Turning Surface Roughness Calculator
Theoretical Ra and Rz from feed and tool nose radius, and the feed needed to hit a target roughness.
Results
What this tool does
The finish left by a turning tool is a row of identical scallops, each one the shape of the tool nose, spaced one feed apart. The geometry alone fixes their depth: halve the feed and the roughness drops to a quarter, while doubling the nose radius halves it. That is why a finishing pass uses a fine feed and a generous nose radius, and why an unexpectedly rough part is usually a feed override left switched on.
Formula
Ra = f² / (32 r) ; Rz = f² / (8 r)
Variables
| Symbol | Meaning | Unit |
|---|---|---|
ff | Feed per revolution | mm |
nr | Tool nose radius | mm |
ra | Target roughness | µm |
RA | Theoretical Ra | µm |
RZ | Theoretical Rz | µm |
FM | Feed for the target roughness | mm |
Worked example
- Feed per revolution0.2 mm
- Tool nose radius0.8 mm
- Target roughness1.6 µm
- Theoretical Ra1.5625 µm
- Theoretical Rz6.2500 µm
- Feed for the target roughness0.2024 mm
Limitations
- The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.
- Coverage and consumption figures vary between products. Take the values from the manufacturer's datasheet for the product you are actually using.
Frequently asked questions
Why is the real surface always rougher than this?
This is the geometric roughness alone: the trace the tool nose leaves as it advances, and nothing else. Built-up edge, vibration, tool wear, insufficient cutting speed and an unstable set-up all add on top of it. Take the calculated value as the floor you cannot go below with that feed and that nose radius, then expect to land somewhat above it.