Calculate surface roughness by finding missing Ra, Rz, or unitless k from any two inputs and converting between µm, mm, and in units.
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Surface Roughness Formula
The calculator uses the relationship between average roughness Ra, maximum height parameter Rz, and the conversion factor k.
- Ra = average roughness, usually measured in micrometers, millimeters, or inches
- Rz = maximum height parameter, usually measured in micrometers, millimeters, or inches
- k = conversion factor, equal to Rz divided by Ra
The calculator lets you enter any two of the three values and solves for the missing one.
- If Ra is missing, it uses Ra = Rz / k.
- If Rz is missing, it uses Rz = k × Ra.
- If k is missing, it converts Ra and Rz to the same unit, then uses k = Rz / Ra.
Ra and Rz must be in compatible length units before comparing them. The calculator converts roughness values internally to micrometers, then converts the result back to the unit you selected.
Common Surface Roughness Conversion Factors
The factor k is not a fixed constant for every surface. It depends on the machining process, surface profile, and measurement standard. For rough estimation, Rz is often several times larger than Ra.
| Surface/profile condition | Typical k range | Meaning |
|---|---|---|
| Fairly uniform machined surface | 4 to 5 | Rz is about 4 to 5 times Ra |
| General approximation | 5 to 7 | Common estimate when only one roughness parameter is known |
| Irregular surface profile | 7 to 10+ | Peaks and valleys are more extreme relative to the average |
Roughness Unit Conversions
| Unit | Equivalent in micrometers |
|---|---|
| 1 µm | 1 µm |
| 1 mm | 1000 µm |
| 1 in | 25,400 µm |
Surface Roughness Examples
Example 1: Calculate Rz from Ra and k
You have an average roughness of Ra = 1.6 µm and a conversion factor of k = 5.
The maximum height parameter is Rz = 8.0 µm.
Example 2: Calculate k from Ra and Rz
You have Ra = 0.8 µm and Rz = 4.8 µm.
The conversion factor is k = 6.
FAQ
What is the difference between Ra and Rz?
Ra is the average roughness of a surface. It represents the average deviation of the surface profile from the mean line. Rz is a height-based roughness parameter that reflects peak-to-valley behavior over the measured length. Because Rz is based on larger profile height differences, it is usually greater than Ra.
Can you convert Ra to Rz exactly?
Not exactly from Ra alone. The same Ra value can come from different surface profiles, and those profiles may have different Rz values. The calculator uses the factor k = Rz / Ra, so the accuracy depends on choosing a suitable k value for the surface or process.
Why does the calculator require exactly two values?
The relationship has three variables: Ra, Rz, and k. Any two values define the third. If you enter fewer than two values, there is not enough information to solve the equation. If you enter all three, there is no single missing value to calculate.
