Stepover and roughness
How to use the slab calculator
The calculator operates in two modes. In the “Ra by step” mode, specify the radius of the spherical cutter (R), the overlap step (ae), the coefficient k and the type of cutter - get the ridge height (scallop h) and the predicted roughness Ra. In the “Step by Ra” mode, specify the target Ra - the calculator will calculate the maximum allowable step ae. The SVG chart and indicator show the ae/R ratio and the risk level of visible passes.
Why overlap pitch determines the quality of a 3D surface
When finishing 3D surfaces with a spherical cutter (ball nose), microridges - scallops - remain between passes. Their height h depends on two parameters: the cutter radius R and the overlap pitch ae. Formula: h = R − √(R² − (ae/2)²). This is pure geometry - works for any material and any speed.
The larger the step, the higher the ridges, the rougher the surface. The smaller the step, the cleaner, but longer the cycle. The technologist’s task is to find a balance: the minimum step at which Ra is within the tolerance, but the processing time remains reasonable. The calculator helps you find this balance in seconds.
What affects ridge height and roughness
Cutter radius (R). A larger radius produces flatter ridges for the same pitch. A cutter Ø 12 mm (R = 6) with ae = 0.5 mm gives scallop h ≈ 5.2 µm. A cutter Ø 6 mm (R = 3) with the same ae - already h ≈ 10.4 µm, twice as rough. Conclusion: for 3D finishing, choose the largest radius that the part geometry allows.
Overlap pitch (ae). The height of the ridge is roughly proportional to the square of the pitch: halving ae reduces the scallop by about a factor of four. Typical range for finishing: ae = 0.1–0.5 mm for Ra 0.8–3.2 µm. For rough 3D (leaving an allowance), ae up to 1–2 mm is acceptable.
Coefficient k. Converts the height of the ridge to Ra: Ra ≈ k × h. Typical value is 0.25–0.35 for good conditions (new tool, rigid system, minimal vibration). With vibrations or wear, k increases to 0.4–0.5, and the actual Ra turns out to be worse than the geometric prediction.
Cutter type. The formula is exact for a spherical cutter (ball nose). For toroidal (bull nose) - approximation: scallop depends on the radius of the fillet, and not on the full radius. For a flat end mill on horizontal surfaces, the scallop is calculated differently (via feed and inclination angle), the calculator gives an estimate only for inclined walls.
The angle of inclination of the surface. On vertical walls, the scallop from the spherical cutter is minimal (the passages almost overlap). On horizontal ones - maximum. The calculator gives an estimate for the “worst case” - a horizontal surface. The actual Ra on sloping areas will be better.
Frequently Asked Questions
What pitch ae is needed for Ra 1.6 µm with a Ø 10 mm ball end mill? For R = 5 mm and k = 0.32: target h = 1.6 / 0.32 = 5 µm = 0.005 mm. The calculator will calculate ae ≈ 0.32 mm. This is a typical step for 3D mold finishing.
Why is the real roughness worse than the calculated one? The formula takes into account only the geometry of the ridges. The real surface is degraded by: vibration (leaves marks between passes), tool runout (ridges of different heights), edge wear (rather than a clean cut - “smearing”), and BUE when processing sticky materials. All these factors increase the k factor.
How to choose between decreasing the pitch and increasing the radius of the cutter? Increasing the radius is more effective: doubling R with the same ae reduces the scallop by half. Reducing ae by half also reduces scallop by about four times, but doubles the cycle time. If the geometry of the part allows it, use a cutter with a larger diameter. If not (narrow grooves, small mating radii), reduce ae.
Does the formula work for a toroidal cutter? Approximately. For a bull nose cutter, use a corner radius instead of the full radius R. For example, a cutter Ø 10 mm with a rounding radius of 2 mm - substitute R = 2 mm. The Scallop will be larger than a full ball end cutter of the same diameter.
What is the optimal ae/R ratio? For finishing: ae/R = 0.1–0.25 (scallop < 3 µm at typical R). For semi-finish: ae/R = 0.25–0.35. Above 0.35 - visible passages. Above 0.6 - rough surface, suitable only for rough 3D. The calculator shows ae/R and warns if it is exceeded.
Need help choosing a cutter and pitch for 3D machining or molds? Contact our specialists - we will select a strategy and parameters to suit your permission.