Bend Deduction and Bend Diameter in Bar Bending: How They're Calculated

Almost every BS 8666:2020 shape code formula includes a deduction term — something like "−0.5r−d" tacked onto the end. That term is the bend deduction, and understanding what it corrects for (and how bend diameter feeds into it) is the difference between a schedule that's approximately right and one that's exactly right.

Why bending shortens a bar

If you measure a bent bar's two legs to where they'd meet as straight lines, and simply add those two numbers together, you'll get a length that's slightly longer than the bar actually needs to be. That's because the bar doesn't travel in two straight lines meeting at a sharp corner — it follows a curved path around the bend, and a curve between two points is always shorter than the two straight legs that would meet at their intersection.

Not to scale — illustrative only

The bend deduction is simply the correction that accounts for this difference — it's subtracted from the sum of the straight legs to arrive at the bar's true cutting length along its actual curved path.

What bend diameter is

The bend diameter (also called mandrel diameter or former diameter) is the diameter of the pin or roller the bar is bent around. It's twice the bend radius, r. BS 8666:2020 sets a minimum mandrel diameter for each bar size in its Table 2, because bending a bar too tightly for its diameter risks cracking the steel or reducing its strength at the bend.

Where d is the bar diameter. These figures are commonly cited approximations of BS 8666:2020's minimum radius requirements — always confirm the exact current value against BS 8666:2020 Table 2 itself, or against your fabricator's actual bending former sizes, since some shops use larger mandrels than the published minimum.

Spring-back: why the finished radius isn't quite the former's radius

Steel has some elasticity, so a bar bent around a former doesn't stay bent to exactly that radius once it's released — it "springs back" very slightly, meaning the finished bend ends up marginally larger in radius than the former it was bent around. BS 8666:2020 accounts for this in its hook-diameter formula (q = 3d + 2r, rounded up to the next 5mm), but for scheduling purposes the practical takeaway is simpler: don't expect a bent bar's radius to measure exactly the nominal former size on site.

How the deduction shows up in shape formulas

Take BS 8666 shape code 11 — a single 90° bend — with the formula:

Here, A and B are the two straight legs, and "−0.5r−d" is the bend deduction for a single 90° bend, combining the radius term and the diameter term into one correction. Different shape codes use different deduction terms depending on how many bends they have and at what angle — a closed stirrup like shape code 51, with four 90° corners, has a larger cumulative deduction (2.5r + 5d) spread across its formula for exactly that reason. You can see the full set of deduction terms in our BS 8666 shape codes guide.

A note on approximate formulas

BS 8666:2020 itself flags that a handful of shape formulas — those for shapes 15, 25, 26 and 46 — are approximate once the bend angle passes 45°, and recommends recalculating more precisely (or scheduling as shape code 99 with a fully dimensioned sketch) once a bend angle approaches 90°. This is a direct consequence of bend deduction: the correction those formulas use is itself an approximation that holds well for shallow bend angles but drifts as the angle increases, so the standard is explicit that precision matters more as the bend gets sharper.

Frequently asked questions

What is bend deduction in bar bending?

Bend deduction is the amount subtracted from the sum of a bent bar's straight legs to get its true cutting length, because bending a bar around a radius follows a shorter path than the straight legs measured to their intersection point.

What is bend diameter (mandrel diameter) in rebar bending?

Bend diameter, also called mandrel or former diameter, is the diameter of the pin or roller a bar is bent around. It's twice the bend radius (r), and BS 8666:2020 sets a minimum mandrel diameter for each bar size to prevent the bar cracking or losing strength at the bend.

What is the minimum bend radius under BS 8666:2020?

BS 8666:2020's minimum bend radius is taken as half the minimum mandrel diameter set out in its Table 2, commonly around 2d for bar sizes from 6mm to 16mm and around 3.5d for bar sizes of 20mm and above, where d is the bar diameter — always confirm the exact current value against BS 8666:2020 Table 2 or your fabricator's actual former sizes.

Why does the actual bend radius end up larger than the former?

Steel has some elasticity, so after a bar is bent around a former and released, it springs back slightly, meaning the finished bend radius ends up a little larger than the radius of the former it was bent around.

This is a general explanation of the principle behind bend deduction, not a substitute for BS 8666:2020 itself (available from BSI) or for a checked, engineer-approved bending schedule. Always verify minimum radii and deductions against the current standard for the actual bar size and grade in use.