^{* Condition of calculation may differ between profile and three-dimensional methods.}

Amplitude Parameters (Peak and Valley)

Maximum height (Rz)

Represents the sum of the maximum peak height Zp and the maximum valley depth Zv of a profile within the reference length.

Indicated as Ry within JIS’94

Profile peak: Portion above (from the object) the mean profile line (X-axis)

Profile valley: Portion below (from the surrounding space) the mean profile line (X-axis)

Pz Maximum height of the primary profile
Wz Maximum height of the waviness

Note
Although frequently used, max height is significantly influenced by scratches, contamination, and measurement noise due to its reliance on peak values.

_{(In the case of a roughness profile)}

Maximum profile peak height (Rp)

Represents the maximum peak height Zp of a profile within the sampling length.

Pp The maximum peak height of the primary profile
Wp The maximum peak height of the waviness profile

_{(In the case of a roughness profile)}

Maximum profile valley depth (Rv)

Represents the maximum peak height Zp of a profile within the sampling length.

Pv The maximum peak height of the primary profile
Wv The maximum peak height of the waviness profile

_{(In the case of a roughness profile)}

Mean height (Rc)

Represents the mean for the height Zt of profile elements within the sampling length.

Profile element: A set of adjacent peaks and valleys

Minimum height and minimum length to be discriminated from the peaks (valleys)

Minimum height discrimination: 10% of the Rz value
Minimum length discrimination: 1% of the reference length

Pc The mean height of the primary profile element
Wc The mean height of the waviness element

_{(In the case of a roughness profile)}

Total height (Rt)

Represents the sum of the maximum peak height Zp and the maximum valley depth Zv of a profile within the evaluation length, not sampling length.

Relationship Rt≧Rz applies for all profiles

Pt The maximum total height of the profile (Rmax in the case of JIS’82)
Wt The maximum total height of the waviness

Note
Rt is a stricter standard than Rz in that the measurement is conducted against the evaluation length. It should be noted that the parameter is significantly influenced by scratches, contamination, and measurement noise due to its utilization of peak values.

_{(In the case of a roughness profile)}

Ten-point mean roughness (Rzjis)

Represents the sum of the mean value for the height of the five tallest peaks and the mean of the depth of the five deepest valleys of a profile within the sampling length.

Indicated as Rz within JIS’94

Note
Rzjis is equivalent to the parameter Rz of the obsolete JIS standard B0601:1994. Although ten-point mean roughness was deleted from current ISO standards, it was popularly used in Japan and was retained within the JIS standard as the parameter Rzjis.

_{(In the case of a roughness profile)}

Amplitude Average Parameters

Arithmetic mean deviation (Ra)

Represents the arithmetric mean of the absolute ordinate Z(x) within the sampling length.

Pa The arithmetic mean height of the primary profile
Wa The arithmetic mean waviness

Note
One of the most widely used parameters is the mean of the average height difference for the average surface. It provides for stable results as the parameter is not significantly influenced by scratches, contamination, and measurement noise.

_{(In the case of a roughness profile)}

Root mean square deviation (Rq)

Represents the root mean square for Z(x) within the sampling length.

Pq The root mean square height for the primary profile
Wq Root mean square waviness

Note
This is one of the most widely used parameters and is also referred to as the RMS value. The parameter Rq ７corresponds to the standard deviation of the height distribution. The parameter provides for easy statistical handling and enables stable results as the parameter is not significantly influenced by scratches, contamination, and measurement noise.

_{(In the case of a roughness profile)}

Skewness (Rsk)

The quotient of the mean cube value of Z (x) and the cube of R8 within a sampling length.

Rsk=0: Symmetric against the mean line (normal distribution)
Rsk>0: Deviation beneath the mean line
Rsk<0: Deviation above the mean line

Psk The skewness of the primary profile
Wsk The skewness of the waviness profile

Note
This parameter concerns height distribution. It is suitable for evaluating the abrasion and oil sump of lubricants for slide planes.

_{(In the case of a roughness profile)}

Kurtosis (Rku)

The quotient of the mean quadratic value of Z (x) and the fourth power of Rq within a sampling length.

Rku=3: Normal distribution
Rku>3: The height distribution is sharp
Rku<3: The height distribution is even

Pku The Kurtosis of the primary profile
Wku The Kurtosis of the waviness profile

Note
This parameter relates to the tip geometry of peaks and valleys and is suitable for analyzing the degree of contact between two objects.

_{(In the case of a roughness profile)}

Spacing Parameters

Mean width (RSm)

Represents the mean for the length Xs of profile elements within the sampling length.

Indicated as Sm within JIS’94

Minimum height and minimum length to be discriminated from peaks (valleys)

Minimum height discrimination: 10% of the Rz value
Minimum length discrimination: 1% of the reference length

Psm Mean width of the primary profile element
Wc Mean width of the waviness element

Note
This parameter is used to evaluate the horizontal size of parallel grooves and grains instead of the height parameters.

_{(In the case of a roughness profile)}

Hybrid Parameters

Root mean square slope (Rdq)

Represents the root mean square for the local slope dz/dx within the sampling length.

Pdq The root mean square slope for the primary profile
Wdq The root mean square slope for the waviness

Note
The steepness of the surface can be numerically represented with this parameter.

_{(In the case of a roughness profile)}

Material Ratio Curves and Related Parameters

Material ratio curve and probability density curves

Material ratio curves signify the ratio of materiality derived as a mathematical function of parameter c, where c represents the height of severance for a specific sample. This is also referred to as the bearing curve (BAC) or Abbott curve. Probability density curves signify the probability of occurrence for height Zx. The parameter is equivalent to the height distribution histogram.

_{(In the case of a roughness profile)}

Material ratio (Rmr(c))

Indicates the ratio of the material length Ml(c) of the profile element to the evaluation length for the section height level c (% or μm).

Pmr (c) The material length rate of the primary profile (formerly tp)
Wmr (c) The material length rate of the waviness

_{(In the case of a roughness profile)}

Profile section height difference (Rdc)

Rdc signifies the height difference in section height level c, matching the two material ratios.

Pdc The section height level difference for the primary profile
Wdc The section height level difference for the waviness profile

_{(In the case of a roughness profile)}

Relative material ratio (Rmr)

Rmr indicates the material ratio determined by the difference Rδc between the referential section height level C_{0} and the profile section height level.

Pmr The relative material length rate of the primary profile
Wmr The relative material length rate of the waviness profile

_{(In the case of a roughness profile)}

Parameters of a Surface with Stratified Functional Properties

Parameters of a surface with stratified functional properties

Rk, Mr1, and Mr2 values are calculated from the linear curve (equivalent linear curve) minimizing the sectional inclination corresponding to 40% of the material ratio curve. Draw a triangle with the area equivalent to the protrusion of the material ratio curve segmented by the breadth of the parameter Rk and calculate parameters Rpk and Rvk.

Rk Core roughness depth
Rpk Reduced peak height
Rvk Reduced valley depth
Mr1, Mr2 Material portion

Note
This function is used to evaluate friction and abrasion. It is also used to evaluate the lubricity of engine cylinder surfaces.

Motif Parameters

Motif parameters

Motif parameters are used for the evaluation of surface contact status based on the enveloped features of the sample surface.

AR Mean spacing of roughness motifs: the arithmetic mean of roughness motifs ARi calculated from the evaluation length
R Mean depth of roughness motifs: the arithmetic mean of the roughness motif depth Hj calculated from the evaluation length
Rx Maximum depth of roughness motifs: the maximum value of the Hj calculated from the evaluation length
AW Mean spacing of waviness motifs: the arithmetic mean of the waviness motif AWi calculated from the evaluation length
W Mean depth of waviness motifs: the arithmetic mean of the waviness motif depth HWj calculated from the evaluation length
Wx Maximum depth of waviness motifs: the maximum value of the HWj calculated from the evaluation length

Note
These parameters are suited to evaluating the slippage of lubrication mechanisms and contact surfaces, such as gaskets.

This parameter expands the profile (line roughness) parameter Rz three dimensionally. The maximum height Sz is equivalent to the sum of the maximum peak height Sp and maximum valley depth Sv.

Note
Although frequently used, this parameter is significantly influenced by scratches, contamination, and measurement noise due to its utilization of peak values.

This parameter expands the profile (line roughness) parameter Ra three dimensionally.

It represents the arithmetic mean of the absolute ordinate Z (x, y) within the evaluation area.

Note
This is one of the most widely used parameters and is the mean of the average height difference for the average plane. It provides stable results since the parameter is not significantly influenced by scratches, contamination, and measurement noise.

This parameter expands the profile (line roughness) parameter Rq three dimensionally.

It represents the root mean square for Z(x, y) within the evaluation area.

Note
This is one of the most widely used parameters and is also referred to as the RMS value. The parameter Rq corresponds to the standard deviation of the height distribution. The parameter generates good statistics and enables stable results since the parameter is not significantly influenced by scratches, contamination, and measurement noise.

This parameter expands the profile (line roughness) parameter Rsk three dimensionally; parameter Rsk, is used to evaluate deviations in the height distribution.

Ssk=0: Symmetric against the mean line
Ssk>0: Deviation beneath the mean line
Ssk<0: Deviation above the mean line

Note
This parameter concerns the height distribution and is suitable for evaluating the abrasion and oil sump of lubricants for slide planes.

The horizontal distance of the autocorrelation function that has the fastest decay to a specified value s (0≤ s < 1). Unless otherwise specified, the parameter is specified as = 0.2.

This parameter is defined as the ratio of the horizontal distance of the autocorrelation function that has the fastest decay to a specified value s to the horizontal distance of the autocorrelation function that has the slowest decay to s (0 ≤ s < 1) and indicates the isotropic/anisotropic strength of the surface.

The Str value ranges from 0 to 1; normally Str > 0.5 indicates a strong isotropy while Str < 0.3 is strongly anisotropic.

Note
These parameters are used to evaluate the horizontal size and complexity of parallel grooves and grains instead of the height parameters.

This parameter expands the profile (line roughness) parameter Rdq three dimensionally. It indicates the mean magnitude of the local gradient (slope) of the surface. The surface is more steeply inclined as the value of the parameter Sdq becomes larger.

Note
The steepness of the surface can be numerically represented in this parameter.

This signifies the rate of an increase in the surface area. The increase rate is calculated from the surface area A_{1} derived by the projected area A_{0}.

Note
Sdr values increase as the surface texture becomes fine and rough.

This parameter expands the material ratio curve parameters (Rk, Rpk, Rvk, Mr1, and Mr2) of the profile parameter three dimensionally.

Sk Core height: the difference between the upper and lower levels of the core
Spk Reduced peak height: the mean height of the protruding peaks above the core
Svk Reduced valley height: the mean height of the protruding dales beneath the core
Smr1 The areal material ratio segmenting protruding peaks from the core (indicated as a percentage)
Smr2 Areal material ratio segmenting protruding valleys from the core (indicated as percentage)

Note
This parameter is suitable for evaluating friction and abrasion. It is also used to evaluate lubricity for engine cylinder surfaces.

The difference in height between the p and q material ratio. Unless specified otherwise, the values p=2.5%, q=50% shall be applied.

The material volume and void volume are calculated from a material ratio curve as indicated in the diagram. The position that corresponds to a material ratio of 10% and 80% is regarded as the threshold segmenting the peak, core, and dale.

Vvv Dale void volume
Vvc Core void volume
Vmp Peak material volume
Vmc Core material volume

Note
This parameter is often used to evaluate abrasion and lubricant retention.

Miscellaneous Parameters

Texture direction (Std)

This parameter indicates the direction angle of the texture (parallel groove orientation, etc.). It is derived from the angle maximizing the angle spectrum of two-dimensional Fourier transformation images.

Note
Std represents the angle for the strongest orientation, although the second and third strongest angles can also be defined on the directional chart.

This is the number of peaks per unit area. Only peaks that exceed a designated size are counted. Unless otherwise specified, the designated size is determined to be 5% of the maximum height Sz.

The parameter is calculated from the number of peaks divided by the projected area.

Arithmetic mean peak curvature (Spc)

Spc indicates the mean principle curvature (average sharpness) of the peaks. Only peaks that exceed a designated curvature are taken into consideration.

Unless otherwise specified, the designated size is determined to be 5% of the maximum height Sz.

The parameter is derived from the arithmetic mean curvatures of peaks within the evaluation area.

Note
This parameter is suited for analyzing the contact between two objects.

The average value of the heights of the five peaks with the largest global peak height added to the average value of the heights of the five pits with the largest global pit height.

Five-point peak height (S5p)

The average value of the heights of the five peaks with the largest global peak height.

Five-point pit height (S5v)

The average value of the heights of the five pits with the largest global pit height.