Enter the average roughness and the maximum roughness depth into the calculator to determine the surface roughness; this calculator can also evaluate any of the variables given the others are known.

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## Surface Roughness Formula

The following formula is used to calculate the surface roughness:

SR = (Ra + Rz) / 2

Variables:

- SR is the surface roughness
- Ra is the average roughness
- Rz is the maximum roughness depth

To calculate the surface roughness, add the average roughness and the maximum roughness depth, then divide the sum by 2.

## What is a Surface Roughness?

Surface roughness, also known as surface texture, is a measure of the texture and roughness of a given surface. It is a critical aspect in many manufacturing processes and has significant implications on the performance, appearance, and wear resistance of a product or component. Surface roughness is typically quantified by the deviations in the direction of the normal vector of a real surface from its ideal form. If these deviations are large, the surface is rough; if they are small, the surface is smooth. These deviations can be due to a variety of factors, including the material properties, the type of manufacturing process used, and the environmental conditions during manufacturing. Surface roughness can be measured using a variety of techniques, including contact methods (such as stylus profilometers) and non-contact methods (such as optical profilometers and interferometers).

## How to Calculate Surface Roughness?

The following steps outline how to calculate the Surface Roughness:

- First, measure the surface profile using a suitable instrument.
- Next, calculate the average roughness (Ra) by finding the arithmetic mean of the absolute values of the profile deviations from the mean line.
- Next, calculate the root mean square roughness (Rq) by finding the square root of the average of the squares of the profile deviations from the mean line.
- Finally, calculate the maximum roughness (Rmax) by finding the maximum peak-to-valley height within the measured profile.
- After performing the calculations, compare the results with the specified surface roughness requirements.

**Example Problem:**

Use the following variables as an example problem to test your knowledge.

Measured surface profile: [2, 4, 1, -3, 0, 5, -2, 1]

Calculate the average roughness (Ra), root mean square roughness (Rq), and maximum roughness (Rmax).