Two tools for surface roughness. The first gives the commonly used approximation range between Ra and Rz, shown as a range because no fixed conversion exists. The second calculates the theoretical Ra and Rz of a turned surface from nose radius and feed, and the feed that a target Ra allows. Metric or inch. Runs entirely in your browser.
An approximation range, not an exact conversion. ISO 4287 defines Ra and Rz but gives no fixed ratio. Range from “Surface Texture From Ra to Rz”, Production Machining / Modern Machine Shop: a ratio range of 4:1 to 7:1 between Rz and Ra, with the actual profile shape having a significant impact and the ratio possibly much higher in the other direction.
The theoretical values describe the geometric cusps left by a round nose, valid for a feed well below the nose radius. Real surfaces are rougher. Background and typical finish by process: surface finish guide.
Ra and Rz are two different statistics of the same profile. Ra is the arithmetic mean deviation from the mean line, Rz is based on peak-to-valley heights over the sampling lengths, and both are defined in ISO 4287. Because they weigh the profile differently, the ratio depends on the profile shape, so we show a range rather than one number:
For a turned surface the ideal profile is the cusp left between two passes of a round nose of radius r moving f per revolution. Its geometry gives, for f small against r:
With f and r in mm the results are in mm, multiplied by 1000 for µm. In inch units the results are in inches, multiplied by 106 for microinches. Conversion used: 1 µin = 0.0254 µm.
Halving the feed cuts the theoretical Ra by a factor of four, while doubling the nose radius halves it. That is why the nose radius is the first lever for a finer finish, and why a worn or chattering setup never reaches the calculated value.
No. ISO 4287 defines both parameters, but it does not define a fixed ratio between them, because the ratio depends on the shape of the profile. This page therefore shows an approximation range. A published rule of thumb puts Rz at about 4 to 7 times Ra, and the ratio can be higher on some profiles. If a drawing calls for Rz, measure Rz.
The ideal profile left by a round nose is a series of cusps. Its peak-to-valley height is Rt = f² / (8 × r) and its mean roughness is Ra = f² / (32 × r), with f the feed per revolution and r the nose radius, in the same length unit. At f = 0.2 mm and r = 0.8 mm that gives Rt = 6.25 µm and Ra = 1.56 µm.
The formulas describe the geometric cusps only. Built-up edge, flank wear, vibration, a soft or sticky material and a nose radius that is large for the setup add roughness on top, so treat the result as the best finish the geometry allows, not a guarantee. Our surface finish guide covers the levers in more detail.
The formulas set the floor; the insert geometry, grade and the rest of the setup decide whether you reach it. Ask the advisor for a grounded, brand-neutral recommendation.
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