Centerline bending radius vs. multipliers

What the multiplier method assumes

The multiplier method treats an offset as a right triangle with sharp corners: the conduit runs straight, turns instantly, runs on the diagonal, and turns instantly again. That's what makes the math so simple. Distance between bends is just the offset depth × 1 ÷ sin(angle).

But conduit can't turn a sharp corner. It wraps around the bender shoe and follows a curve.

What centerline radius is

The centerline radius (CLR) is the radius of that curve, measured to the center of the conduit. The bender shoe sets it, so it's the same every time you use that bender, and it gets bigger as the conduit gets bigger.

Typical radii grow quickly with conduit size. These are the NEC minimum radii for one-shot and full-shoe benders (NEC Chapter 9, Table 2). Your bender's radius may be larger, so check its specs.

The math with a real radius

With a radius, each bend is an arc instead of a corner. Each arc rises R × (1 − cos θ) on its own, so the straight diagonal between the arcs only has to cover what's left:

straight section = (offset depth − 2R(1 − cos θ)) ÷ sin θ

Your bend marks sit at the center of each arc. The distance between them, measured along the conduit, is half of each arc plus the straight section:

distance between marks = straight section + R × θ

(Here θ is in radians: degrees × π ÷ 180.)

Put the two methods side by side and most of the terms cancel. What's left is surprisingly simple:

multiplier spacing − true spacing = R × (2 tan(θ/2) − θ)

Two things jump out of that formula:

• The offset depth isn't in it. A 4″ offset and a 40″ offset have the same error. Only the radius and the angle matter.
• The error grows with the radius and grows fast with the angle. Double the radius and the error doubles. Double the angle and it grows about eight times, roughly with the cube of the angle.

How far off is the multiplier spacing?

How much longer the multiplier makes the distance between marks than the true spacing, using the radii above:

Shrink is off even more

Because the curve cuts inside the corner, the real conduit path is shorter than the sharp-corner path, so the true shrink is less than the multiplier shrink. This error doesn't depend on the offset depth either, and it's about twice the spacing error. How much the multiplier overstates shrink:

Worked examples

1. Small conduit, shallow angle: the multiplier is fine. A 10″ offset at 22.5° with a 1/2″ EMT bender (4 1/2″ radius). Multiplier: marks 26 1/8″ apart, 2″ of shrink. With the radius: 26 1/8″ apart, 1 15/16″ of shrink. The difference is 1/16″ of shrink, well within normal bending tolerance.

2. Bigger conduit, 45°: now it shows. A 12″ offset at 45° in 2″ conduit (9 1/2″ radius). Multiplier: marks 17″ apart, 5″ of shrink. With the radius: 16 9/16″ apart, 4 1/8″ of shrink. That's 7/16″ of spacing error and about 7/8″ of shrink error. Enough to miss a box.

3. Large conduit, steep angle: the multiplier breaks down. A 20″ offset at 60° in 4″ conduit (16″ radius). Multiplier: marks 23 1/8″ apart, 11 9/16″ of shrink. With the radius: 21 3/8″ apart, 8 1/8″ of shrink. The multiplier is off by 1 3/4″ on spacing and almost 3 1/2″ on shrink.

Some offsets are too shallow for the angle

The two arcs alone rise 2R(1 − cos θ). If your offset is shallower than that, there's no room for a straight section and the offset can't be made at that angle. The multiplier method will still give you numbers, but they won't work. For example, 4″ conduit with a 16″ radius needs at least about 9 3/8″ of offset at 45°, and 16″ at 60°. Use a shallower angle instead.

Compare the two methods

Pick a conduit size (or enter your bender's radius), an angle and an offset depth.

So when should you use which?

• 1/2″ to 1″ EMT at 30° or less: the multiplier method is within about 1/8″. Use it.
• 45° on any size, or 30° on 1 1/4″ and larger: the shrink error runs from 3/16″ to over an inch. Account for the radius.
• Large conduit at 60°: the multiplier can be off by inches. Always use the radius.

iBend Pipe calculates every bend using the centerline radius of your actual bender, from nearly 300 real benders, so you get the right marks at any size and angle.