Worked example
A turning insert with a 0.8 mm nose radius cuts at 0.2 mm per revolution. Rt = 0.2² / (8 × 0.8) = 0.04 / 6.4 = 0.00625 mm = 6.25 µm, and Ra ≈ 1.56 µm. To get Ra 0.8 µm the feed would have to drop to about 0.14 mm/rev (0.14² / 25.6 = 0.77 µm Ra), or the nose radius would have to grow.
Levers for a finer surface
- Lower the feed: roughness falls with the square of the feed – halving f cuts Rt to a quarter.
- Bigger nose radius: roughness falls in proportion to r, but a larger radius pushes the tool away more and can cause chatter on slender parts.
- Wiper inserts flatten the ridges and allow a higher feed for the same roughness.
- The feed then sets the machining time: a finer finish costs time.
For milled surfaces see the ball-nose stepover calculator.
Frequently asked questions
How do I calculate theoretical surface roughness in turning?
Rt = f² / (8 × r) with the feed per revolution f and the nose radius r, in the same unit; Ra is about Rt / 4. A feed of 0.2 mm/rev and a 0.8 mm radius give Rt 6.25 µm and Ra about 1.56 µm.
How do I get a finer surface?
Lower the feed – roughness falls with its square – or use a larger nose radius, or a wiper insert, which allows a higher feed for the same finish.
Is the calculated value what I will measure?
It is a lower bound for a sharp, stable cut. Built-up edge, vibration, tool wear and the material make real surfaces rougher.
What feed gives Ra 0.8 µm with a 0.8 mm radius?
About 0.14 mm/rev: Ra ≈ f² / (32 × r) = 0.0196 / 25.6 mm = 0.77 µm.
More free machinist calculators
- Inch to mm – Convert inches to millimetres and back, fractions like 1 3/8 included. Exact factor 25.4, with a chart of every 1/64 inch.
- RPM and feed – Calculate spindle RPM from surface speed and diameter, surface speed from RPM, and feed rate from chip load – metric and imperial, with formulas.
- Taper – Taper ratio, half angle and taper per foot from the large and small diameter and the length, or the small diameter from the angle.
- Bolt circle – X and Y coordinates of evenly spaced holes on a bolt circle, with the hole spacing, start angle and centre offset. Copy the table into your program.
- Sine bar – Gauge block height for a sine bar angle, or the angle from a known stack, for 5 in, 10 in, 100 mm, 200 mm or any other bar length.
- Metal removal rate – Metal removal rate in cm³/min or in³/min from depth, width and feed – milling and turning, metric and imperial, with the formulas.
- Drill point depth – Length of a drill's point cone from diameter and point angle, and the total depth needed for a full-diameter hole to depth.
- Right triangle – Hypotenuse and angles from two legs, or the legs from the hypotenuse and an angle – for chamfers, dovetails, tapers and hole positions.
- Machining time – Cutting time from length, feed and spindle speed – turning with feed per revolution, milling with feed rate and number of passes.
- Decimal to fraction – Turn a decimal inch or a millimetre value into the nearest fraction – 8ths to 128ths – with the error in millimetres.
- Degrees to DMS – Convert decimal degrees to degrees, minutes and seconds and back, with the angle in radians.
- SFM to m/min – Convert surface feet per minute to metres per minute and back, and inches per minute to mm per minute, with the exact factors.
- TPI to pitch – Convert a thread pitch in millimetres to threads per inch (TPI) and back, for matching metric and inch threads.
- Cpk calculator – Paste measurements from Excel, enter USL and LSL and get Cp, Cpk, Pp and Ppk. Says plainly when 25 values are too few for an index.
- Tolerance stack-up – Add up the tolerances of a chain of parts: closing gap, worst case and statistical RSS for up to eight dimensions. Free, in your browser.
- Fit clearance – Enter hole and shaft limits and get minimum and maximum clearance and the kind of fit – clearance, transition or interference.
- Chip thinning – Feed per tooth to program when the radial width of cut is below half the cutter diameter, so the real chip thickness stays right.
- Ball-nose stepover – Scallop height left by a ball-nose cutter from the stepover, or the stepover for a wanted scallop height, on a flat surface.
- Torque and power – Torque from power and speed in newton-metres or pound-feet, and power from torque and speed. The formulas with worked examples.
- Spur gear – Pitch and outside diameter, centre distance, ratio and circular pitch of a pair of external spur gears from the module and the tooth numbers.
Making parts for a customer who wants paperwork?
Automotive and aerospace customers ask for proof that the parts match the drawing. See first article inspection (FAI), PPAP explained and the true position calculator.