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Pipe Saddle Coping

Calculate the exact peak-to-valley cut depth for 90-degree pipe saddles (fishmouth cuts). Essential for pipe fabricators and welders to ensure a perfect fit.

Main Header OD

Branch Pipe OD

Laying Out a Saddle Cut

A 90-degree "fishmouth" saddle requires removing material from the end of the branch pipe so it fits perfectly against the radius of the header.

Cut Depth: This is the peak-to-valley measurement. Mark a line around the end of your pipe. At 0° and 180°, you measure down exactly this depth and scribe your curve.
Perfect Fit: For a perfect fit, you must use the **Outside Diameter (OD)** of the pipes, not the nominal size (e.g., 2" pipe is actually 2.375" OD).
Beveling: Remember that even with a perfect coping cut, you still need to grind a bevel for full penetration welds on heavier wall pipe.

Max Cut Depth

7/8"

0.8814" Decimal

Branch Stats

14.137"

Circumference (C)

Layout Marks

0° Mark:Depth

90° Mark:Full Length

180° Mark:Depth

270° Mark:Full Length

For estimation purposes only. Always consult a licensed professional before beginning work. Full Trade Safety Notice →

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What is Pipe Saddle Cuts: The Geometry of Branch-to-Header Joints?

In pipe fabrication, a 'saddle cut' (or 'fishmouth' or 'cope') is the curved profile cut into the end of a branch pipe so it seats perfectly against the curved surface of a larger header pipe at 90°. The cut depth varies around the branch circumference — deepest at the sides, zero at the top and bottom.

Mathematical Foundation

Fishmouth Cut Depth (90° Saddle)

Depth = R - \sqrt{R^2 - r^2}

R

= Radius of the header (main) pipe = OD / 2

r

= Radius of the branch pipe = OD / 2

Depth

= Maximum cut depth at the 0° and 180° points of the branch

Laws & Principles

Always Use OD, Not Nominal: A '2-inch' pipe is actually 2.375 inches OD. A '4-inch' pipe is 4.500 inches OD. The formula uses actual OD/2 for the radii. Using nominal pipe size produces incorrect cut depths.
Branch ≤ Header: The branch pipe OD cannot exceed the header pipe OD. If it does, the saddle formula produces an imaginary number (negative under the square root). Use a reducing tee or fabricated transition instead.
Layout Points: The calculated depth applies at the 0° and 180° points (sides of the branch). The 90° and 270° points (top/bottom) sit at full pipe length — zero material is removed there.
Equal-Size Intersection: When branch OD equals header OD, the cut depth equals the header radius — you remove a full half-circle.

Step-by-Step Example Walkthrough

" Joining a 4-inch Sch 40 branch (4.500" OD) to a 6-inch Sch 40 header (6.625" OD). "

1. Header radius: R = 6.625 / 2 = 3.3125 inches.
2. Branch radius: r = 4.500 / 2 = 2.250 inches.
3. R² = 10.972, r² = 5.0625.
4. R² - r² = 5.9095.
5. √5.9095 = 2.431 inches.
6. Depth = 3.3125 - 2.431 = 0.882 inches.

Final Result: The fishmouth cut depth is 0.882 inches (approximately 7/8 inch) at the deepest point.

Quick Answer: How Deep Is a Pipe Saddle Cut?

Use the formula Depth = R - √(R² - r²), where R is the header pipe radius and r is the branch pipe radius. For example, a 4-inch branch on a 6-inch header: Depth = 3.3125 - √(10.972 - 5.0625) = 0.882 inches. This depth is measured at the deepest point of the fishmouth (0° and 180° positions). The calculator above does this instantly for any pipe combination and outputs the profile you need to mark on the branch.

Common Saddle Cut Depths (90° Branch, Schedule 40)

Branch Pipe	Header Pipe	Cut Depth	Fraction
2" (2.375" OD)	4" (4.500" OD)	0.367"	~3/8"
2" (2.375" OD)	6" (6.625" OD)	0.219"	~7/32"
4" (4.500" OD)	6" (6.625" OD)	0.882"	~7/8"
4" (4.500" OD)	8" (8.625" OD)	0.626"	~5/8"
6" (6.625" OD)	8" (8.625" OD)	1.576"	~1-9/16"
6" (6.625" OD)	12" (12.75" OD)	0.927"	~15/16"

Cut depth increases dramatically as the branch-to-header size ratio approaches 1:1. A 6-inch branch on an 8-inch header cuts nearly 1.6 inches deep — far more than most fabricators expect without calculating first.

Saddle Cut Failures

The Nominal Size Mistake

A pipe fitter calculates the saddle cut for a 4-inch branch on a 6-inch header using nominal sizes: R = 3.0, r = 2.0. Depth = 3.0 - √(9 - 4) = 3.0 - 2.236 = 0.764 inches. However, the actual ODs are 4.500" and 6.625", giving R = 3.3125, r = 2.250, and Depth = 0.882 inches. The 0.764" cut is 0.118 inches too shallow — the branch won't seat against the header surface. There's a visible gap on both sides that must be filled with excess weld metal, weakening the joint and failing visual inspection. The calculator uses OD by default to prevent this.

The Template Method

An experienced pipe shop wraps the branch pipe with flexible cardboard, marks 8 equally-spaced points around the circumference, transfers the calculated depth at each point using the full saddle equation (not just the peak depth), and connects the dots to create a saddle template. The template is taped to the pipe and cut with a plasma torch or band saw. Using the calculator's peak depth plus intermediate points at 22.5° intervals produces a template that fits on the first try with less than 1/16" gap — well within weld fill tolerance.

Pro Tips for Saddle Cuts

Do This

✓Always use actual OD from a reference table or micrometer, not nominal pipe size. Nominal pipe sizes are trade names, not dimensions. "2-inch pipe" is 2.375 inches OD. "6-inch pipe" is 6.625 inches OD. Enter the actual OD into the calculator for precise results.
✓Cut slightly shallow and grind to fit. It is always easier to remove a small amount of material with a grinder than to add it. Cut the saddle 1/16 inch shallow, test-fit on the header, then grind the high spots until the branch mates flush. This is standard practice in pressure pipe fabrication.

Avoid This

✗Don't eyeball the saddle profile on large-diameter branch connections. When the branch-to-header ratio exceeds 0.7, the saddle depth is substantial (1+ inches). Eyeballing produces visible gaps that require excessive weld buildup, create stress concentrations, and fail inspection. Always calculate and template.
✗Don't forget that this formula is for 90° branches only. Angled branches (45°, 60°) produce asymmetric saddle profiles that require different math. A 45° branch has an elliptical hole in the header, not a circular one — the resulting cope is longer on one side. This calculator is specifically for perpendicular (90°) intersections.

Frequently Asked Questions

What happens when the branch and header are the same size?

When R = r, the formula gives Depth = R - √(R² - R²) = R - 0 = R. The cut depth equals the full radius of the pipe. You are cutting a complete half-circle out of the branch end. This creates the deepest possible fishmouth for a given pipe size. In practice, equal-size branch connections are usually avoided because the resulting saddle joint is extremely difficult to weld (no flat area at the toes).

How do I mark the saddle profile on the pipe?

Wrap the pipe end with flexible material (cardboard, thin sheet metal, or coping wrap). Mark the 0° point (deepest cut) and the 90° point (no cut). Divide the quadrant into 4 equal segments (22.5° increments). Calculate the depth at each angle using the full parametric formula — not just the peak depth. Connect the dots with a smooth curve. Cut 1/16" outside the line and grind to fit. Professional shops use pipe coping software that outputs a flat template pattern you wrap around the pipe.

Can I use this for tube steel (square/rectangular)?

No. This formula is specifically for round-to-round pipe intersections based on circular geometry. Square and rectangular tube connections require straight mitre cuts with compound angles calculated from the tube dimensions and connection angle. For round branch to square header (or vice versa), the profile becomes a hybrid that cannot be solved with this formula. Use dedicated tube notching calculators for non-circular profiles.

Why is my saddle cut not perfectly fitting the header?

Three common causes: 1) Using nominal pipe size instead of actual OD — this is the number one mistake. 2) Pipe out-of-round — many pipes are slightly oval, especially after transit. Measure OD at coping point with calipers. 3) Only using the peak depth without plotting intermediate points — the full saddle curve is a sinusoidal profile, not a simple arc. You need at least 8 plotted points (every 22.5°) for an accurate template.