Surface roughness calculator
The drawing says Ra 1.6 and you want to know what feed to set on the machine. Or the other way round: you know the feed and you want to know how rough the surface will come out. The four tabs below do those calculations.
Find the surface from nose radius and feed
Enter the nose radius of the insert and the feed you are running; this shows the surface you can expect in theory.
Find the feed for the Ra you need
Enter the Ra the drawing asks for and the nose radius you will use; this shows the highest feed you can run.
Rough conversion between Ra and Rz
Use it when the drawing calls for Rz but what you have is Ra, or the other way round, and you just want an idea of the number. It is not an exact conversion.
Which filter should I set on the instrument?
Every surface roughness instrument has a «cut-off» (filter) setting. Set it wrong and the same surface gives a different number. Enter the value you expect and this shows the setting the standard calls for.
What is surface roughness?
No surface that comes off a machine is really flat. Even a shaft that looks like a mirror is a mountain range under a microscope: peaks and valleys. Surface roughness is the measure, in microns, of how deep those peaks and valleys are.
One micron (µm) is a thousandth of a millimeter. So when we say Ra 1.6, the height difference we are talking about is 1.6 thousandths of a millimeter. You cannot feel it with your finger, but it decides how much oil a bearing surface will hold, whether a seal will leak, and how quickly the part will wear.
What is the instrument actually measuring?
The stylus of the instrument runs along a line on the surface and records the ups and downs. But three things are mixed together in that record:
- Overall shape — the curvature or crown of the part itself
- Waviness — the broad, gentle waves that come from machine vibration
- Roughness — the fine marks left by the cutting edge
The instrument separates them. Ra, Rz and the rest look only at the last group, the fine marks left by the cutting edge. The thing that does the separating is the filter (cut-off) setting, which is what the fourth tab is about.
Ra, Rz, Rt: what each one means
Ra — average roughness
Along the line it traces, the instrument draws a mean line and measures how far the surface departs from it. The average of all those departures is Ra. It is the value you meet most often on drawings.
Here is Ra's weak point: it does not care whether a departure is a peak or a valley, it averages them all. So if there is one deep scratch on the surface, Ra will barely show it. Two surfaces that look completely different can give the same Ra. Where a single scratch is enough to cause a problem, such as sealing, Ra on its own is not enough.
Rz — average peak-to-valley height
The instrument divides the traced path into five equal parts. In each part it measures the difference between the highest peak and the deepest valley, then averages those five numbers. That is Rz.
Rz shows deep marks far better than Ra does. That is why drawings ask for Rz instead of Ra where bearing surfaces, sealing and fatigue matter.
Rt — total height
No dividing into five: it is the difference between the highest peak and the deepest valley over the whole traced path. A single bad spot pulls Rt up. That makes Rt the hardest of the three to hold. If the drawing says Rt, it means not even one scratch is acceptable on the part.
Remember the order
On the same surface it is always Ra < Rz ≤ Rt. If a measurement report shows Rz larger than Rt, something is wrong with it.
| Value | What it measures | When it is asked for |
|---|---|---|
| Ra | Average of the departures | General machine parts. The most common request. |
| Rz | Average peak-to-valley height over five zones | Bearing, seal and gasket faces; anywhere fatigue is a concern. |
| Rt | Largest peak-to-valley height over the whole path | Surfaces where not even one scratch is accepted. |
| Rp | Average height of the peaks only | Rubbing surfaces and parts that need running in. |
| Rmr | How much solid material remains at a given depth (%) | Where wear behavior and oil retention matter. |
On metal parts the Ra values you meet are usually between 0.02 and 3.5 µm. 0.02 µm is mirror level.
Where does the calculation come from?
The tip of a turning insert is round. Every time the part turns one revolution the tool advances by f and leaves the print of that round tip behind it. The surface ends up covered in small arc-shaped marks side by side, as if it had been combed. The ridge left between two marks is exactly what we are measuring.
The height of those ridges depends on two things:
- Feed (f): the larger it is, the further apart and deeper the marks
- Nose radius (rε): the larger it is, the flatter and shallower the mark
The formulas used are these:
- Rt = f² × 125 / rε — height from peak to valley, in µm
- Ra ≈ f² / (32 × rε) — average roughness, comes out in mm, multiplied by 1000
Those two together give Rt ≈ 4 × Ra. The 32 in there is a rounded figure; solving the arc geometry exactly puts Ra about 3% higher. In real machining that difference sits below the measurement uncertainty anyway.
The one rule worth remembering
Feed acts as a square. Halve the feed and Ra drops to a quarter. Double it and Ra goes up four times. When the surface is not holding, the feed is always the first place to look.
The nose radius works the other way and only in direct proportion: doubling the radius halves Ra. So instead of dropping the feed a long way, fitting an insert with a bigger radius is often the smarter move — the surface holds and the cycle time does not suffer.
The calculation was right but the surface was not — why?
This calculation only describes the geometry: the ideal mark left by the cutting edge. On a real machine other things spoil the surface, and none of them appear in the formula.
Vibration
This is the most common cause. Long tool overhang, weak workholding, a long slender part, work run without tailstock support. If instead of a regular pattern the surface shows a wavy, fish-scale look, the problem is vibration; dropping the feed usually does not help and can make it worse.
A worn insert
A worn edge does not cut, it squashes. The surface comes out shiny but ragged. If a program that gave a good finish yesterday gives a poor one today, change the insert before anything else.
Chips wrapping
Long chips that will not break rub against the finished surface and scratch it. Whatever the calculation says, the surface will not come good while chips are wrapping. You need an insert with a suitable chipbreaker, or a different feed.
Built-up edge
When the cutting speed is too low, material welds itself onto the cutting edge, tears away and leaves marks on the surface. It is common in mild steel and aluminum. The cure is not to lower the feed but to raise the cutting speed.
Constant spindle speed on a taper
Where the diameter changes along the cut, running at fixed rpm means the cutting speed changes all the way; the surface degrades at the small-diameter end. Constant surface speed (G96) with a spindle speed clamp should be used.
Too small a feed
This one surprises people but it is real: below a certain feed the insert stops cutting and starts squashing and rubbing instead. The surface gets worse, not better. If you keep dropping the feed and watch the finish deteriorate, this is why.
Frequently asked questions
The drawing just shows a tick symbol and «3.2». What does that mean?
With no letter beside it, that value is Ra in microns. If Rz is wanted the drawing writes a letter, as in «Rz 8»; for Rt it writes «Rt 4». No letter means Ra.
Older drawings say N7, N8. What are those?
The N grades are the older notation and they map straight onto Ra: N6 = Ra 0.8, N7 = Ra 1.6, N8 = Ra 3.2, N9 = Ra 6.3. The first tab also shows which N grade the calculated Ra falls into.
They want Ra 0.4. Can I hold that on a lathe?
On paper, yes: with a 1.2 mm nose radius you need about 0.12 mm/rev. But in that region the surface is no longer set by the feed; it is set by the rigidity of the machine, the sharpness of the insert and vibration. On a suitable machine with solid workholding it works; on a weak setup it does not. Where Ra 0.4 and below is called for, grinding is usually chosen instead.
If I fit a bigger nose radius, does everything improve?
No. A larger radius improves the theoretical surface but it also raises the cutting force. On a long slender part a large radius pushes the work away, vibration starts and the surface gets worse. If the setup is rigid, go bigger; if it is not, do not.
Does depth of cut affect the surface?
It is not in the formula but it does in practice. At a very small depth of cut the insert rubs rather than cuts. Rather than leaving a finishing pass so thin it is barely dust, leave enough stock for the insert to cut cleanly and the surface comes out better.
Does this calculation work for milling?
No. This one is for turning. In milling the surface comes from feed per tooth, cutter runout, the number of teeth, the pass overlaps and how square the cutter is to the axis. A milled surface is usually spoiled where the tool passes meet, not by the formula.
Two instruments give different Ra on the same part. Which is right?
Most likely both are right for their own settings. First check that both are on the same filter (cut-off) value. Direction matters too: the stylus must travel across the tool marks, not along them. Measure along the marks and Ra reads far too low and misleads you.