Enter a feed and a tool nose radius and this returns theoretical Ra and Rz, a realistic achievable band rather than the geometric floor, the maximum feed that still hits the Ra on your print, and scallop height for ball and bull nose work. It also tells you when the callout is not reachable by cutting at all, which is the answer nobody wants and the one worth knowing before you quote.
Last updated July 2026
Theoretical roughness is a geometric floor set by feed marks alone. It ignores built-up edge, tool wear, runout, vibration, chatter and smearing. Real parts come out worse than theoretical, never better. Use the theoretical figure to rule a target out, and the realistic band to plan for it.
The geometry alone already exceeds the print. At 0.0080" feed on a 0.0313" radius the feed marks are 63.9 uin before anything goes wrong. Drop the feed to 0.0052" or fit a 0.0730" radius. Nothing about tooling or coolant recovers a geometric shortfall.
Gummy in T6 and T651 and the most built-up-edge prone of the group. BUE welds aluminum to the cutting edge, then it tears off and takes finish with it, which happens whatever the feed is. On the Aluminum Association A to E scale, which rates chip form and achievable finish, the commonly reproduced tables put 6061-T6 and T651 at C against B for 7075, though sources differ by a letter. That is not a speed ranking: 6061 runs faster and pulls less power than 7075, it just does not finish as cleanly.
The feed and nose radius model fits turning and boring best, because one edge makes every mark and the geometry repeats exactly once per revolution.
Best case for aluminum. Flushes chips out of the cut so they are not recut, and keeps the edge cool enough to slow built-up edge.
Gummy in T6 and T651 and the most built-up-edge prone of the group. BUE welds aluminum to the cutting edge, then it tears off and takes finish with it, which happens whatever the feed is. On the Aluminum Association A to E scale, which rates chip form and achievable finish, the commonly reproduced tables put 6061-T6 and T651 at C against B for 7075, though sources differ by a letter. That is not a speed ranking: 6061 runs faster and pulls less power than 7075, it just does not finish as cleanly.
Ranges are typical process capability on aluminum, not guarantees, and they assume a sharp tool and a rigid setup. The Rz column uses the geometric convention Rz is about four times Ra, which holds on a clean turned or milled profile. On a torn or smeared surface the ratio climbs, which is why Ra and Rz are not interchangeable and no single conversion is exact.
| Process | Ra (microinches) | Ra (micrometres) | Rz approx (microinches) | Relative cost |
|---|---|---|---|---|
| Bandsawn cut, as-cut | 500 to 2,000 | 12.5 to 50 | 2,000 to 8,000 | Included in the cut, no extra operation |
| Rough milled | 250 to 500 | 6.3 to 12.5 | 1,000 to 2,000 | Baseline, material removal rate is the goal |
| Rough turned | 125 to 250 | 3.2 to 6.3 | 500 to 1,000 | Baseline |
| As-milled, standard finish pass | 63 to 125 | 1.6 to 3.2 | 250 to 500 | Baseline, what you get when the print has no callout |
| Finish turned or bored | 32 to 63 | 0.8 to 1.6 | 125 to 250 | Slight, one extra light pass |
| Finish milled, sharp tool, light feed | 32 to 63 | 0.8 to 1.6 | 125 to 250 | Slight, one extra light pass |
| Reamed | 32 to 63 | 0.8 to 1.6 | 125 to 250 | Extra tool and an extra operation per hole |
| Cast tool and jig plate, as-supplied machined face | 32 to 63 | 0.8 to 1.6 | 125 to 250 | Included in the plate, but porosity pits read worse than the profile |
| Fine turned, wiper insert, low feed | 16 to 32 | 0.4 to 0.8 | 63 to 125 | Moderate, wiper insert plus a slower finish feed |
| Fine finish milled, polished flute, short stickout | 16 to 32 | 0.4 to 0.8 | 63 to 125 | Moderate, finishing cycle time roughly doubles |
| Surface or cylindrical ground | 8 to 32 | 0.2 to 0.8 | 32 to 125 | High, separate machine and setup |
| Fine ground | 4 to 16 | 0.1 to 0.4 | 16 to 63 | High, frequent dressing and slow infeed |
| Honed | 4 to 16 | 0.1 to 0.4 | 16 to 63 | High, bores only, dedicated tooling |
| Single crystal diamond turned | 1 to 8 | 0.025 to 0.2 | 4 to 32 | Very high, dedicated machine and a fragile tool |
| Lapped | 1 to 8 | 0.025 to 0.2 | 4 to 32 | Very high, per part labor |
| Polished or superfinished | 0.5 to 4 | 0.012 to 0.1 | 2 to 16 | Highest, per part labor with no dimensional control |
| Bead blasted, non directional cosmetic | 60 to 150 | 1.5 to 3.8 | 250 to 600 | Low, but it hides marks rather than reducing Ra |
| Type II anodize over a 63 uin base | 63 to 125 | 1.6 to 3.2 | 250 to 500 | Anodize does not smooth, it follows and slightly roughens the base |
The grade column is the Aluminum Association A to E machinability rating, which scores chip form and achievable finish only. It is not a speed or power ranking. 6061 rating a letter below 7075 surprises people, and the reason is exactly the subject of this tool: 6061 in T6 and T651 is gummy and built-up-edge prone, and built-up edge ruins finish no matter what the feed is. 6061 still runs at higher cutting speeds and pulls less power than 7075.
Basis for the grade column: published A to E tables differ by a letter between sources and between tempers of the same alloy, so treat the letter as a relative ranking of chip form and finish, not as a spec value, and do not quote it to a customer as one. The finish factor column is what this calculator actually uses. It is a calibrated planning figure derived from how much built-up edge and smearing each alloy adds on top of the feed marks, and it is set independently of the letter.
| Material or condition | Machinability grade | Finish factor | Note |
|---|---|---|---|
| 6061-T651 | C | 1.15x | Gummy, the most built-up-edge prone of the group, but runs faster and pulls less power |
| 7075-T651 | B | 1.00x | Best chip form and finish of the group, shorter chips and less smearing |
| 7075-T7351 | B | 1.02x | Overaged and slightly softer, marginally more smearing than T651 |
| 7050-T7451 | B | 1.02x | Thick-section standard, finishes the same at the bottom of a deep pocket as at the top |
| 5000 series cast tool and jig plate | C to D | 1.25x | Porosity and hard particles show as pits no feed change removes, and it anodizes blotchy |
| Flood coolant | n/a | 1.00x | Best case, clears chips and slows built-up edge |
| MQL | n/a | 1.12x | Chips linger and recut chips leave witness marks |
| Dry | n/a | 1.30x | Invites built-up edge and smearing, worst case on 6xxx |
All lengths are in inches unless noted. Multiply an inch value by 1,000,000 to read it in microinches, and multiply microinches by 0.0254 to read micrometres.
f is feed per revolution for turning and boring, and feed per tooth for milling, both in inches.
fz is feed per tooth, used where the distinction matters.
r is the tool nose or insert corner radius in inches.
R is the ball or bull nose cutter radius in inches, which is half the diameter on a full ball.
ae is the stepover between adjacent passes in inches.
h is scallop or cusp height, the ridge of uncut material left between passes.
Rz is the peak to valley height of the profile, Ra is the average absolute deviation from the mean line of the same profile.
Rz is pure geometry. A round tool nose of radius r advancing f per revolution leaves a cusp whose height is the sagitta of a chord of length f on a circle of radius r, which is r minus the square root of r squared minus f squared over four. Expanding the root for f much smaller than r gives the shop form f squared over 8r. On the default case, a 0.008 inch feed on a 0.0313 inch nose, the exact form gives 256.6 microinches and the shop form gives 255.6, a 0.4 percent difference. Truncating the series always drops a positive term, so the shop form is always slightly below the exact height, never above it. The calculator reports both.
Ra is not an independent constant, it follows from Rz. Treat one cusp as a parabola of depth Rz over a pitch f. The mean line then sits two thirds of Rz below the peak line, and integrating the absolute deviation about that mean line gives Ra equal to 0.2566 times Rz, which is f squared over 31.18 times r. The rounded engineering convention Ra equals Rz over 4, that is f squared over 32r, sits 2.6 percent below that derivation, so it is very slightly optimistic rather than conservative. It is still the form used here, because it makes f equals the square root of 32 r times Ra_target an exact inverse that round trips, and 2.6 percent is far inside the 1.3 to 2.0 times real-world band that sits on top of it. Published imperial versions bracket the same ground: one widely used form is Ra in microinches equals 31,675 times f squared over r, against 31,250 for the 1/32 convention and 32,075 for the parabolic derivation, so the whole spread is under 3 percent.
The scallop approximation ae squared over 8R is the same expansion applied to stepover instead of feed. On a 0.250 inch cutter radius at a 0.030 inch stepover the exact form gives 450.4 microinches and the approximation gives 450.0, so the approximation is 0.09 percent low, in the same direction and for the same reason as the feed cusp. At practical stepovers either is fine. The exact form is what the calculator reports.
The realistic multiplier band is a planning range, not a published constant, and it is deliberately shown as a band. Its basis is that every mechanism the geometry ignores adds roughness and none removes it: built-up edge, tool wear, runout, spindle and fixture vibration, chatter and smearing. Measured finish on a rigid setup with a sharp tool and flood coolant commonly lands 1.3 to 2.0 times theoretical, and degrades from there as conditions do. The material and lubrication factors scale that band, and a per process absolute floor is then applied because no feed change gets carbide much below roughly 8 microinches on a turned aluminum surface, 12 on a face mill or 16 on a ball nose. That floor is applied as a band from the floor to twice the floor, not as a single number, because once the feed stops being the limit the surface is set by edge condition and machine dynamics, and those scatter wider than the feed math does.
It does not convert between roughness units, use the surface finish converter for Ra, Rz, RMS and CLA. It does not calculate RPM, feed rate or chipload, use the speeds and feeds calculator. It does not model deflection, stickout, length to diameter ratio or chatter, which are the usual reason a finish comes out worse than this predicts, so run the tool deflection and chatter calculator alongside it. And it judges one Ra callout in isolation, so for whether a whole set of dimensional callouts is achievable use the tolerance feasibility checker.
Finish starts with the stock. Consistent temper and known residual stress mean the finish pass cuts the same on the last part as it did on the first, so get an instant quote on 6061, 7075 and 7050 plate cut to size with a mill cert on every order, because a surface finish problem that turns out to be a temper substitution is the most expensive kind.
A normal finish pass on 6061 or 7075 plate lands between 63 and 125 microinches Ra with no special effort. A deliberate finish pass with a sharp tool and a light feed gets you 32 to 63 microinches. Getting inside 32 microinches takes polished-flute uncoated carbide or a ZrN or TiB2 coating, a high helix, minimum tool stickout and flood coolant, and it roughly doubles cycle time. Below about 16 microinches you are at the practical limit of carbide on aluminum, and below 4 microinches you are in lapping and polishing, not machining.
It is accurate as a floor and useless as a prediction. Ra = f squared divided by 32 times the nose radius describes the feed marks a round tool nose leaves and nothing else. It ignores built-up edge, tool wear, runout, spindle and fixture vibration, chatter and smearing, every one of which adds roughness and none of which removes it. Real parts measure worse than theoretical, never better. Use the theoretical number to rule a target out, because if the geometry alone exceeds the print no tooling or coolant change will save it, then use a realistic band of roughly 1.3 to 2.0 times theoretical on a rigid setup to plan what you will actually measure.
Rearrange the roughness formula: f equals the square root of 32 times the nose radius times the target Ra, with all three in inches. For a 63 microinch target on a 0.0313 inch nose radius insert that gives 0.0079 inch per revolution. That is the geometric answer. Because real finish runs a multiple of theoretical, divide the target Ra by the top of your realistic multiplier before taking the square root, which on gummy 6061 with flood coolant drops the same case to about 0.0052 inch per revolution.
On chip form and achievable finish, usually yes. The Aluminum Association machinability scale runs A to E and rates chip form and finish quality only, not speed or power, and in the commonly reproduced tables 7075-T6 and T651 sit at B against C for 6061-T6 and T651. Published tables do vary by a letter between sources and tempers, so treat that as a relative ranking rather than a spec value. The physical reason behind it is not in dispute: 6061 in T6 and T651 is gummy and the most built-up-edge prone of the common plate alloys, and built-up edge wrecks finish independently of feed. That is not the same as saying 7075 machines better overall. 6061 runs at higher cutting speeds and pulls noticeably less power, so 7075 costs you cycle time and spindle load to buy the cleaner surface.
Scallop or cusp height is the ridge of uncut material left between adjacent passes of a round-bottomed cutter. The exact form is h equals R minus the square root of R squared minus stepover squared over four, where R is the cutter radius. The common approximation h equals stepover squared over 8R agrees within about a tenth of a percent at practical stepovers, so either is fine, and the exact form is what this calculator reports. On a real three dimensional contour the effective radius drops on steep walls, so the same stepover leaves a taller scallop there than it does on a flat floor.
Because the calculation only covers feed marks. The usual culprits on aluminum, in the order worth checking, are built-up edge on the cutting edge, recut chips because coolant is not clearing the pocket, tool deflection and chatter from too much stickout, spindle or toolholder runout, and insert height scatter on a face mill where one insert cutting proud sets the whole surface. None of these appear in the feed and radius math. If the measured value is two to three times theoretical, that is normal. If it is five times or more, you have a process problem, not a feed problem.
No. Anodize follows the surface underneath it and usually reads slightly rougher, because the coating grows into and out of the substrate rather than filling it. A 63 microinch base finish anodizes to roughly 63 to 125 microinches. If a print calls out both a fine Ra and an anodize, the Ra has to be achieved before the tank, not by it. Cast 5000 series tool and jig plate is a special case, because it anodizes blotchy regardless of how well it was machined, so do not plan a cosmetic anodize over it.