Worked example
A Ø10 mm ball-nose cutter (R = 5) with a stepover of 1 mm: h = 5 − √(25 − 0.25) = 5 − 4.9749 = 0.0251 mm. To keep the cusp at 0.01 mm: s = 2 × √(2 × 5 × 0.01 − 0.0001) = 2 × √0.0999 = 0.632 mm. Halving the stepover cuts the scallop to a quarter, because h grows with the square of s – which is why the last bit of surface quality is so expensive in machining time.
Choosing the stepover
- Decide the tolerable scallop height from the drawing's surface requirement or from what a later polishing step can remove, then compute the stepover.
- A bigger ball gives a smaller scallop for the same stepover: h ≈ s² / (8 R).
- Cutting time grows as the stepover shrinks: halving it doubles the passes. See the machining time calculator.
- For turned surfaces, the equivalent is the theoretical surface finish calculator.
Frequently asked questions
How do I calculate scallop height for a ball-nose cutter?
h = R − √(R² − (s/2)²), where R is the ball radius and s the stepover. A Ø10 ball (R = 5) with a 1 mm stepover leaves 0.025 mm.
How do I calculate stepover for a given scallop height?
s = 2 × √(2 × R × h − h²). For R = 5 and h = 0.01 the stepover is 0.632 mm.
How does the scallop change with the stepover?
It grows with the square: for small values h ≈ s² / (8R), so halving the stepover cuts the scallop to a quarter.
Do these formulas work on sloped surfaces?
Only on a flat surface with parallel passes. On slopes the real scallop depends on the angle between the tool axis and the surface; CAM software computes it from the model.
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.
- Surface finish – Theoretical Rt and estimated Ra of a turned surface from the feed per revolution and the tool nose radius.
- 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.