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Ball End Mill Scallop Height Calculation

Guide · Updated October 28, 2026

When a ball end mill steps across a flat or contoured surface, it leaves small ridges, called scallops or cusps, between passes. Their height depends only on the ball radius and the stepover. A smaller stepover or a bigger ball gives a smaller scallop and a better finish, but more passes. The same geometry also gives the effective cutting diameter when the ball cuts at a shallow depth, which sets the real surface speed.

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Step by step

Know the ball radius: R = cutter diameter ÷ 2.
Pick a stepover or target scallop: Either choose the stepover s and find the scallop h, or choose h and find s.
Calculate: h = R − √(R² − (s/2)²), or s = 2√(2Rh − h²).
Find the effective diameter: Deff = 2√(D × ap − ap²) at axial depth ap.
Set rpm on effective diameter: rpm = 3.82 × SFM ÷ Deff.
Check the surface: Measure finish or look at the cusps under a loupe.

The formulas

Scallop height on a flat: h = R − √(R² − (s/2)²)
Approximation for small stepover: h ≈ s² ÷ (8R)
Stepover for target height: s = 2√(2Rh − h²) ≈ √(8Rh)
Effective diameter at depth ap: Deff = 2√(D × ap − ap²)

On a convex surface the scallop is a little smaller and on a concave surface a little larger than on a flat for the same stepover.

Worked example: 1/2 in ball, 0.020 stepover

R = 0.250 in, s = 0.020 in. h = 0.250 − √(0.0625 − 0.0001) = 0.250 − 0.24980 = 0.00020 in. The approximation gives 0.020² ÷ 2 = 0.00020 in as well.

For a 0.0001 in scallop, s = 2√(2 × 0.25 × 0.0001 − 0.0001²) = 2 × 0.00707 = 0.0141 in, so you need about 40% more passes to halve the scallop.

Worked example: 6 mm ball, metric

R = 3 mm, target h = 0.002 mm. s = 2√(2 × 3 × 0.002 − 0.002²) = 2 × 0.1095 = 0.219 mm. At 0.5 mm stepover, h = 3 − √(9 − 0.0625) = 0.0104 mm.

Worked example: effective diameter

A 1/2 in ball cutting 0.020 in deep has Deff = 2√(0.5 × 0.02 − 0.0004) = 2 × 0.0980 = 0.196 in. At 600 SFM the rpm should be 3.82 × 600 ÷ 0.196 = 11,690, not the 4584 rpm you would get using the full diameter. Many machines cannot reach that, so use the top rpm and accept a lower surface speed, or tilt the tool so the ball cuts off center.

Scallop height and surface finish

Scallop height is a peak-to-valley value, closer to Rt or Rz than to Ra. A rough rule is that Ra is about one quarter of the scallop height for a pure cusp profile, but tool runout, deflection and feed marks add to it. Measure with a profilometer when the print calls Ra.

Common problems

Using the full diameter for rpm at shallow depths, setting the stepover from the cutter diameter instead of the radius, and forgetting that worn balls and runout raise the real scallop. Check the ball diameter with a mic and runout with an indicator.

FAQ

How do I calculate scallop height?

h = R − √(R² − (s/2)²), roughly s²/(8R).

What stepover gives a 0.0001 in scallop with a 1/2 in ball?

About 0.014 in.

What is effective diameter?

The diameter of the ball actually cutting at a shallow depth, 2√(D·ap − ap²).

How do I check a ball end mill diameter?

Check the gage itself before trusting a measurement: gage blocks set mics, calipers and indicators; build any stack free at gageblockcalc.com.

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General shop information only — follow your drawing, tool maker's data and your quality system.