Speeds, feeds and chatter is the highest volume technical argument in machining, and most threads end in it depends. This one does not. Enter tool diameter, stickout and the cut and it returns cantilever tip deflection in thousandths, the radial chip thinning factor, the largest radial depth that holds your deflection target, and a ranked list of what to change first. Deflection goes with stickout cubed, so stickout is almost always the answer, not the alloy.
Last updated July 2026
The deflection multiplier column is exact arithmetic, not opinion. It is the ratio of L cubed at that stickout to L cubed at the 3 x D reference, so a 6 x D tool deflects exactly 8.000 times as far as the same tool at 3 x D under the same cutting force. The engagement and depth columns are shop guidance consistent with round tool vendor long reach tables, intended as starting points, not limits.
| Stickout L / D | Deflection vs 3 x D, (L/D)^3 / 27 | Recommended max radial depth ae | Recommended axial depth ap | Risk band | Action |
|---|---|---|---|---|---|
| 1.5 x D | 0.125 | up to 1.0 D (slot) | up to 1.5 D | Low | Run book parameters, no reduction |
| 2 x D | 0.296 | up to 0.75 D | up to 1.5 D | Low | Run book parameters, no reduction |
| 3 x D | 1.000 | up to 0.50 D | up to 1.0 D | Low | Reference case, last stickout that needs no reduction |
| 4 x D | 2.370 | 0.25 D | 1.0 D | Moderate | Cut radial engagement, expect measurable wall taper |
| 5 x D | 4.630 | 0.15 D | 0.75 D | Moderate | Spring pass on finish walls, check with an indicator not a mic |
| 6 x D | 8.000 | 0.10 D | 0.50 D | High | Necked tool with a full diameter shank behind the neck |
| 7 x D | 12.70 | 0.07 D | 0.50 D | High | Necked tool, shrink fit or high accuracy hydraulic holder |
| 8 x D | 18.96 | 0.05 D | 0.40 D | High | Last band where a conventional tool is realistic |
| 10 x D | 37.04 | 0.03 D | 0.30 D | Severe | Tapered or necked tool mandatory, consider a carbide extension |
| 12 x D | 64.00 | 0.02 D | 0.25 D | Severe | Tapered tool or heavy metal shank, treat finish as a separate operation |
| 15 x D | 125.0 | 0.015 D | 0.20 D | Severe | Redesign the fixture or the part approach, do not fight it with feeds |
Deflection is inversely proportional to E, so the stiffness ratio column inverts straight into deflection: carbide at 2.90 times the stiffness of HSS deflects 1 / 2.90, or 0.34 times as far, under the same force at the same geometry. Carbide modulus falls as cobalt binder content rises, which is why a tough high cobalt grade is measurably springier than a micrograin grade at the same geometry. Use 87 million psi unless your vendor publishes a number for the specific substrate.
| Tool or shank material | E (psi) | E (GPa) | Published range | Stiffness vs HSS |
|---|---|---|---|---|
| Solid carbide, WC with about 10 percent Co | 87,000,000 | 600 | 80 to 94 million psi (550 to 650 GPa) | 2.90 |
| Cobalt HSS, M42 or M35 | 31,000,000 | 214 | 30 to 33 million psi (207 to 228 GPa) | 1.03 |
| HSS, M2 | 30,000,000 | 207 | 29 to 31 million psi (200 to 214 GPa) | 1.00 |
| Tungsten heavy alloy anti-vibration shank | 45,000,000 | 310 | 45 to 55 million psi (310 to 380 GPa), rises with tungsten content | 1.50 |
Corrected feed per tooth assumes a programmed 0.0040 inch per tooth. Past half immersion the engagement arc already contains the point of maximum chip thickness, so peak chip thickness equals feed per tooth and the factor pins at 1.0000. Any calculator that keeps climbing past 0.5 immersion is using the formula outside its domain.
| Radial immersion ae / D | Engagement angle (deg) | sin(phi_max) | Chip thinning factor RCTF | Corrected fz from 0.0040 in |
|---|---|---|---|---|
| 0.05 | 25.84 | 0.4359 | 2.2942 | 0.0092 |
| 0.10 | 36.87 | 0.6000 | 1.6667 | 0.0067 |
| 0.15 | 45.57 | 0.7141 | 1.4003 | 0.0056 |
| 0.20 | 53.13 | 0.8000 | 1.2500 | 0.0050 |
| 0.25 | 60.00 | 0.8660 | 1.1547 | 0.0046 |
| 0.35 | 72.54 | 0.9539 | 1.0483 | 0.0042 |
| 0.50 | 90.00 | 1.0000 | 1.0000 | 0.0040 |
| 0.75 | 120.00 | 1.0000 | 1.0000 | 0.0040 |
| 1.00 (slot) | 180.00 | 1.0000 | 1.0000 | 0.0040 |
This is the table that settles the argument. Elastic modulus across 6061, 7075 and 7050 spans 10.0 to 10.4 million psi, a 4 percent range, and none of it appears in the tool deflection math anyway. Ultimate shear strength spans 30 to 48 ksi, a 60 percent range, so 7075 is roughly 1.6 times as strong in shear as 6061. Measured cutting force does not follow the strength ratio though: published unit power for aluminum runs 0.25 to 0.35 horsepower per cubic inch per minute, which puts the real 7075 to 6061 force ratio near 1.25, because the harder alloy shears a thinner, better formed chip. Specific cutting force Kc for aluminum spans roughly 60,000 to 150,000 psi depending on alloy, chip thickness and edge condition, so treat every force number as indicative.
| Alloy and temper | Modulus E (10^6 psi) | Ultimate shear strength (ksi) | Kc used here (psi) | Unit power = Kc / 396,000 (hp per in^3/min) | Force relative to 6061 |
|---|---|---|---|---|---|
| 6061-T651 | 10.0 | 30 | 100,000 | 0.253 | 1.00 |
| 7075-T651 | 10.4 | 48 | 125,000 | 0.316 | 1.25 |
| 7075-T7351 | 10.4 | 44 to 45 | 120,000 | 0.303 | 1.20 |
| 7050-T7451 | 10.3 | 43 to 44 | 122,000 | 0.308 | 1.22 |
| Spread across the three alloys | 4 percent | 60 percent | 25 percent | 25 percent | stiffness barely moves, force moves |
Basis for these numbers. The moduli are the standard published values for these alloys, 10.0 million psi for 6061, 10.4 million for 7075 and 10.3 million for 7050, and they are well settled to better than a percent. Ultimate shear strength for 6061-T6 at 30 ksi and 7075-T651 at 48 ksi are long established handbook values and are the pair that gives the 1.6 ratio quoted above. The overaged tempers are softer figures: published shear strengths for 7075-T7351 and 7050-T7451 plate land between 43 and 45 ksi depending on the source and the plate thickness, so they are shown as ranges rather than as single values. None of the shear numbers are used in the calculator. Kc is derived from unit power, and the conversion is exact arithmetic, not a correlation: 1 horsepower is 396,000 inch pounds force per minute, so 0.25 hp per cubic inch per minute is 99,000 psi.
Everything is in inches, pounds force and psi. The tool is a uniform cantilever beam fixed at the holder face with the cutting force applied at the tip.
D tool diameter in inches. neck reduced neck diameter in inches, defaults to D. d the diameter that governs stiffness, the smaller of the two. L stickout from the holder face to the tool tip in inches. I area moment of inertia of the round section in inches to the fourth. E elastic modulus of the tool material in psi, 87 million for solid carbide, 31 million for cobalt HSS, 30 million for HSS.
ae radial depth of cut, the width of the cut measured perpendicular to the feed direction. ap axial depth of cut, the depth along the tool axis. fz feed per tooth in inches, sometimes called chip load. z number of flutes. x radial immersion, ae divided by D.
phi_max the angular position of maximum chip thickness inside the engagement arc. phi total engagement angle of the arc the tooth sweeps while cutting. h_max peak undeformed chip thickness. RCTF radial chip thinning factor, the ratio of programmed feed per tooth to the chip the tooth actually takes. z_cut average number of teeth engaged. Below 1.0 the cut is interrupted, every tooth enters and exits with nothing else in contact.
Kc specific cutting force for the alloy in psi, the force per unit of chip cross section. Ft peak tangential force on the engaged tooth, in the direction of cutting. Fr peak radial force, normal to the cut and pushing the tool away from the wall. This is the component that produces dimensional error, which is why deflection is computed from it. The resultant of Ft and Fr is about 1.06 times Ft, so the total tip motion is slightly larger than the wall error, but the extra is along the feed direction where it does not show up on the print. delta tip deflection in inches, reported in thousandths.
Two things this model deliberately does not do. It does not predict achievable surface finish from feed and nose radius, use the surface finish predictor for that and the surface finish converter to move between Ra, Rz and RMS. And it does not judge whether a print callout is producible in the first place, which is what the tolerance feasibility checker and the stack tolerance calculator are for.
The model is static and elastic. It ignores holder and spindle compliance, which on a light machine can contribute as much tip motion as the tool itself, and it ignores workpiece and fixture stiffness entirely. It says nothing about regenerative chatter, which is a dynamic instability governed by natural frequency and damping at the tool tip. Reducing static deflection generally helps stability because it usually means a shorter, fatter, better held tool, but the two are not the same thing and this page will not pretend otherwise. When you have proved a setup and need the plate to run it on, get an instant quote on DFARS 6061, 7075 and 7050 plate cut to your size with a mill cert on every order, so the temper you programmed for is the temper that shows up on the pallet.
Because chatter is almost never a material property. It is a stiffness and dynamics problem in the tool, the holder, the fixture and the machine. The number that matters most is stickout, because tip deflection goes with stickout cubed. Double the stickout and you get eight times the deflection from the same cut. For tool deflection the alloy does not enter the math at all, and even for workpiece deflection 6061, 7075 and 7050 are within 4 percent of each other in elastic modulus, 10.0, 10.4 and 10.3 million psi. What the alloy does change is cutting force, roughly 20 to 30 percent more force in 7075 than in 6061 at the same chip load. If you shortened the tool by a quarter and the chatter went away, it was never the plate.
Up to 3 times diameter is low risk and needs no parameter reduction. From 3 to 5 times diameter is moderate, drop radial engagement to about a quarter of diameter and expect visible wall taper. From 5 to 8 times diameter is high risk, you are down around 0.05 to 0.15 of diameter radially and you should be looking at a necked tool. Over 8 times diameter is severe, a straight shank at that reach is a spring and you need a necked or tapered tool in a shrink fit or high accuracy hydraulic holder. These are shop guidance bands consistent with round tool vendor long reach tables, not a stability guarantee.
Treat the tool as a cantilever beam fixed at the holder face with the cutting force at the tip. Moment of inertia is I = pi x d to the fourth over 64, using the smaller of the cutter diameter and any reduced neck diameter. Tip deflection is delta = F x L cubed divided by 3 x E x I, where E is 87 million psi for solid carbide and about 30 million psi for HSS. Get F from the peak chip load: peak chip thickness h_max = fz x sin of the maximum engagement angle, tangential force Ft = Kc x h_max x axial depth, and radial force Fr is about 0.35 of Ft for a sharp high helix aluminum cutter. Kc for aluminum runs 100,000 to 125,000 psi depending on alloy.
Yes, more than almost anything else you can change. Moment of inertia goes with diameter to the fourth power, so stepping a 0.500 inch cutter up to 0.625 inch at the same stickout cuts deflection to (0.500 / 0.625) to the fourth, which is 0.41, about 59 percent less. It also drops radial immersion at the same radial depth, which thins the chip and lowers the force further. The catch is part geometry: you can only go up in diameter if the internal corner radius allows it. When it does not, a necked tool with a full diameter shank behind the neck is the next best answer.
No, and neither can any other web form. A chatter free spindle speed comes from the stability lobe diagram of your specific setup, which depends on the natural frequency and damping ratio measured at the tool tip with a tap test, plus the specific cutting force coefficients of the material. Change the holder, the tool length, the fixture or the part and the lobes move. What this tool gives you is a static deflection number, which is real arithmetic, and a risk band from L to D ratio and radial immersion, which is honest ranking. Anyone promising a chatter free RPM from a web form without a tap test on your machine is selling something.
Axial depth, by a wide margin. Force is linear in axial depth, so halving axial depth halves the tool load. Peak chip thickness only goes with the square root of radial engagement, so you have to cut radial depth to a quarter to halve the force. That surprises most people, because reducing radial engagement is the usual reflex. It is still useful, it is just weak per unit of cycle time you give up. Ranked by exponent the order is diameter to the fourth, stickout cubed, axial depth and feed per tooth linear, radial depth as a square root, and the alloy last. Stickout is usually the one you actually change, because it costs nothing and does not depend on the corner radius in the part.
Yes, and it works against you twice. At 0.100 inch radial on a 0.500 inch cutter, radial immersion is 0.2 and the chip thinning factor is 1.25, so the tooth is only taking 0.0032 inch when you programmed 0.004 inch. Compensating by raising feed per tooth to 0.005 inch restores the chip and restores the surface finish, but it also puts peak chip thickness and therefore cutting force and deflection right back where a full immersion cut would have them. Chip thinning compensation is a productivity move, not a deflection move. Decide which one you are buying before you dial it in.