Where do conduit bending multipliers come from?

The offset is a right triangle

Look at an offset from the side. The conduit runs straight, bends up, travels on a diagonal, then bends back to run straight again. That diagonal section, together with the offset depth and the floor under it, forms a right triangle.

• The offset depth is the side opposite the bend angle.
• The distance between bends is the long diagonal side (the hypotenuse).
• The bend angle (θ) is the angle you put on the bender.

The multiplier is just 1 ÷ sin(angle)

From trigonometry, the sine of an angle is the opposite side divided by the hypotenuse:

sin θ = offset depth ÷ distance between bends

Flip that around to solve for the distance between bends:

distance between bends = offset depth × (1 ÷ sin θ)

That 1 ÷ sin θ is the multiplier. Mathematicians call it the cosecant. Because sin 30° is exactly 0.5, the multiplier at 30° is exactly 2. That's why 30° is the easiest offset to do in your head.

Example: a 6″ offset at 30° needs marks 6 × 2 = 12″ apart. At 45° it's 6 × 1.414 = 8 1/2″.

Where shrink comes from

Going up and over takes more conduit than running straight. In the triangle above, the conduit travels the diagonal, but it only moves forward by the run. The difference is the shrink:

shrink = distance between bends − run

Work that through with the trig and you get shrink per inch of offset = (1 ÷ sin θ) − (1 ÷ tan θ). Multiply it by the offset depth for the total shrink. At 30° it's 2 − 1.732 = 0.268, or about 1/4″ for every inch of offset.

The numbers

The field numbers are rounded so you can do the math on the job without a calculator. Our offset calculator uses the exact values.

What about saddles?

A 3-point saddle is two half-offsets back to back. With a 45° center bend, each side climbs at 22.5°, so the exact spacing from the center mark to each outer mark is the obstruction height × 2.613. Many field references round that to 2.5, others to 2.6. Our saddle calculator uses the common 2.5 with 3/16″ of shrink per inch.

And rolling offsets?

A rolling offset adds a second right triangle. The rise and the roll are its two short sides, so the true offset is √(rise² + roll²), the Pythagorean theorem. After that, you treat it like any other offset and use the same multipliers. Try it in the rolling offset calculator.

Why your bender's marks can differ a little

The triangle assumes each bend is a sharp corner. Real conduit curves around the bender shoe, so the true geometry depends on your bender's centerline radius. For most offsets the difference is small, which is why the multiplier method works well in the field.

See centerline bending radius vs. multipliers for how big the difference gets with conduit size and angle.

When you want marks that account for the radius of your exact bender, iBend Pipe calculates them for nearly 300 real benders.