Convert Ra to Rz or Rz to Ra using a typical roughness factor (4–7, default 5.5) or your own, or calculate Ra and Rq from profile height samples.

There is no exact Ra–Rz conversion; the result is an estimate that depends on the factor.

Common rule of thumb: Rz ≈ 4–7 × Ra. 5.5 is the midpoint; enter your own factor if you know it for your surface.

Optional settings

Related Calculators

Surface Roughness Formula

The estimate modes relate arithmetic mean roughness Ra and the height-based parameter Rz using an explicitly assumed, dimensionless factor k. This algebra is a profile-dependent estimate, not an exact conversion between roughness parameters.

k = Rz / Ra
Rz = k × Ra
Ra = Rz / k
  • Ra = arithmetic mean roughness; enter it in µm, µin, or mm
  • Rz = height-based roughness parameter whose exact definition depends on the measurement standard; enter it in µm, µin, or mm
  • k = assumed Rz/Ra ratio; matched measurements can inform a factor, but there is no universal value

Choose a solve mode. The two estimate modes require one known roughness parameter and a positive assumed factor. The raw-sample mode uses a list of heights instead; the calculator does not solve for k.

  • Estimate Ra from Rz and k using Ra = Rz / k.
  • Estimate Rz from Ra and k using Rz = k × Ra.
  • Summarize supplied height samples using centered, equally weighted raw-sample Ra, Rq and peak-to-valley statistics.

Ra and Rz must be in compatible length units before comparing them. The calculator converts roughness values internally to micrometers, then converts the result back to the unit you selected.

Illustrative Rz/Ra Factor Assumptions

The factor k is not fixed across surfaces. Profile shape and the chosen measurement definition matter: the same Ra can correspond to different Rz values. The following numbers are illustrative assumptions for sensitivity calculations, not validated process ranges or specification limits. Use matched measurement evidence for the intended surface and conditions. Kemet explains the distinction between Ra, Rz and Rq.

Illustrative scenario Assumed k range Meaning
Lower-factor assumptions 4 to 5 The estimated Rz is 4 to 5 times the entered Ra
Middle-factor assumptions 5 to 7 Sensitivity arithmetic only; not a validated default range
Higher-factor assumptions 7 to 10+ A larger assumed k increases estimated Rz; it does not diagnose a profile

Roughness Unit Conversions

Unit Equivalent in micrometers
1 µm 1 µm
1 mm 1000 µm
1 in 25,400 µm

Surface Roughness Examples

Example 1: Calculate Rz from Ra and k

You have an average roughness of Ra = 1.6 µm and choose an assumed factor of k = 5.

Rz = k × Ra
Rz = 5 × 1.6 = 8.0 µm

The estimated parameter is Rz = 8.0 µm; this is not a substitute for measuring Rz.

Example 2: Calculate a Paired-Measurement Ratio Manually

You have Ra = 0.8 µm and Rz = 4.8 µm.

k = Rz / Ra
k = 4.8 / 0.8 = 6

The paired-data ratio is k = 6. This manual example can inform an assumption for matching measurement conditions; it does not establish a universal conversion or a k-solving calculator mode.

Raw-Sample Statistics

In raw-sample mode, enter at least three finite height values, including negative values where appropriate, and select the height and result units. Each supplied point has equal weight. If the points are intended to represent a length profile, use uniform spacing; this calculator cannot apply length weights to unevenly spaced points.

For n heights zi, the calculator subtracts their arithmetic mean z̄ before summarizing them:

Mean height: z̄ = Σzi / n.
Raw-sample Ra: Σ|zi − z̄| / n.
Raw-sample Rq: √[Σ(zi − z̄)² / n].
Sample peak-to-valley height: max(zi) − min(zi).

These are descriptive statistics of the entered points. Centering removes their constant height offset, but it does not remove slope or curvature, apply cutoff filters, set an evaluation length, or separate roughness from waviness. The sample peak-to-valley height is not a standards-evaluated Rz result. See Mitutoyo’s guide to profiles, filters and roughness parameters. These raw statistics are not an ISO 21920 conformity result.

For example, heights −0.4, −0.3, −0.2, −0.1, 0.1, 0.2, 0.3 and 0.4 µm have mean 0, raw-sample Ra = 0.25 µm, raw-sample Rq ≈ 0.273861 µm and sample peak-to-valley height = 0.8 µm.

FAQ

What is the difference between Ra and Rz?

Ra is the arithmetic mean of the absolute profile-height deviations from the mean line. Rz is a height-based roughness parameter whose definition and evaluation depend on the specified standard. They summarize different profile features, so one value alone does not determine the other.

Can you convert Ra to Rz exactly?

Not exactly from Ra alone. The same Ra value can come from different surface profiles, and those profiles may have different Rz values. The calculator uses the factor k = Rz / Ra, so the accuracy depends on choosing a suitable k value for the surface or process.

What does each calculator mode require?

To estimate Rz, enter Ra and an assumed k. To estimate Ra, enter Rz and an assumed k. Raw-sample mode instead requires a height list and its units. Complete the fields shown for the selected mode; hidden fields from other modes are not needed.