Theoretical Surface Roughness Ra Calculator for Turning
Optimize your machining processes with our online cutting parameters calculator. Select the operation type (turning, milling, drilling or threading) and instantly get the critical calculations for your shop: cutting speed (Vc), revolutions per minute (RPM), feed per revolution or per tooth, machining time and the theoretical roughness (Ra / Rz) based on the insert nose radius. To fine-tune those values live at the machine, use the interactive machining calculator.
Cutting calculator
Which operation are you machining?
What do you want to calculate?
Configura rugosidad teórica
Formula
Result
Ra teórica
1.27µm
Rz aprox.: 5.06 µm
Material, power and warnings
Pick material and tool: that gives you the Vc and feed ranges, and also whether your machine can take the cut.
Power, torque and warnings
RPM and feed only tell you how fast it spins. This tells you whether your machine can take it: metal removal rate, the power you have to ask of the spindle, torque and the process warnings that usually cost you a tool.
Pick a material above to estimate power: the specific cutting force depends on it.
Fill in material, diameter, Vc/RPM and feed to see the power.
Rough estimate: kc1.1 is defined per material family and the tool's real geometry matters. Use it to decide whether a cut fits the machine, not as a substitute for a dry run.
Do you want to adjust these values live?
Here you get the recommendation (Vc, feed, roughness, threading). In the interactive machining calculator you can move Vc, diameter, RPM and feed with linked scales, locks and time/power estimation.
Open interactive calculator →Surface roughness in turning: formula, example and table
Ra ≈ f² × 1000 / (32 × r)
Theoretical Ra in µm from the feed f (mm per revolution or per tooth) and the nose or corner radius r in mm. The real finish is worse with vibration, built-up edge or a worn insert; take the table as the best case in turning.
Worked example: f 0.15 mm and r 0.8 mm → Ra ≈ 0.15² × 1000 / (32 × 0.8) = 0.88 µm.
In turning, roughness is set almost only by the feed and the nose radius: doubling the radius halves Ra, doubling the feed multiplies it by four. Wiper inserts let you double the feed for the same Ra; always check the first part with a roughness tester.
| Feed f (mm) | Ra r 0.2 (µm) | Ra r 0.4 (µm) | Ra r 0.8 (µm) | Ra r 1.2 (µm) |
|---|---|---|---|---|
| 0.05 | 0.39 | 0.2 | 0.1 | 0.07 |
| 0.1 | 1.56 | 0.78 | 0.39 | 0.26 |
| 0.15 | 3.52 | 1.76 | 0.88 | 0.59 |
| 0.2 | 6.25 | 3.13 | 1.56 | 1.04 |
| 0.25 | 9.77 | 4.88 | 2.44 | 1.63 |
| 0.3 | 14.06 | 7.03 | 3.52 | 2.34 |
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