Free Engineering Tool
Estimate theoretical surface roughness from feed per revolution and tool nose radius, with output in micrometres and microinches.
This tool models the ideal geometric feed marks produced by a turning or boring insert. It is useful for choosing feed and nose radius, then verifying the real surface with a profilometer.
Surface finish Ra is the arithmetic average roughness of a measured profile, commonly reported in micrometres (µm) or microinches (µin). For an ideal turning or boring cut, a useful geometric estimate is Ra ≈ f² / (32 × r), where f is feed per revolution and r is the tool nose radius in the same length unit. A 0.2 mm/rev feed with a 0.4 mm nose radius gives about 0.003125 mm, or 3.125 µm Ra; the ideal peak-to-valley value is about 12.5 µm. Larger nose radius or lower feed reduces the calculated feed-mark height, but cutting force, chatter, built-up edge, tool wear and material behaviour also control the measured result. Ra and Rz use different profile definitions and should not be converted with one universal multiplier. Zhejiang Balford Mechatronics Co., Ltd. reviews machined surfaces at its 12,000 m² production facility against the drawing and an agreed measurement method.
This is an ideal geometric estimate derived from feed marks. Real surface finish also depends on tool wear, built-up edge, vibration, material inclusions, coolant, cutting speed, depth of cut and machine rigidity. Use a profilometer and a trial cut for acceptance.
The formula describes the ideal geometric roughness left by feed marks. It is a process-starting calculation rather than a predicted measured value.
| Feed per revolution | Theoretical Ra | Theoretical Rmax | Relative effect |
|---|---|---|---|
| 0.05 mm/rev | 0.195 µm | 0.781 µm | Very light finishing feed |
| 0.10 mm/rev | 0.781 µm | 3.125 µm | Fine finishing range |
| 0.15 mm/rev | 1.758 µm | 7.031 µm | Fine-to-medium finishing |
| 0.20 mm/rev | 3.125 µm | 12.500 µm | Common finishing-starting point |
| 0.30 mm/rev | 7.031 µm | 28.125 µm | Roughing or medium finish |
| 0.40 mm/rev | 12.500 µm | 50.000 µm | Coarser feed-mark height |
Ideal geometry only. Real measured values can be higher or lower because of tool wear, built-up edge, vibration, material inclusions, coolant and machine rigidity.
A turning operation uses 0.2 mm/rev feed and a 0.4 mm nose radius. Theoretical Ra = 0.2² / (32 × 0.4) = 0.003125 mm = 3.125 µm = 123.0 µin. The ideal peak-to-valley estimate is 12.5 µm.
For an ideal turning or boring cut, theoretical average roughness can be estimated as Ra ≈ f² / (32 × r), where f is feed per revolution and r is the tool nose radius. Both dimensions must use the same length unit; the result is then converted to micrometres or microinches.
At the same feed, a larger nose radius reduces theoretical peak-to-valley height and Ra because the feed marks become shallower. It can also increase cutting force, chatter risk and part deflection, so a larger radius is not automatically better for every operation.
Lower feed normally reduces the geometric feed-mark height, but measured finish can stop improving or worsen because of built-up edge, tool wear, rubbing, vibration or insufficient chip thickness. The formula describes geometry, not the complete cutting process.
Ra is the arithmetic average roughness over the measured profile. Rz is a peak-to-valley height descriptor and its exact definition depends on the reporting standard. They are not interchangeable, and a fixed conversion factor is not safe for drawing acceptance.
No. It estimates the ideal geometric result from feed marks. Actual acceptance requires a traceable profilometer measurement, a defined cutoff and evaluation length, and a representative trial cut using the specified material, tool, coolant and machine process.
Send the drawing, material, measured or required Ra, evaluation method and the machining feature. Send the drawing to shawn@balford.net. We normally reply within 24 hours, China Standard Time.