
• Solve a rolling offset with two measurements
• Keep parallel pipes evenly spaced through a turn
• Lay out a run on grade from one reference point
• Check your layout, and someone else's, before anything is cut

Terms You Need

• Offset: How far the pipe has to move sideways or up, measured center to center between the two parallel runs. Some fitters call this the set.
• Travel: The length of the angled piece, center to center of the two fittings.
• Run: The distance the offset uses along the direction of the pipe.
• Take-out: How much of the center-to-center length the fitting uses up. It is the distance from the fitting's center to the point where the pipe stops inside it. Some fitters call it the fitting allowance.
• Reference line: One fixed line or point that every measurement starts from.

The Offset Table

Every offset is a right triangle. The offset is one side, the run is the other, and the travel is the long side. Choose your fitting angle, and these multipliers do the rest.

A 45-degree offset is the one you will use most. Its run equals its offset, so it is easy to lay out. Lower angles flow more smoothly and take up more room.

Worked example. A pipe must move over 14 inches to clear a column, using 45-degree fittings. The travel is 14 x 1.414, or 19.8 inches. The run is 14 x 1.000, or 14 inches. The offset uses 14 inches of length along the wall.

If the same 14-inch offset had to use 22-1/2 degree fittings, the travel would be 14 x 2.613, or 36.6 inches, and the run would be 14 x 2.414, or 33.8 inches. That is a gentler move, but it needs more than twice the wall length.

From Travel to Cut Length

Travel is a center-to-center number. Pipe does not reach the center of a fitting, so you have to take something off.

Cut length = center-to-center length, minus the take-out of each fitting.

Take-outs come from the maker's dimension sheet for that exact fitting and size. They differ between brands and between solder, press, and solvent fittings. Keep a sheet in the truck, or measure one fitting and write the number on a card.

Worked example. The travel is 19.8 inches, with a 45-degree fitting at each end. The sheet gives a take-out of 3/8 inch (0.375) for each fitting. 19.8 minus 0.75 gives 19.05 inches. To change the decimal to a fraction, multiply the part after the point by 16. 0.05 x 16 is 0.8, which rounds to 1/16. Cut the pipe 19-1/16 inches.

Pick one method at the start of the job and stay with it. If you measure end to end instead of center to center, you must not subtract the take-outs. Mixing the two methods is the most common cause of a piece that is short by exactly one fitting.

Rolling Offsets

A simple offset moves the pipe in one direction. A rolling offset moves it in two at once, such as up and over. You measure two things:

• Rise: The vertical move
• Spread: The horizontal move

Then find the true offset, which is the straight-line distance between the two centers.

True offset = the square root of (rise x rise, plus spread x spread).

After that, treat it as a simple offset.

Worked example. A pipe must rise 9 inches and move over 12 inches, using 45-degree fittings. 9 x 9 is 81, and 12 x 12 is 144. They add up to 225, and the square root of 225 is 15. The true offset is 15 inches. The travel is 15 x 1.414, or 21.2 inches. The run is 15 inches.

The angled piece is not level and not plumb, so fittings have to be rotated. Set both fittings with a level across the openings, or use a laser. Always set the fittings against the same reference. When the angle looks right but the far end misses, one fitting is usually rolled the wrong way.

A Quick Check

A 9 and 12 triangle is a 3-4-5 triangle times 3, so the long side is 15. You can use this on site. Measure 3 feet along one line, 4 feet along the other, and the diagonal should be 5 feet if the corner is square. Larger multiples, like 6-8-10, catch smaller errors.

Parallel Offsets

Pipes that run side by side look best, and hang most easily, when they stay evenly spaced through a turn. If you start each offset at the same point, they will squeeze together. Each pipe's starting point has to shift. The shift is called the stagger.

Stagger = spacing between pipes x the number in this table.

Worked example. Three pipes run on 8-inch centers and turn through a 45-degree offset. The stagger is 8 x 0.414, or 3.31 inches. The second pipe's fitting sits about 3-5/16 inches from the first one's. The third sits another 3-5/16 inches on, or 6-5/8 inches from the first. Which way you shift depends on which side is the inside of the turn. The inside pipe turns first.

Lay it out on the floor or wall at full size once. Put your tape on the marks. It takes five minutes and saves a row of cut pipe.

Holding Grade Across a Run

A drain must fall the whole way, without a dip. Do not hang a run by checking each hanger with a short level. Short-level errors add up, and small sags pass the bubble. Work out the height at each hanger from a reference point.

Worked example. A 2-inch branch runs 28 feet at 1/4 inch per foot, and starts at 110 inches above the floor. The total fall is 28 x 1/4, or 7 inches, so the far end sits at 103 inches. Hangers go every 4 feet, so each one sits 1 inch lower than the last.

Mark these with a laser set to a known height, and measure down from the beam. Check the floor first, because concrete floors are rarely flat. Use the laser line as your reference, not the floor.

An offset in a sloped drain still has to fall. Use the total horizontal distance the pipe covers for the fall, and check that neither end of the offset sits above where you planned. In tall buildings, codes add rules for offsets in drainage stacks, including limits on branch connections near them. Check your code before you offset a stack.

Planning the Route

Math does not help if the pipe is in the wrong place. Before you cut:

1. Set one reference. Use a laser, a chalk line, or a marked gridline. Measure everything from it. Chaining one measurement off the last adds up each small error.
2. Measure from finished surfaces. Know the wall and floor build-up, as you do for fixtures.
3. Gravity goes first. Drains cannot go uphill, so route them before any pressure pipe. Large pipe goes before small, because small pipe bends around things more easily.
4. Walk it with the other trades. Ducts, cable trays, and sprinkler mains compete for the same space. A coordination drawing beats an argument.
5. Plan for access. Valves, cleanouts, and unions need room to work.
6. Check structure. Follow the limits for drilling and notching, and never cut a truss or engineered joist without approval.

Building Spools

A spool is an assembled section of pipe made at a bench, then hung as one piece. Bench work is cleaner, safer, and faster than overhead work. It only pays off if the math is right.

• Draw the spool with center-to-center dimensions.
• List each cut length with take-outs already deducted.
• Mark each piece and give each spool a tag that matches the drawing.
• Leave a closure piece, a short pipe cut to fit on site, in long runs. It absorbs the small errors in the building.

PEX and Bends

Flexible pipe uses bend radius in place of fittings. The minimum cold bend is commonly 6 times the outside diameter, unless the maker says otherwise. 3/4-inch PEX has an outside diameter of 7/8 inch, so 6 x 7/8 gives a radius of about 5-1/4 inches. Allow that room on your layout. Long runs of PEX also grow when hot, so you do not cut flexible pipe to exact length the way you cut copper.

Checking the Work

A lead checks a cut list before a saw comes out. Look for these things:

• Is every number center to center, or end to end? Is it the same throughout?
• Are the take-outs for the actual fitting, from the correct sheet?
• Does the total fall work with the height of the connection at the end?
• Do the staggers go the right way?
• Are the units right? 19.05 inches is not 19 feet 5 inches.

A second person with a calculator catches more than a careful first person does.

Common Mistakes

Check Your Understanding

1. An apprentice hands you a cut list for a 45-degree offset that moves a line over 18 inches. The angled piece is listed at 25-7/16 inches, and the sheet shows a 1/2-inch take-out. Do you sign off on it?

No. 18 x 1.414 is about 25-7/16 inches, but that is center to center. Take off 1 inch for the two fittings, and the piece should be about 24-7/16 inches.

2. A vent has to clear a beam by going up 16 inches and over 12 inches in one move. A helper adds the two and works from 28 inches, using 45s. What should the figure be, and how far off is the helper's piece?

16 x 16 is 256, and 12 x 12 is 144. They add up to 400, whose square root is 20, so the true offset is 20 inches and the travel is 28.3 inches. The helper's 28 gives 39.6 inches, which is about 11 inches too long.

3. Two pipes are 10 inches apart, and turn through a 45-degree offset. How far do you shift the second one's fitting?

10 x 0.414 is about 4-1/8 inches.

4. A 3-inch drain falls at 1/8 inch per foot over 40 feet. It starts at 96 inches on your laser reference. Where does it end?

40 x 1/8 is 5 inches of fall. It ends at 91 inches.

Key Takeaways

• Travel is offset x the multiplier for the fitting angle.
• Cut length is center to center, minus take-outs from the real fitting sheet.
• For a rolling offset, find the true offset first.
• Parallel pipes need a stagger of spacing x the table value.
• Work grade from one reference, not from one hanger to the next.
• Check the cut list before you cut.