CNC Scallop Height Calculator - Ball End Mill Surface Finish

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加工參數

mm
0.1 ~ 100 mm
兩種計算共用此刀徑
給步距 → 看 Ra
mm
0.01 ~ 100 mm
得到 Ra 1.56 µm
給目標 Ra → 看步距
µm
建議步距 ≤ 0.506 mm
1.6 µm
建議步距取此上限以內(含刀徑與行間限制),達標較有把握。
殘料高度示意圖

殘料高度 h 與步距 s 示意圖

加工時間估算
加工時間估算(選填)
mm²
mm/min
預估加工時間 20.0 分鐘

計算結果

這是範例參數,請改成你的實際數值
Tool dia. 10 mm + Stepover 0.5 mm → Ra 1.56 µm
殘料高度
6.25 µm

表面粗糙度
Ra (算術平均)
1.56 µm
Rz (十點平均)
6.25 µm
良好 (精加工) ISO N7
典型對應:一般精加工面,多數機械零件可直接使用。是否需研磨/拋光仍須依圖面要求與用途判斷。
詳情
目前步距 0.5 mm (5%)
表面品質等級 Ra 0.8-3.2 µm
理論幾何值(球刀近似 h ≈ s²/8R)。實際表面受刀具跳動、材料、進給、機台剛性影響,通常比理論值高 20-50%,請預留餘量。
粗糙度比較
說明與公式
注意:以上為理論計算值。實際表面粗糙度受刀具磨損、機台精度、材質、切削參數等因素影響,可能與理論值有差異。
公式來源:h = R - √(R² - (s/2)²),其中 R 為刀具半徑,s 為步距

About the CNC Scallop Height Calculator

This calculator helps CNC operators and CAM programmers estimate ball end mill scallop height and theoretical Ra/Rz roughness. Use it to compare stepover choices before committing to a toolpath.

How to Use

  1. Enter the ball end mill diameter.
  2. Enter stepover in millimeters or as a percentage of tool diameter.
  3. Review scallop height, estimated Ra/Rz and ISO roughness guidance.
  4. Optionally reverse-calculate stepover from a target Ra.

Formula Reference

Scallop height formula: h = R - √(R² - (s/2)²), where R is the tool radius (diameter / 2) and s is the stepover. When stepover is much smaller than the tool diameter, this simplifies to h ≈ s²/(8R). Surface roughness estimate: Ra ≈ h/4, Rz ≈ h (theoretical values).

ISO N-Grade Surface Finish Reference

ISO Grade Ra (µm) Typical Use
N6 0.8 Precision fits, mating surfaces
N7 1.6 General finish machining
N8 3.2 Standard machined parts
N9 6.3 Rough machining, non-critical surfaces

Frequently Asked Questions

Q: What is scallop height?

Scallop height is the small ridge left between adjacent ball end mill toolpaths. As the ball end mill's rounded profile passes back and forth across a workpiece at a given stepover, it leaves a wave-shaped ridge on the surface; the height of that ridge is the scallop height.

Q: What's the difference between Ra and Rz?

Ra is the "arithmetic mean roughness" — the average absolute deviation of the profile from the centerline, and the most commonly used roughness metric. Rz is the "ten-point mean roughness" — the average height difference between the five highest peaks and five lowest valleys, making it more sensitive to sharp peaks and deep valleys. As a rule of thumb, Rz ≈ 4×Ra, though the actual ratio varies by machining method.

Q: What stepover should I use?

General guidance: use 30-50% of tool diameter for roughing, 10-20% for finishing, and 5-10% or smaller for precision finishing. Smaller stepover gives a smoother surface but longer machining time. Estimate the roughness you need with this calculator first, then work backward to the right stepover.

Q: Why can real roughness differ from the calculated value?

The calculated value is theoretical. Actual roughness is affected by many factors: tool wear, machine rigidity and accuracy, material properties, cutting speed and feed rate, coolant use, and vibration. Real-world Ra is typically 20-50% higher than the theoretical value, so plan for a safety margin.

Q: The stepover this tool gives me doesn't match my CAM software's recommendation — why?

CAM software (such as Fusion 360 or Mastercam) may factor in additional variables like tool runout and surface curvature changes. This calculator gives the theoretical value for flat-plane milling, which is useful for quick estimates and understanding the underlying math. For production work, use your CAM software's recommendation combined with shop experience.

Related Calculators

For shop setup work, pair this with the tap drill size calculator or the unit converter.

Last updated: November 2025 | For estimating and planning only. Validate critical finishes with inspection.

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