How Surface Height Is Quantified — From Ra to Rz

Surface roughness parameters play a critical role in product performance and quality control. They influence decisions made based on:

• Friction and wear
• Coating adhesion
• Lubrication retention
• Optical performance
• Sealing behavior
• Fatigue life

As a result, they are widely used in industries such as:

• Precision machining
• Automotive
• Semiconductor manufacturing
• Aerospace
• Additive manufacturing
• Medical device production

To ensure consistency and traceability, surface roughness parameters are defined and standardized in international specifications, including ISO 29120 for profile (2D) parameters, ISO 25178 for areal (3D) surface texture parameters, and ASME B46.1 for surface texture measurement and reporting. These standards define not only the parameters themselves, but also how surfaces should be filtered, measured, and reported to ensure meaningful and repeatable results across different instruments and facilities.

By selecting the appropriate roughness parameters and measurement method, engineers can better link surface texture to functional requirements - turning surface metrology results into simple, tangible next steps to solve root problems both quickly & effectively.

Ra is best for quick comparisons,
Rz highlights outliers and surface damage, and
Sa provides a more complete representation of complex or textured surfaces.

Definition:

Ra is the arithmetic mean of the absolute values of surface height deviations from the mean line over the evaluation length. This is defined by the equation shown below:

Where:

• L = evaluation length
• z(x) = vertical deviation of the surface profile from the mean line

In practice, for discrete measured data points, Ra is calculated as:

Where:

• N = number of sampled points
• z_i = height deviation of each point from the mean line

Average roughness (Ra) describes how much a surface’s height varies, on average, from its mean line. Put simply, Ra answers the question: “How rough is this surface overall?”

Rather than focusing on individual peaks or valleys, Ra averages the absolute height deviations across a defined evaluation length. This makes it easy to compare surfaces and set general finish requirements without analyzing every microscopic feature.

Because of its simplicity and long history, Ra is the most commonly specified surface roughness parameter on engineering drawings and inspection reports. It is widely used for:

• General machining quality checks
• Incoming inspection and supplier qualification
• Trend monitoring in production environments

However, Ra does not describe surface shape or extremes. Two surfaces can have the same Ra value while exhibiting very different textures, such as one dominated by sharp peaks and another by deep valleys.

While Ra is useful, it can be misleading for functional surfaces. It does not account for:

• Peak sharpness or valley depth
• Surface directionality or lay
• Local defects such as scratches or pits

For applications involving sealing, lubrication retention, wear performance, or optical quality, engineers often supplement Ra with additional parameters such as Rz, Rq, Rp, or 3D areal parameters defined in ISO 25178.

Modern non-contact optical profilometers and 3D surface measurement systems (such as the VK-X3000 Series) make it possible to capture full 3D surface topography, enabling engineers to move beyond a single roughness number and correlate surface texture with real-world performance quickly & accurately.

Definition:

Under ISO 21920-2, Rz is defined as the mean height of profile elements, calculated from individual sampling lengths within the evaluation length.

Where each profile element height Z_i is:

Where:

• n = number of sampling lengths within the evaluation length
• Z_p,i = height of the highest profile peak within sampling length i
• Z_v,i = depth of the deepest profile valley within sampling length i
• All heights are measured relative to the mean line of each sampling length

In most practical measurements, n = 5, but ISO 21920 allows this to be defined by the selected evaluation length and filter settings.

Where:

• Z_p,i = height of the highest peak in the i-th sampling length
• Z_v,i = depth of the deepest valley in the i-th sampling length

Each peak-to-valley value is measured relative to the mean line within its sampling length.

Definition:

In ASME B46.1, Rz is often defined as the average difference between the five highest peaks and five deepest valleys over the evaluation length:

Where:

• P_i = height of the i-th highest peak
• V_i = depth of the i-th deepest valley

Because these two definitions are not mathematically identical, it is critical to specify the standard used when reporting Rz values.

In practical terms, Rz answers the question: “How tall are the peaks and how deep are the valleys?”

Rz can be more sensitive to noise or isolated defects than Ra and should be interpreted alongside other parameters. Because it focuses on surface extremes, Rz is well suited for:

• Detecting scratches, dents, and machining marks
• Evaluating sealing and contact surfaces
• Monitoring tool wear and process instability

Rz is commonly specified when:

• Excessive peaks may cause wear or sealing failure
• Valley depth affects lubrication or coating behavior
• Surface defects must be tightly controlled

For complex or functional surfaces, engineers increasingly supplement Rz with 3D areal parameters (Sz, Sa, Sq) obtained from optical surface metrology systems. We’ll cover those in more detail in a future article.

Definition:

Rq (or RMS roughness) is the square root of the mean of the squared height deviations.

Where:

• Rq = root mean square roughness (µm)
• L_t = evaluation length (after filtering, ISO 21920 defines cut-offs and profile separation)
• z(x) = height deviation from the mean line at position x

Interpretation:

Because it squares the deviations, Rq gives more weight to larger peaks and valleys than Ra. It’s particularly useful when extreme variations are important.

Use Cases:

• Optical components and semiconductor wafers.
• Coating adhesion studies.
• Fatigue analysis where micro-defects can act as stress concentrators.

Definition:

Rp measures the distance from the mean line to the highest peak within the evaluation length.

Interpretation:

Rp emphasizes surface protrusions, which are critical in cases where peaks can cause premature wear or affect coating thickness uniformity.

Use Cases:

• Coating adhesion and paint coverage control.
• Contact-sensitive surfaces (optical mounts, lenses).
• Wear-resistant component design.

Definition:

Rv is the distance from the mean line to the deepest valley in the evaluation length.

Interpretation:

Rv indicates the depth of surface depressions and is especially relevant for lubrication retention, fatigue initiation, and sealing performance.

Use Cases:

• Oil-retaining surfaces (engine components, bearings).
• Analyzing defects caused by pitting or corrosion.
• Evaluating post-polish surface integrity.

Definition:

Rt is the vertical distance between the highest peak and lowest valley over the entire evaluation length.

Interpretation:

Rt reflects the most extreme surface feature combination which is useful for identifying defects, scratches, or tool marks that exceed tolerance limits.

Use Cases:

• Outlier detection in precision machining.
• High-spec inspection for aerospace and optical components.
• Ensuring no catastrophic peaks or valleys compromise sealing or wear.

The VK-X3000 Series 3D Surface Profiler features an advanced software function that automatically analyzes data from two or more surfaces and identifies which roughness parameters show the greatest differences between them. In addition, comprehensive data can be output for dozens of parameters, ensuring you have the detailed insight needed to make confident, informed decisions without needing to be an expert on roughness measurements.