K-Factor Calculator

K-Factor Calculator results give the sheet metal K-factor from a test bend, the flat blank and bend deduction for a part, or a fire sprinkler's K-factor from its flow and pressure.

K-Factor Calculator for Sheet Metal and Sprinklers

K-factor means two different things in the trades. In sheet metal it marks where the neutral axis sits inside a bend, and in fire protection it is the discharge coefficient that links a sprinkler's flow to its pressure.

Press brake operators and sheet metal designers use the bending side to get flat patterns right the first time. They either measure K from a test bend or use a known K to size a blank. Fire sprinkler designers and inspectors use the other side to match measured flow and pressure to a nominal sprinkler.

The K-Factor Calculator covers both. For bends, it returns the K-factor, bend allowance, bend deduction, setback, neutral radius and Y-factor, and for sprinklers it returns K, the nearest nominal head, flow at 7 psi and design density.

Three Ways to Use the K-Factor Calculator

K-Factor From a Test Bend takes the thickness, inside radius, bend angle, the flat length before bending and the two measured outside flanges. Flat Length From K-Factor swaps the starting length for a K value and returns the blank size for the flanges you want.

Sprinkler K-Factor takes the flow in gpm, the pressure at the head in psi and the floor area each head covers. Metric mode switches to millimeters, L/min and bar.

The accordion sets whether the angle is the bend angle or the included angle, plus the bending method and material hardness. Those last two only pick the chart value the result is compared against.

Finding K From a Test Bend

Cut a strip, measure its flat length, bend it once, then measure both flanges from the outside to the sharp corner where the outside surfaces would meet. The outside setback is the distance from each flange end of the bend to that corner.

$$OSSB=(R+T)\times \tan \left(\frac{\theta }{2}\right)$$

The bend deduction is how much shorter the flat strip is than the two outside flanges added together. Twice the setback minus that deduction gives the bend allowance, the arc length of the neutral axis.

$$BD=A+B-L_0$$

$$K=\frac{BA/\theta -R}{T}$$

The default is 0.06 inch steel with a 0.06 inch inside radius, a 4 inch strip and flanges of 2.053 and 2.052 inches after a 90° bend. That gives a 0.105 inch deduction, a 0.135 inch bend allowance and a K-factor of 0.4324.

Measuring has to be tight. On this strip, a 0.001 inch error in the flanges moves K by about 0.011, or 2.5%, so use calipers, measure several bends and average them, as the fourth card's sensitivity row shows.

The common mistake is mixing up the bend angle and the included angle. A 90° bend has a 90° included angle, but a 45° bend leaves 135° between the flanges, so set Angle Entered As to match how your part is drawn.

Bend Allowance, Deduction and Flat Length

With K known, the bend allowance follows the formula in the SOLIDWORKS K-Factor help page, with the angle in radians. The flat length is then the two outside flanges minus one bend deduction.

$$BA=\theta \times (R+K\times T)$$

$$L_{flat}=A+B-(2\times OSSB-BA)$$

Entering K 0.44 in the K-Factor Calculator's flat length mode for the same strip gives a 0.1043 inch deduction and a 4.0007 inch blank. The choice of K matters more than it looks, since K 0.33 and K 0.50 differ by 0.016 inch per bend on this part, and a box with eight bends multiplies that error.

The fourth card lists the deduction at 45° and 135° with your K, 0.0319 and 0.3769 inch here, so one test bend covers the other common angles. Bend those angles with the same die and material, since K only carries over when the setup stays the same.

Holes for fasteners are usually punched while the blank is still flat. The Clearance Hole Calculator gives the hole size for each bolt, and the Punch Force Calculator checks the press tonnage needed to punch them in this thickness.

K-Factor Chart by Bending Method

The K-Factor Calculator's third card compares your K with a generic chart based on Machinery's Handbook, as reproduced on sheetmetal.me. It is sorted by bending method, by the ratio of inside radius to thickness (R/T) and by material hardness.

Published K tables disagree with each other, and some put bottoming below air bending rather than above it. Treat the chart as a starting point, and trust a test bend made on your own press brake, die and material lot over any table.

Neutral Axis and Y-Factor

K is the depth of the neutral axis from the inside surface divided by the thickness. A K of 0.50 puts it at mid-thickness, and tighter bends push it toward the inside, which is why the chart drops for radii under one thickness.

For the default strip, the neutral radius is 0.0859 inch, 0.0259 inch in from the inside face. The K-Factor Calculator also gives the Y-factor, K × π/2, which some CAD systems use instead, and a Y-factor of 0.5 matches a K of 0.318, the pair one Pro/ENGINEER user on MCAD Central reports working with.

A test bend that returns K below zero or above 0.50 points to a measuring error rather than real material behavior. The tool flags both, and the usual culprits are the inside radius or reading flanges to the bend instead of the sharp corner.

How to Calculate K-Factor in a Sprinkler System

For sprinklers, K ties the flow from the head to the pressure at the head. NFPA 13 uses this discharge equation in hydraulic calculations, with flow in gpm and pressure in psi.

$$Q=K\times \sqrt{P}$$

Rearranged, K is the flow divided by the square root of the pressure. Fire protection designer Kamal Ram's hydraulic calculation example has an end sprinkler flowing 19.5 gpm over 130 square feet, and at 12.1 psi that works out to K 5.61, which the K-Factor Calculator matches to a nominal K-5.6 head.

The same example notes that NFPA 13 allows no sprinkler to operate below 7 psi. A K-5.6 head flows 14.8 gpm at that minimum, and because flow follows the square root of pressure, doubling the pressure raises flow by only about 41%.

Metric K-factors use L/min and bar and are about 14.4 times the US value, so K-5.6 is listed as K-80. Hydraulic calculations use the nominal K from the sprinkler listing, so the tool checks a measured value against the K range NFPA 13 allows for each size.

For K-5.6 that range is 5.3 to 5.8 with a 1/2 inch NPT thread, so the example's 5.61 matches, while a reading of 6.50 falls between sizes and is flagged for a recheck. The fourth card and the table give each nominal K's range, thread and flow as a percent of K-5.6, up to K-28.0 (K-400).

K-Factor Questions

What is the K-factor for a 90-degree bend?

The K-factor depends on the material, thickness, inside radius and tooling, not mainly on the angle. A 90° test bend is the usual way to measure it because the setback math is simplest, and the default 0.06 inch steel strip gives 0.432.

Once measured, the same K covers other angles with the same setup. With K 0.432 on that strip, the bend deduction is 0.105 inch at 90°, 0.032 inch at 45° and 0.377 inch at 135°.

What K-factor should I use for A36 steel or 304 stainless?

For air bending, the generic chart gives mild steel such as A36 a K of 0.38 when the inside radius is under one thickness and 0.43 up to three thicknesses. Stainless steel such as 304 sits slightly higher at 0.40 and 0.45, and both reach 0.50 on large radii.

Some references quote 0.44 to 0.50 for these materials, closer to the chart's bottoming values. Since the tables disagree, run a test bend in the K-Factor Calculator for the steel and die you actually use.

Can I calculate K-factor in Excel?

Yes. With named cells for thickness T, inside radius R, bend angle A in degrees, flat length L and flanges FA and FB, enter =((2*(R+T)*TAN(RADIANS(A)/2)-(FA+FB-L))/RADIANS(A)-R)/T.

That returns 0.4324 for the default strip. Keep every length in the same unit, and use the outside flange dimensions measured to the sharp corner, not to the start of the bend.