How this instrument works
This page is not a general bend-allowance tool; it is a fixed practice problem built around one formula, BA = θ(rad) × (R + K·T), so the same four inputs always produce the same checkable answer. That matters because bend allowance itself is a small, easy-to-mangle piece of arithmetic — an angle, a radius, a thickness and a fitted constant, multiplied together in a particular order — and a shop or a classroom benefits more from rehearsing that order correctly than from another explanation of sheet-metal theory.
The quantity being tested is how much extra flat stock one curve eats up, tracked along the single layer inside the sheet that comes out of the bend at its original length — everything closer to the outside stretched a little, everything closer to the concave face got squeezed. K-factor is a dimensionless dial that locates that layer: a small K parks it close to the concave face, a larger K slides it toward the middle. Multiplying the angle by radius-plus-K·T works because it is just the schoolbook arc-length relation, s = rθ, applied to that layer's own radius instead of the tool radius — which is also why the angle has to already be in radians before that multiplication happens.
Because the drill fixes K at 0.33, it deliberately sidesteps the harder judgment call of picking a K-factor for a real job, where the right value drifts with tooling, bend method and alloy. Treat a correct answer here as proof the formula and the unit handling are solid, not as proof that 0.33 belongs on every job travel sheet — that second decision still needs a bend-deduction chart or test coupon.
- Leave Bend angle at 90, or set your own test angle — the field takes degrees and the instrument converts to radians before doing anything else.
- Set Inside bend radius to the punch-nose figure you want to check, in millimetres.
- Set Material thickness to the stock thickness being bent.
- Set K-factor to the constant you're testing — 0.33 reproduces this page's answer key exactly.
- Compare the Bend allowance readout against your own hand calculation; a mismatch almost always traces back to a missed degree-to-radian step.
Answer key — 90°, 3 mm radius, 2 mm stock, K = 0.33
Set the four inputs to the drill's default case: Bend angle 90, Inside bend radius 3 mm, Material thickness 2 mm, K-factor 0.33. Before anything gets multiplied, 90 degrees has to become radians, since the formula is an arc-length relation and arc length only comes out right in radians: 90 × π ⁄ 180 = 1.5707963267949 rad. Skipping that step and multiplying by 90 directly is the mistake that trips up this check most often.
Next, R + K·T in metres: 0.003 + (0.33 × 0.002) = 0.003 + 0.00066 = 0.00366 m. That sum locates the unstretched layer's own radius — the inside radius nudged outward by roughly a third of the sheet's thickness, which is where K = 0.33 places the one layer whose length survives this tight a curve unchanged.
Multiply the two: 1.5707963267949 × 0.00366 = 0.00574911455607 m, which reads as 5.749115 mm in the Bend allowance field. Land on that figure, to the sixth decimal in metres or the nearest thousandth of a millimetre, and the arithmetic — angle conversion, the K·T addition, and the final product — is confirmed correct.
Questions
Why must the bend angle be converted to radians before multiplying?
Because the formula is an arc-length relation, s = rθ, and that relation is only true when θ is measured in radians — a radian is defined so that arc length equals radius times angle directly, with no extra constant. Multiply by 90 instead of 1.5707963267949 and the result comes out roughly 57 times too large, since 180/π ≈ 57.3.
Is K = 0.33 the correct value for every bend, or just this drill?
Only for this drill's own case. 0.33 is a common rule-of-thumb constant when R/T, radius divided by thickness, sits below roughly 2 — here that ratio is 3 mm over 2 mm, or 1.5, squarely inside that tight-bend range. A gentler curve, a different alloy, or a different brake pushes the real constant toward 0.4 or 0.5, and a working job should pull K from a bend-deduction chart or a test coupon rather than assume 0.33.
My hand calculation gives a different answer than 5.749115 mm — what did I miss?
Check three spots in order: whether 90 degrees actually got converted to 1.5707963267949 radians before multiplying, whether K was multiplied by thickness and then added to radius rather than multiplied by the sum, and whether thickness and radius were both expressed in the same unit before the addition.
How does this drill differ from the site's full Bend Allowance Calculator?
The calculator is built for a real job: any angle, radius, thickness, and K-factor you enter, with unit menus and a flat-pattern workflow around it. This page fixes those four numbers to one known case so the output has a single correct answer — useful for testing whether the formula, not the job, has been understood.
Does getting 5.749115 mm here mean springback is accounted for?
No — this drill only sizes the flat blank that goes into the press. It says nothing about the few degrees a formed part relaxes back once the tooling opens, which fabricators handle as a separate correction, typically over-bending past the target angle or programming a compensation value into the brake. That relaxation gets layered on top of, not folded into, the bend allowance figure this page checks.