Tube Bend Calculator
Twelve bend calculations for instrument techs, pipefitters, and conduit workers. Offset, rolling offset, saddle bends, arc length, gain, back to zero, and more — with fractional output for any denomination.
Inch inputs accept decimals 6.5 or fractions 6-5/8 · 5/8 · 6 5/8
How tube bend math works
Every tube bend calculation reduces to the same three ingredients: an angle, a radius, and a measurement of where you are in space. The formulas change depending on what you know and what you're solving for — which is why having all twelve modes in one place matters.
SAG (Setback · Advance · Gain)
One combined mode that returns the three numbers a single bend needs from one radius + angle. Setback is the tangent distance from the bend's tangent point to the corner (CLR × tan of half the angle). Advance is the arc the centerline actually travels (CLR × angle × π ÷ 180). Gain is what the bend saves versus a square corner — twice the setback minus the advance. Because all three come from a single input, you can lay out a multi-bend tube without tracking accumulated gain by hand.
Offset & Bend Loss
A two-bend offset steps around an obstacle while keeping the tube parallel. You need rise, bend angle, and travel — any two determine the third. Bend loss is subtracted from your layout to account for the arc consuming more length than a straight corner would. On a 45° offset with a 6" rise, loss is about 2.5".
Rolling Offset
Moves the tube in two directions at once — vertical and horizontal — with a single pair of bends. The key output is the roll angle: how far you rotate the tube around its axis before bending. Set it correctly and both offsets resolve simultaneously. The true offset drives the travel calculation.
3-Point Saddle
Steps over a round obstacle like a pipe or conduit. The center bend is exactly double the two outside bends. Spread is the distance from the center mark to each side mark. A 45° side angle is common — it works with most hand benders without exceeding bend capacity.
4-Point Saddle
Steps over a rectangular obstacle like a beam, box, or duct. Four equal bends create a flat-topped bridge. The leg travel is the diagonal of each outside section; the flat top spans the obstacle width exactly.
Arc Length
The distance along the tube's centerline through the bend — also the stop point on the bender scale. This is what you read off the bender when making a precise stop. Not the straight-line distance; the actual path the centerline travels through the arc.
Gain
The difference between the tangent projection through a corner and the shorter arc. On a 90° bend at 1.5" CLR, gain is ~0.43". On multi-bend pieces, accumulated gain affects where the far end lands — six 90° bends at 1.5" CLR adds up to about 2.6" if you don't account for it.
Back to Zero (B2Z)
The distance from your next bend mark back to the bender's zero reference. Knowing B2Z lets you position the tube correctly for each successive mark on a multi-bend piece without remeasuring from a new datum each time.
Equal Spread
The mark spacing for a bank of parallel tubes making identical offsets. Get it right and all tubes come out parallel and dressed. Get it wrong and the run looks like a staircase. Critical on instrument tube bundles and conduit banks.
Reverse Bend
A reverse bend changes direction opposite to the previous bend — used when a run needs to jog back toward its original centerline. Enter your offset rise and angle; the calculator gives you travel and loss so your marks land correctly on both bends.
Sloped Tubing
Calculates the bend angle and total rise for any run with a required minimum slope — drain lines, instrument sample lines, or any tube that must maintain a grade. Enter slope in inches per foot (1/4"/ft is typical for instrument drains) and run length.
Figure Degree
Calculates the sine, cosine, and tangent of any bend angle — the raw trig values that drive every other formula on this page. Useful when you're working a custom angle that isn't in your head and need to verify a multiplier before committing marks to tube.
Finding your bend radius on a large bender
Most of these calculations — gain, arc length, back to zero, reverse bend, and SAG — need the centerline radius (CLR) of the bend. On hand benders the radius is fixed and usually stamped on the shoe. On larger rotary-draw and hydraulic benders you often have to figure out the die's radius yourself. Three reliable ways:
1. Read the die
Most forming dies and shoes are stamped with the nominal tube size and frequently the CLR itself. The manufacturer's marking is the most reliable number you'll get — check there first, and if it's marked, use it.
2. Measure the die groove
Measure from the die's center (the pivot) straight out to the bottom of the groove, then add half the tube's outside diameter:
The groove bottom rides the inside of the bend, so the tube's centerline sits half a diameter farther out. If it's easier to measure all the way across the die, take the diameter to the groove bottom, halve it, then add ½ OD.
3. Back it out of a test bend
If the die isn't marked and you can't get at the groove, bend a scrap piece and measure it.
Quick 90° trick: on a 90° bend the setback equals the radius. Setback = CLR × tan(½ × angle), and tan 45° = 1 — so the distance from where the bend starts (the tangent mark) to the corner where the two leg centerlines cross is your CLR. Bend a 90°, measure it, done.
Any-angle (sagitta) method: lay a straightedge across the bend like a chord. Measure the chord length c and the height h from the middle of the chord up to the tube, then:
Measured against the outside of the tube that gives the outside radius — subtract ½ OD for the centerline.
Once you've pinned down the CLR for a die, paint or scribe it right on the die — it never changes, and you'll never have to measure it again.