Surface Roughness Calculator

Compute key surface roughness parameters from profile height data. Visualize the surface profile and understand the meaning of Ra, Rq, Rz, and Rt. Essential for mechanical engineering, tribology, and quality control.

Enter at least 5 positive numbers representing profile heights (in micrometers).
? Ground finish
✨ Polished surface
⚙️ Milled surface
? Random profile
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Undestanding Surface Roughness

Surface roughness is a measure of the texture of a surface. It quantifies the vertical deviations of a real surface from its ideal form. Roughness is critical in applications involving friction, wear, lubrication, fatigue, and sealing. The most common parameters are defined in international standards (ISO 4287, ASME B46.1).

Ra = 1/n Σ |yi – ȳ|

Rq = √(1/n) Σ (yi – ȳ)²

Rz = max(y) – min(y)   (simplified)

Where yi are height values, ȳ is the arithmetic mean.

1. Ra – Arithmetic Mean Roughness

Ra is the most widely used parameter. It represents the average absolute deviation of the profile from the mean line. It is easy to measure and provides a general description of height variations. However, Ra does not distinguish between peaks and valleys and is insensitive to occasional high peaks or deep valleys. Typical Ra values:

  • Polished surface: 0.05 – 0.2 μm
  • Ground surface: 0.4 – 1.6 μm
  • Milled or turned: 1.6 – 6.3 μm
  • Rough cast: > 12.5 μm

2. Rq – Root Mean Square Roughness

Rq is the geometric average; it gives more weight to larger deviations than Ra. It is more sensitive to outliers and is often used in optical scattering and contact mechanics. For a Gaussian surface, Rq ≈ 1.11 × Ra, but this varies with profile shape.

3. Rz – Maximum Height (Simplified) and Standard Definition

In this calculator, we define Rz as the maximum peak-to-valley height (difference between highest and lowest point). The ISO standard Rz (sometimes called RzISO) is the average of the five largest peak-to-valley heights within a sampling length. For a quick estimate, the simplified version is often used in industry. Rt (total height) is identical to this simplified Rz, but some standards distinguish them.

4. Other Important Parameters

  • Rsk (Skewness): Indicates asymmetry of the profile. Negative skew means valleys dominate, positive skew means peaks dominate.
  • Rku (Kurtosis): Measures sharpness of the height distribution. Rku > 3 indicates spiky surfaces, < 3 indicates bumpy surfaces.
  • Rc, Rsm: Mean width of profile elements, related to spatial frequency.

5. Measurement Methods

Surface roughness is measured using contact profilometers (stylus) or optical methods (interferometry, confocal microscopy). The stylus traverses the surface, and the vertical displacement is recorded. The raw profile is then filtered to separate roughness from waviness and form. A cutoff filter (e.g., λc) is applied according to ISO 4288.

6. Applications and Selection of Parameters

  • Bearings and seals: Low Ra (≤0.2 μm) for smooth operation.
  • Fatigue-critical components: Rz and Rq are important because stress concentrations depend on peak heights.
  • Painting/coating: A certain roughness (Ra 2‑5 μm) ensures adhesion.
  • Optical surfaces: Rq is directly related to scatter (Total Integrated Scatter TIS ≈ (4π Rq / λ)²).
Case Study: Cylinder Liner Honing

In engine cylinder liners, a plateau‑honed surface is produced with deep valleys for oil retention and smooth plateaus for low friction. Typical roughness parameters: Ra ≈ 0.5 μm, Rz ≈ 5 μm, negative skew (Rsk < 0) and high kurtosis (Rku > 3). Our calculator can help compare measured profiles with specifications. For example, the preset "ground finish" approximates a honed surface.

How to Interpret the Profile Chart

The chart displays the height values (in μm) versus sample index. The horizontal line indicates the mean height. The difference between highest peak and deepest valley gives Rz (simplified). Ra and Rq are computed from deviations about the mean.

Filtering and Cutoff Wavelength

In practice, roughness is separated from waviness using a high-pass filter with a cutoff wavelength λc. The choice of λc depends on the surface type (ISO 4288). For example, for Ra 0.1‑2 μm, λc = 0.8 mm is typical. Our calculator does not apply filtering; it computes parameters directly from the raw heights. For accurate comparison with standards, ensure your data represents the roughness profile after appropriate filtering.

Common Pitfalls

  • Using too few points – at least 5‑10 per sampling length are needed.
  • Not removing form (e.g., curvature) – leads to overestimation of roughness.
  • Confusing Rz definitions – always specify whether it's maximum height or average of five peaks.

This tool is developed by GetZenQuery Tech team. Methodologies align with ISO 25178 and industry standards for surface texture analysis. Last reviewed: March 2026.

All calculations run locally; no data is collected.

Frequently Asked Questions (Extended)

Ra is the arithmetic mean of absolute deviations, while Rq is the root mean square (quadratic mean). Rq gives more weight to larger deviations, so for a surface with occasional spikes, Rq will be significantly higher than Ra. For a sinusoidal profile, Rq = (π/2) Ra ≈ 1.11 Ra.

At least 5‑10 points per sampling length are recommended, but modern profilometers acquire thousands of points. More points improve statistical significance. For a quick estimate, 10‑20 points can give a rough idea. Our calculator works with any number ≥ 2.

Rz (maximum height) is sensitive to the highest peak and deepest valley, while Ra averages all deviations. For most surfaces, Rz is 4‑10 times Ra. If the ratio is much larger, the surface may have isolated defects. Our simplified Rz uses the absolute max-min, which can be even larger than the ISO Rz (average of five).

According to ISO 4288, the cutoff λc should be chosen based on the expected Ra. For Ra 0.1‑2 μm, λc = 0.8 mm; for Ra 2‑10 μm, λc = 2.5 mm; for Ra >10 μm, λc = 8 mm. The evaluation length should include several sampling lengths (typically 5). Our calculator does not filter; use data already filtered by your profilometer.

This tool computes profile (2D) roughness from a line scan. For areal parameters (Sa, Sq, Sz, etc.), a 3D dataset is required. However, the formulas are analogous (e.g., Sa is the areal extension of Ra). We plan to release a 3D surface texture calculator soon.

Enter heights in micrometers (μm). Results are also in μm. 1 μm = 0.001 mm. Most roughness measurements are expressed in μm or microinches (1 μin = 0.0254 μm).
References: ISO 4287:1997 "Geometrical Product Specifications (GPS) – Surface texture: Profile method – Terms, definitions and surface texture parameters"; ASME B46.1-2019 "Surface Texture (Surface Roughness, Waviness, and Lay)"; Whitehouse, D.J. "Handbook of Surface and Nanometrology" (2nd ed., 2011); NIST Surface Roughness Calibrations.