Speeds and feeds
Surface finish calculator
Theoretical Ra = f^2 / (32 x r); a 1/32 in nose radius at 0.006 IPR gives 36 µin Ra (0.91 µm).
Technical review pending. Formulas and values are cited. This notice comes down after a machinist review.
Turning finish from nose radius and feed
Theoretical Ra
µin
Ra = f^2 / (32 x r) = 0.006^2 / (32 x 0.03125) = 0.000036 in = 36 µin
0.91 µm Ra. Rmax 144 µin (3.66 µm). Geometry only; the part finish is a measurement.
| Value | Result | Formula with your numbers |
|---|---|---|
| Rmax, peak to valley | 144 µin (3.66 µm) | Rmax = f^2 / (8 x r) = 0.006^2 / (8 x 0.03125) = 0.000144 in = 144 µin |
| Ra, shop form | 36 µin (0.91 µm) | Ra = f^2 / (32 x r) = 0.006^2 / (32 x 0.03125) = 0.000036 in = 36 µin |
| Ra, geometric form | 37 µin (0.94 µm) | Ra = f^2 / (18 x sqrt(3) x r) = 0.006^2 / (18 x sqrt(3) x 0.03125) = 0.000037 in = 37 µin |
Ball end mill scallop height
Scallop height
in
h = R - sqrt(R^2 - (s / 2)^2) = 0.25 - sqrt(0.25^2 - (0.02 / 2)^2) = 0.000200 in
200 µin (5.08 µm). Approximation h = s^2 / (8 x R) = 0.02^2 / (8 x 0.25) = 200 µin.
Source: Machinery's Handbook (surface texture; theoretical finish in turning); ASME B46.1 (surface texture) for the Ra definition.
Theoretical values come from tool geometry. The finish on the part is a measurement, not a calculation.
How it works
Turning finish
Rmax = f^2 / (8 x r); Ra = f^2 / (32 x r); f = sqrt(32 x r x Ra)
| Symbol | Meaning | Unit |
|---|---|---|
| f | Feed per revolution | in/rev or mm/rev |
| r | Tool nose radius | in or mm |
| Rmax | Theoretical peak-to-valley height | in or mm (shown in µin and µm) |
| Ra | Arithmetic average roughness, Rmax / 4 in the shop form | in or mm (shown in µin and µm) |
Ball end mill scallop
h = R - sqrt(R^2 - (s / 2)^2); s = 2 x sqrt(h x (2 x R - h))
| Symbol | Meaning | Unit |
|---|---|---|
| R | Ball radius, half the ball diameter | in or mm |
| s | Stepover between passes | in or mm |
| h | Scallop (cusp) height | in or mm |
Results in inches times 1,000,000 give µin; results in millimeters times 1,000 give µm; 1 µm is 39.37 µin. For small stepovers, h = s^2 / (8 x R) is a close shortcut.
Worked example: turning finish, inch
A 1/32 in (0.03125 in) nose radius at 0.006 IPR.
- f^2 = 0.006 x 0.006 = 0.000036.
- Rmax = 0.000036 / (8 x 0.03125) = 0.000036 / 0.25 = 0.000144 in = 144 µin.
- Ra = 0.000036 / (32 x 0.03125) = 0.000036 / 1.000 = 0.000036 in = 36 µin (0.91 µm).
- Geometric form: 0.000036 / (31.18 x 0.03125) = 37 µin.
Result: 36 µin Ra, theoretical.
Worked example: turning finish, metric
A 0.8 mm nose radius at 0.20 mm/rev.
- f^2 = 0.20 x 0.20 = 0.04.
- Rmax = 0.04 / (8 x 0.8) = 0.04 / 6.4 = 0.00625 mm = 6.25 µm.
- Ra = 0.04 / (32 x 0.8) = 0.04 / 25.6 = 0.0015625 mm = 1.56 µm.
Result: 1.56 µm Ra (62 µin), theoretical.
Worked example: feed for 63 µin Ra
A 1/32 in nose radius and a 63 µin Ra callout.
- Ra in inches: 63 µin = 0.000063 in.
- f = sqrt(32 x 0.03125 x 0.000063) = sqrt(0.000063).
- f = 0.0079 IPR.
Result: 0.0079 IPR theoretical. Start lighter; the measured finish runs rougher.
Worked example: scallop, inch
A 1/2 in ball end mill (R = 0.250 in) at 0.020 in stepover.
- (s / 2)^2 = 0.010^2 = 0.0001; R^2 = 0.0625.
- h = 0.250 - sqrt(0.0625 - 0.0001) = 0.250 - 0.2498 = 0.000200 in.
- Stepover for a 0.0001 in scallop: s = 2 x sqrt(0.0001 x 0.4999) = 0.0141 in.
Result: 0.0002 in scallop at 0.020 in stepover; 0.0141 in stepover for 0.0001 in.
Worked example: scallop, metric
A 10 mm ball end mill (R = 5 mm) at 0.5 mm stepover.
- (s / 2)^2 = 0.25^2 = 0.0625; R^2 = 25.
- h = 5 - sqrt(25 - 0.0625) = 5 - 4.99375 = 0.00625 mm.
Result: 0.0063 mm (6.25 µm).
Shop notes
- Real finish runs worse than theoretical from vibration, built-up edge, tool wear and machine condition. Light machines show it most.
- Wiper inserts do not follow the nose radius formula. Use the insert maker's data.
- The geometric form, Ra = f^2 / (18 x sqrt(3) x r) = f^2 / (31.18 x r), reads about 3% higher than the shop form: 37 µin instead of 36 µin in the first example.
- Drawings call out finish in µin Ra (US) or µm Ra (ISO). 63 µin is about 1.6 µm.
FAQ
How do you calculate surface finish from feed and nose radius?
Ra = f^2 / (32 x r). A 0.006 IPR feed with a 1/32 in nose radius gives 0.000036 in, or 36 µin Ra (0.91 µm), in theory.
What feed gives a 63 µin Ra finish?
With a 1/32 in nose radius, about 0.0079 IPR: f = sqrt(32 x 0.03125 x 0.000063). That is the theoretical feed; the part will measure rougher.
How do you calculate scallop height?
h = R - sqrt(R^2 - (s / 2)^2). A 1/2 in ball (R = 0.250 in) at 0.020 in stepover leaves 0.0002 in.
Why is the measured finish worse than the calculator says?
The formula covers tool geometry only. Chatter, built-up edge, tool wear and machine condition all add to it.
How do you convert Ra µm to µin?
Multiply by 39.37. The metric example gives 1.5625 µm Ra, shown as 1.56 µm: 1.5625 x 39.37 = 62 µin.
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