Used and loved by millions
Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com
arithmetic mean roughness
Grammar usage guide and real-world examplesUSAGE SUMMARY
The phrase "arithmetic mean roughness" is correct and usable in written English.
It is typically used in contexts related to surface roughness measurements in engineering and manufacturing. Example: "The arithmetic mean roughness of the surface was measured to ensure it met the required specifications for the product."
✓ Grammatically correct
Science
Alternative expressions(3)
Table of contents
Usage summary
Human-verified examples
Expert writing tips
Linguistic context
Ludwig's wrap-up
Alternative expressions
FAQs
Human-verified examples from authoritative sources
Exact Expressions
7 human-written examples
Coatings with a maximum universal hardness HU = 25 GPa and arithmetic mean roughness Ra = 0.03 μm could be deposited.
We conclude that the arithmetic mean roughness parameter is suitable for relating bare laminate surface roughness to final paint quality with roughness thresholds being developed.
Open image in new window Fig. 2 Surface roughness average (Ra): the arithmetic mean roughness of all points from a plane (centre line) fitted to the test surface .
Implant surface roughness was measured using a laser scanning microscope VK-97100, Keyence, Osaka, Japan), and the arithmetic mean roughness (Ra) was found to be 0.16 μm.
(c) Arithmetic mean roughness (R a ): the average roughness or deviation of all points from a plane (centre line) fitted to the test surface (Fig. 2).
It is suggested that such an approach provides better correlation between the bondcoat morphology and thermal barrier coating-lifetime than the calculation of the arithmetic mean roughness (Ra) of the bondcoat frequently used in industrial practice.
Human-verified similar examples from authoritative sources
Similar Expressions
53 human-written examples
In efforts to precisely predict and compare few significant WEDM machinability aspects like surface roughness [arithmetic mean roughness (Ra), root mean square roughness (Rq) and maximum peak-to-valley height (Rz)] and micro-hardness (MH) of shape memory alloy nitinol, general regression neural network (GRNN) model was developed.
Science
Arithmetic mean surface roughness (Ra) and maximum peak to valley height (Rz) are used as response variables to assess the surface roughness of incrementally formed parts.
Ra is the arithmetic mean surface roughness in nanometers.
Science
The arithmetic mean surface roughness of four regions with different stress levels was measured at incremental fatigue cycles until the fracture of the specimen.
Attempts were made to correlate the arithmetic mean surface roughness Ra and the 10-point height values Rz of atmospheric plasma-sprayed (APS) chromium oxide coatings with fractal properties such as the relative area for 2 μm2 patch size (RAPS), the smooth-rough crossover (SRC) and the area-scaled fractal complexity (ASFC).
Expert writing Tips
Best practice
When reporting "arithmetic mean roughness" values, always include the units of measurement (e.g. micrometers, nanometers) to ensure clarity and avoid misinterpretation.
Common error
Avoid using "arithmetic mean roughness" interchangeably with other roughness parameters like root mean square roughness (RMS or Rq) or maximum peak-to-valley height (Rz). Each parameter provides different information about the surface texture, so using the correct one is crucial for accurate analysis.
Source & Trust
83%
Authority and reliability
4.1/5
Expert rating
Real-world application tested
Linguistic Context
The phrase "arithmetic mean roughness" functions as a technical term, specifically a noun phrase, in engineering and scientific contexts. As Ludwig AI suggests, this phrase is used to define a specific measurement of surface texture. The phrase identifies a quantified attribute.
Frequent in
Science
100%
Less common in
News & Media
0%
Formal & Business
0%
Academia
0%
Ludwig's WRAP-UP
The phrase "arithmetic mean roughness" is a technical term used to quantify the texture of a surface. As Ludwig AI confirms, it's grammatically correct and most commonly encountered in scientific contexts. "Arithmetic mean roughness", often abbreviated as Ra, is the average of the absolute values of the height deviations measured from the mean line of the roughness profile, providing a general measure of surface texture. Alternatives include "average surface roughness" or "mean surface roughness". When using this term, remember to specify the units of measurement and avoid confusing it with other roughness parameters like RMS or Rz.
More alternative expressions(6)
Phrases that express similar concepts, ordered by semantic similarity:
average surface roughness
Focuses on the general concept of average roughness, omitting the specific type of average.
mean surface roughness
Reorders the words while retaining the same meaning.
Ra roughness parameter
Uses the symbol 'Ra' to represent arithmetic mean roughness.
roughness average
A shorter version omitting "arithmetic mean".
average profile roughness
Emphasizes that the roughness is derived from a profile measurement.
surface finish average
Refers to the smoothness of a surface in terms of its average variations.
center line average roughness
Specifies that the roughness is measured relative to the center line.
texture average roughness
Specifically relates to the average roughness of surface texture.
Rq root mean square roughness
Uses a different statistical measure of roughness.
ten-point average roughness
Refers to the average of the five highest peaks and five lowest valleys within a sampling length.
FAQs
How is "arithmetic mean roughness" (Ra) calculated?
The "arithmetic mean roughness", often denoted as Ra, is calculated as the average of the absolute values of the height deviations measured from the mean line of the roughness profile. It provides a general measure of surface texture.
What are some alternatives to using the term "arithmetic mean roughness"?
Depending on the context, you can use alternatives such as "average surface roughness" or "mean surface roughness". The abbreviation Ra is also commonly used.
What is the difference between "arithmetic mean roughness" and root mean square roughness?
"Arithmetic mean roughness" (Ra) calculates the average of the absolute values of the height deviations, while root mean square roughness (Rq) calculates the square root of the average of the squared height deviations. Rq is more sensitive to large peaks and valleys, providing a different perspective on surface texture.
In what fields is the term "arithmetic mean roughness" commonly used?
The term "arithmetic mean roughness" is frequently used in fields like materials science, engineering, manufacturing, and tribology to characterize surface texture and assess the quality of surface finishes.
Editing plus AI, all in one place.
Stop switching between tools. Your AI writing partner for everything—polishing proposals, crafting emails, finding the right tone.
Table of contents
Usage summary
Human-verified examples
Expert writing tips
Linguistic context
Ludwig's wrap-up
Alternative expressions
FAQs
Source & Trust
83%
Authority and reliability
4.1/5
Expert rating
Real-world application tested