Use the calculator below to help select a tool nose radius for turning. In practice, nose radius is a tool geometry choice: you can estimate the nose radius required to achieve a target theoretical surface finish (Ra) from feed rate (Surface Finish tab), and you can use depth of cut as a guideline for choosing a reasonable starting-point radius (Nose Radius tab).
- Chip Per Tooth Calculator
- Feed Rate Calculator
- Feed Per Tooth Calculator
- All Miscellaneous Calculators
Tool Nose Radius Formula
A common ideal geometric relationship between feed per revolution, tool nose radius, and arithmetic average roughness in turning is:
Ra \approx \frac{f^2}{32\,r} \quad \Rightarrow \quad r \approx \frac{f^2}{32\,Ra}Variables:
- r is the tool nose radius (mm or in)
- f is the feed per revolution (mm/rev or in/rev)
- Ra is the arithmetic average surface roughness (in the same length units as f and r; commonly reported as µm or µin)
To estimate the nose radius required for a target Ra, square the feed per revolution and divide by (32 × Ra). This gives an idealized (geometry-only) estimate; real surface finish also depends on material, tool wear, vibrations/chatter, cutting speed, and edge preparation.
What is a Tool Nose Radius?
The tool nose radius is the radius of the rounded tip of a cutting tool used in turning operations. It is an important parameter that affects the surface finish of the machined part, the cutting forces, and the tool life. A larger nose radius can improve the surface finish and distribute the cutting forces over a larger area, reducing wear on the tool. However, it may also require more cutting power and could lead to chatter or poor surface finish if not matched with the appropriate feed rate and cutting conditions.
How to Calculate Tool Nose Radius?
The following steps outline how to estimate the Tool Nose Radius from a target theoretical surface finish.
- Determine the feed per revolution (f), for example in mm/rev.
- Determine your target surface roughness (Ra), and convert it to the same length unit system as f (e.g., µm to mm).
- Use the formula: r ≈ f² / (32 × Ra).
- Calculate the tool nose radius (r) and then select the nearest available standard insert radius.
- Optionally, use depth of cut as a guideline for tool strength/stability (see the Nose Radius tab), and verify results with the calculator above.
Example Problem :
Use the following variables as an example problem to test your knowledge.
Feed per revolution (f) = 0.2 mm/rev
Desired surface roughness (Ra) = 1.6 µm, giving nose radius r ≈ 0.7813 mm (≈ 0.8 mm standard).
