Centerline radius, gain and deduct

A bender doesn’t fold conduit at a point. It wraps it around a shoe, so every bend is an arc. The size of that arc, the centerline radius, sets the deduct, the gain and the spacing of every mark the calculator gives you. Bender Specs shows these numbers for the shoe you have selected.

The words

• Centerline radius (R): the radius of the bend measured to the center of the conduit, not its inside or outside. It changes with trade size and conduit type.
• Setback: from the start of a bend to the corner where the two straight legs would meet if you carried them on. It is R × tan(angle/2), so for a 90 it equals the radius.
• Developed length: the conduit the bend itself uses, measured along its center: R × the angle in radians, or R × 1.571 for a 90. Bender Specs calls it Arc length.
• Gain: two setbacks minus the developed length. Going round the arc is shorter than going out to the corner and back, and the gain is the difference.
• Deduct (take-up): for a 90, the distance from the arrow on the bender to the back of the finished bend. Take it off the stub length to find the mark.
• Start of bend: how far past the arrow, on the side away from the hook, the arc begins: deduct − (R + OD/2). Bender Specs lists it with the Shoe center marks.

The gain printed on benders

Stub and leg lengths are measured to the back of a 90, the outside of the conduit, which is half the OD past the centerline corner on each leg. So the gain a manufacturer prints, and the Gain (back of 90) in Bender Specs, is the centerline gain plus the whole OD.

If all you have is the printed deduct and gain, the radius can be worked back from the gain: R = (gain − OD) ÷ 0.429, which gives 4 3/16" for the bender above. Add your own bender does this when you leave the radius blank. If you edit the Gain (back of 90) of a bender, the calculator treats it as a correction and scales the gain at every angle by the same factor, so cut lengths and bend spacing follow your number while the deduct, and so a 90’s mark, stay as they were.

Why the numbers are smaller than the chart’s

A multiplier chart treats every bend as a sharp corner, a radius of zero. Each real bend saves one gain’s worth of conduit, so the distance between two bend centers comes out one gain shorter than the chart’s, and an offset’s shrink two gains smaller. The gain grows quickly with the angle and in step with the radius (double the radius, double the gain). That is why the difference hardly shows on a shallow bend in 1/2" EMT, and matters on steep bends and big shoes.