Surface Texture and Finish

A surface has lay, waviness and roughness

Every manufactured surface carries marks from the process that made it. Surface texture describes those marks: which way they run, how far apart they are, and how tall they stand.

Roughness: The finest, closely spaced marks, such as the feed marks a cutting tool leaves at each pass or the scratches of abrasive grit.
Waviness: A longer, gentler undulation that the roughness sits on, for example from vibration or deflection while the part was made.
Lay: The direction of the main surface pattern, set by how the tool or the part moved.
Form: The overall shape, such as a face that is slightly curved. Size and geometric tolerances control form; surface texture is what is left on top of it.

Heights drawn 50 times larger than widths. A made-up 5.6 mm patch of surface with parallel marks 0.2 mm apart running front to back, on a gentle waviness. At true scale the marks would be far too small to see. The lines are the crests of the marks; the blue line is a stylus trace across them.

A stylus traces one line, and a filter splits it; Watch out

A stylus traces one line, and a filter splits it

A contact instrument drags a fine stylus along a straight line and records its height. That record is the measured profile. Everything else is worked out from it.

Trace direction: Usually across the lay, so the stylus crosses the marks. If the drawing specifies a measuring direction, that direction governs.
Mean line: A smooth line the filter draws through the measured profile, a weighted average of the heights around each point. This mean line is the waviness.
Cutoff λc: The wavelength where the filter splits the profile. Undulations much longer than λc stay in the mean line; marks much shorter than λc are left over for the roughness. A wave exactly λc long is shared half and half.
Roughness profile: The measured profile minus the mean line.
Evaluation length: The part of the trace the numbers come from. In this lab it is five sections, each λc long. The trace runs one more λc at each end so the filter has heights on both sides of every evaluated point.

The same trace, before and after the filter, with λc 0.8 mm. Top: the measured profile and its gold mean line; the shaded ends are the extra trace. Bottom: the roughness profile over the five sections, with each section’s peak (▼) and valley (△), its height as a red bar, and ±Ra dashed. Heights are drawn far larger than lengths; each plot gives its factor at the right.

The filter decides what counts as roughness, not the size of the undulation. Change λc and the same undulation can move from the waviness into the roughness. That is why a measurement result needs its cutoff, and why a drawing or its standard says which one applies.

Ra, Rz and Rt read the roughness differently

All three come from the same roughness profile. They answer different questions about it. This lab uses the older ISO 4287 convention with five sections for Rz; the drawing-symbol comparison separately shows older and current graphics.

Ra: The average distance of the roughness profile from its mean line over the evaluation length. Peaks and valleys count alike.
Rz: The average of the sections’ peak-to-valley heights. Each section counts once, whatever is in it.
Rt: The largest peak-to-valley height over the whole evaluation length: the single highest peak to the single deepest valley.

Ra = average of |roughness| over the evaluation length

Rz = (Z1 + Z2 + Z3 + Z4 + Z5) ÷ 5

For the trace above: Ra 1.55 µm; Rz = (6.55 + 6.56 + 6.70 + 6.57 + 6.87) ÷ 5 = 6.65 µm; Rt 7.10 µm.

The values are in micrometres (µm). They can also be given in microinches (µin): one inch is exactly 25.4 mm, so 1 µin is exactly 0.0254 µm, and Ra 1.6 µm is 63.0 µin.

Name the standard. Current documents use the ISO 21920 series. Many existing drawings and instruments use the older ISO 4287 parameters and ISO 1302 symbols. The names Ra, Rz and Rt carried over, but the standards are not identical, so this page says which one each symbol comes from and does not mix them. For a real part, check which standard the drawing invokes.

Surface texture lab: trace a surface and hold it to a drawing; Interactive

Surface texture lab: trace a surface and hold it to a drawing

Change the surface, the trace and the drawing, and watch the numbers. Start with experiment 1.

The block is a few millimetres of surface. Lines are the crests of the marks; the blue line is the stylus trace, solid over the evaluation length.
The plots are that trace: the measured profile with its mean line, then the roughness profile with its five sections.
The drawing holds one requirement against this one trace and writes it as a callout in the view you choose.

Parallel marks 0.2 mm apart, mark height 6 µm, λc 0.8 mm unless stated. Teaching surfaces, not predictions for any process.
Experiment	Setting	Ra, µm	Rz, µm	Rt, µm
Across or along the marks	Trace left to right, across	1.55	6.65	7.10
Across or along the marks	Trace front to back, along	0.328	1.59	1.70
Where waviness ends	12 µm waviness, λc 0.8 mm	1.57	6.75	7.43
Where waviness ends	Same surface, λc 2.5 mm	2.11	11.3	11.8
One deep scratch	No scratch	1.55	6.65	7.10
One deep scratch	Scratch three times the mark height	1.88	10.5	23.4

The same-Ra experiment is the figure in the next section.

Same Ra, different surfaces

These three roughness profiles all have Ra 1.6 µm. They are not the same surface. All three plots use the same height scale.

Rounded valleys, sharp crests. Ra 1.6, Rz 6.86, Rt 7.32 µm.

Flat tops, narrow grooves. Ra 1.6, Rz 10.8, Rt 11.2 µm. Most of the profile sits above the mean line.

Narrow peaks, flat valleys. Ra 1.6, Rz 10.8, Rt 11.2 µm. Most of the profile sits below the mean line.

Ra alone cannot tell these apart.
Rz separates the rounded marks from the other two, but not flat tops from narrow peaks.
Where the extremes sit, above or below the mean line, separates those two.

One number does not describe a surface. That is why a drawing names the parameter, not just a value.

Reading a surface texture symbol

The symbol’s point touches the line that represents the surface in a drawing view. Its shape says how the surface may be made; the text beside it says what texture is required.

The three process requirements, in the older and the current graphics. Schematic drawings: the standards dimension the symbols exactly.
Symbol	Older, ISO 1302	Current, ISO 21920-1	Meaning
Basic			Any manufacturing process is permitted. This does not forbid machining; it simply does not require it.
Bar			Material removal is required: the surface must be produced by removing material, for example by machining.
Circle			Material removal is prohibited: the surface must not be machined or otherwise have material removed to meet this requirement.

Current or older: An ISO 21920-1 symbol carries a short separate dash above the short leg, touching neither leg. The older ISO 1302 graphic has none, so the familiar older marks are not the current symbols unchanged.
The requirement: The parameter and its limit, such as Ra 3.2, sit below the long line, to the right of the long leg, in both.
The lay: In an ISO 21920-1 callout the process and the lay sit above the long line. In the older symbols the lay symbol sits beside the long leg, below the line.

A complete specification can state more than this page draws, such as the measuring direction. The process mark is a requirement about how the surface is made; a profile measurement checks the texture, not whether material was removed.

Lay symbols belong to the drawing view

A lay symbol says which way the marks run. = and ⊥ are judged against the plane of projection of the view the symbol is drawn in, not against the page or the screen.

= Parallel. Parallel to the plane of projection of the view in which the symbol is used.

⊥ Perpendicular. Perpendicular to the plane of projection of the view in which the symbol is used.

X Crossed. Crossed in two oblique directions relative to the plane of projection of the view in which the symbol is used.

M Multidirectional. Multidirectional.

C Circular. Approximately circular relative to the centre of the surface to which the symbol applies.

R Radial. Approximately radial relative to the centre of the surface to which the symbol applies.

P Particulate. Particulate, non-directional or protuberant.

The first two figures are the same surface. Its marks run front to back: parallel to the right side view’s plane of projection, so = there, and perpendicular to the front view’s, so ⊥ there. The arrow shows which way each view looks.

Lay and trace direction are different things. The lay says how the marks run. The trace direction says how they were measured; it is usually across the lay unless the drawing specifies one.

The lay symbols and meanings here are those of ISO 1302:2002.

Older notation: N grades and triangle marks; Interactive

Older notation: N grades and triangle marks

Older drawings may give a roughness grade number or a row of triangles instead of a parameter and value.

Roughness grade numbers

Each grade number stands for one Ra value. A grade is an Ra value: it does not convert to Rz.

Grade numbers and the Ra values they stand for. Microinches are exact conversions, rounded for display.
Grade	Ra, µm	Ra, µin
N1	0.025	1.0
N2	0.05	2.0
N3	0.1	3.9
N4	0.2	7.9
N5	0.4	15.7
N6	0.8	31.5
N7	1.6	63.0
N8	3.2	126
N9	6.3	248
N10	12.5	492
N11	25	984
N12	50	1969

Triangle marks

One catalog prints a comparison of downward triangle marks with Ra values, under the heading “Extract from JIS B 0601-2001”. It calls the comparison approximate, not rigorous. It gives no acceptance limits, no dates for the marks, and no Rz equivalents, so read it as a rough historical guide.

The catalog’s comparison, as printed.
Marks	Ra values listed, µm
4 triangles	0.012, 0.025, 0.05, 0.1, 0.2
3 triangles	0.4, 0.8, 1.6
2 triangles	3.2, 6.3
1 triangle	12.5, 25

One requirement, four ways

Slide the Ra limit and compare the current symbol, the older symbol, the grade number and the triangle marks for the same value.

Read the callout; Interactive

Read the callout

Ten short questions on the symbols, the lay, the older notations and what the numbers respond to.

The older ISO 1302 symbol with a circle in its V, and Ra 3.2. May this surface be machined to reach Ra 3.2 µm? No: material removal is prohibited. The circle in the V prohibits material removal. Material removal is prohibited: the surface must not be machined or otherwise have material removed to meet this requirement.
A current symbol with an open V, no connecting material-removal crossbar or circle, a separate identifying dash above the short leg, and Ra 6.3. Does this callout forbid machining the surface? No, any process is permitted. The V has no connecting material-removal crossbar or circle: it is the basic symbol. The separate floating dash identifies ISO 21920; it does not require machining. Any manufacturing process is permitted. This does not forbid machining; it simply does not require it.
A symbol with a bar closing its V, a short separate dash above the short leg, and Ra 0.8. Which standard's graphic is this? ISO 21920-1 (current). The short separate dash above the short leg, touching neither leg, marks an ISO 21920-1 symbol. The older ISO 1302 graphic has no dash.
A block of surface whose marks run front to back. An arrow shows the right side view looking at its right side. The marks run front to back. Which lay symbol belongs on this surface in the right side view? =. The right side view looks along the arrow. Marks running front to back are parallel to that view's plane of projection, so the symbol is =. The same surface takes ⊥ in the front view: the symbol depends on the view, not on the screen or page.
A block of surface whose marks run front to back. An arrow shows the front view looking at its front. The marks run front to back. Which lay symbol belongs on this surface in the front view? ⊥. The front view looks along the arrow. Marks running front to back are perpendicular to that view's plane of projection, so the symbol is ⊥. The same surface takes = in the right side view: the symbol depends on the view, not on the screen or page.
The grade number N8. An older drawing gives grade N8. What does that stand for? Ra 3.2 µm. N8 stands for Ra 3.2 µm (126 µin). Each step of the grade number doubles or halves the Ra value, near enough.
Three downward triangles. In the catalog comparison, which Ra values sit beside three triangles? 0.4, 0.8, 1.6 µm. Three triangles sit beside Ra 0.4, 0.8, 1.6 µm. The catalog calls this comparison approximate, not rigorous. Read it as a rough historical guide, not as acceptance limits.
A current symbol with Rz 6.3. Which N grade means the same as this Rz 6.3 µm requirement? None: grades are Ra values. Grade numbers each stand for an Ra value; N9 is Ra 6.3 µm, not Rz 6.3 µm. Ra and Rz measure different things, and how they compare depends on the shape of the profile, as the same-Ra experiment in the lab shows.
One deep scratch crosses this otherwise even trace. Which number has the largest proportional change? Rt. In the lab, a scratch three times the mark height takes Rt from 7.10 to 23.4 µm, Rz from 6.65 to 10.5 µm and Ra from 1.55 to 1.88 µm. Rt spans the highest peak to the deepest valley over the whole length. Rz averages five section heights, diluting localized extremes; filtering can spread a scratch across section boundaries. Ra averages every point.
A block of surface with parallel marks running front to back, and a stylus trace running left to right across them. The trace on this surface crosses the marks. Traced along the marks instead, Ra would be: Much smaller. In the lab, Ra is 1.55 µm across the marks and 0.328 µm along them: the stylus misses the marks when it runs beside them. Tracing across the lay is the usual choice, but a direction the drawing specifies governs.

What this lab leaves out

The lab is a teaching model of one straight trace. A real measurement and a real acceptance decision involve more:

The instrument. A real stylus has a tip radius, and instruments apply a short-wavelength filter and remove the part’s form before filtering. The lab’s stylus is sharp and its part is flat.
The filter and parameters. This lab follows the older ISO 4287 teaching convention of five sections for Rz, with a Gaussian mean line having 50% transmission at λc. Dense samples resolve the narrow marks; numerical integration on a coarser grid computes the smooth mean line. This is not a compliant instrument or a complete ISO 21920 inspection setup, and a drawing or standard can call for other settings.
The decision. The lab compares one trace with one limit. The drawing and its standard say how many traces are taken, where, and how the results are judged.
The process. No trace shows whether material was removed. The process requirement is checked against how the part was made.
Scratches and pits. Whether an isolated flaw counts against a texture requirement is for the drawing and its standard to say.
Symbols. The drawings are schematic. The lay symbols are those of ISO 1302:2002; the lab writes the same symbols in the ISO 21920-1 lay position. Check the current standard before relying on one there. Inch-drawing (ASME) practice is not covered here.