Enter profile data
Paste equally spaced height samples (one profile). Values can be separated by commas or new lines.
Formula used
- Mean line: \u03BC = (1/n)\u2211 zi, deviations yi = zi \u2212 \u03BC.
- Ra: Ra = (1/n)\u2211 |yi|.
- Rq: Rq = \u221a[(1/n)\u2211 yi2].
- Rt: Rt = max(y) \u2212 min(y).
- Rp, Rv: Rp = max(y), Rv = |min(y)|.
- Rz (discrete): average of top N peaks plus average valley depth of bottom N samples.
- Skewness: Rsk = [(1/n)\u2211 yi3] / Rq3.
- Kurtosis: Rku = [(1/n)\u2211 yi4] / Rq4.
- Mean abs slope: Sa = mean(|\u0394y/\u0394x|), with dx given.
- Profile length: Lp \u2248 \u2211\u221a(dx\u00b2 + \u0394y\u00b2).
Note: Standards define filtering and sampling rules. This tool applies discrete formulas directly to your samples.
How to use this calculator
- Measure a surface profile and export height samples.
- Paste the height values into the input box.
- Select input and output units for the report.
- Set Rz N to match your preferred peak count.
- Optionally enter dx to compute slope and length data.
- Press Calculate to view results above the form.
- Use the CSV or PDF buttons for documentation.
Example data table
Sample heights in µm (mean-line deviations computed internally).
| # | Height (µm) |
|---|---|
| 1 | 0.2 |
| 2 | -0.15 |
| 3 | 0.05 |
| 4 | -0.3 |
| 5 | 0.1 |
| 6 | 0.25 |
| 7 | -0.05 |
| 8 | 0.18 |
| 9 | -0.22 |
| 10 | 0.12 |
| 11 | -0.08 |
| 12 | 0.06 |
Try pasting the example values into the calculator to reproduce them.
Surface roughness interpretation guide
1) What this tool measures
Surface roughness describes small height variations that affect friction, sealing, wear, and optical scatter. This calculator converts your height profile into standard amplitude statistics (Ra, Rq, Rz, Rt) and shape descriptors (Rsk, Rku). It operates directly on the samples you paste, after defining a mean reference line.
2) Mean line and deviations
Many instruments export absolute heights. Roughness parameters are typically evaluated about a reference line, so the calculator forms deviations yi = zi − μ, where μ is the average height of the pasted series. If you already supply deviations, enabling mean removal keeps the profile centered without changing its spread.
3) Ra versus Rq
Ra is the arithmetic mean of absolute deviations and is widely reported for machined surfaces. Rq is the root-mean-square deviation and weights larger peaks or valleys more strongly. For many near-Gaussian surfaces, Rq is about 1.25×Ra, but non‑Gaussian textures can deviate substantially.
4) Rz, Rp, Rv, and Rt
Peak and valley behavior matters for contact and leakage. Rp is the highest peak above the mean line, Rv is the deepest valley magnitude, and Rt is the full peak‑to‑valley range. Rz here is computed discretely as the mean of the top N peaks plus the mean depth of the bottom N valleys, useful when isolated extremes should not dominate.
5) Skewness and kurtosis with real meaning
Rsk indicates whether the profile is peak‑dominated (positive) or valley‑dominated (negative). Valley‑dominated textures can retain lubricant but may reduce sealing performance. Rku quantifies tail heaviness: values near 3 suggest Gaussian‑like behavior, while higher values indicate more outliers that can accelerate wear or initiate cracks.
6) Sampling interval and slope metrics
When you provide dx, the calculator estimates mean absolute slope (Sa) and RMS slope (Sq) from successive points. These help compare textures with similar Ra but different sharpness. It also approximates developed profile length Lp and the length ratio Lp/L, where L is the projected length, highlighting how “wrinkled” the profile is.
7) Practical data quality checks
Use enough samples to represent the texture; very short series can produce unstable Rz, Rsk, and Rku. Remove obvious spikes from measurement glitches before analysis. If you apply filtering in your instrument software, document it, because filtering changes Ra and Rq noticeably by suppressing longer‑wavelength waviness components.
8) Reporting and engineering decisions
When specifying surfaces, report units, sampling length, and whether the profile was filtered. For sealing faces, combine Ra with peak/valley metrics such as Rt and Rz. For sliding contacts, consider Rsk and Rku to anticipate asperity contact severity. Exporting CSV or PDF from this tool helps keep results consistent across inspections.
FAQs
1) What is the difference between roughness and waviness?
Roughness covers short‑wavelength texture from machining or polishing. Waviness is longer‑wavelength form variation from vibration, tool deflection, or thermal drift. Filtering separates them, and the reported parameters depend on that separation.
2) Why does Rq often exceed Ra?
Rq squares deviations before averaging, so larger peaks and valleys contribute more. If the distribution has occasional high asperities, Rq increases faster than Ra, making Rq more sensitive to outliers.
3) How should I choose N for Rz?
Common practice uses 5 peaks and 5 valleys, but you can increase N for noisy data to reduce sensitivity to single extremes. Keep N much smaller than your total sample count for meaningful averaging.
4) What does negative skewness imply?
Negative Rsk means valleys dominate over peaks relative to the mean line. This can improve lubricant retention and reduce initial contact area, but it may also indicate deep scratches that compromise sealing or fatigue strength.
5) What does a high kurtosis value suggest?
High Rku indicates heavy tails: more extreme asperities than a Gaussian profile. Such surfaces may show intermittent high contact stress, increasing wear risk. Verify with repeated measurements to rule out instrument spikes.
6) Do I need dx to compute Ra and Rq?
No. Ra, Rq, and the peak/valley metrics use the height values only. dx is needed for slope estimates and length ratio calculations, which add information about sharpness and developed profile length.
7) How many points should I paste for reliable results?
More is usually better. Aim for at least a few hundred points when available, especially if you use Rz, Rsk, or Rku. Very short profiles can vary widely between runs and may not represent the surface well.