How does step-over drive the scallop height?

The cusp is the sagitta of the ball radius. For small stepovers it grows with the square of the step-over, so halving the step-over cuts the scallop to about a quarter.

Which value is compared with the finish limit?

The microinch row. Enter the cusp height limit in microinches. A drawing Ra is about 0.26 times the cusp height for a ball-nose pass, so divide an Ra callout by 0.26 first.

Can a flat end mill use this formula?

No. A flat end mill leaves square steps rather than a curved cusp. This geometry belongs to the ball nose, whose round tip forms the sagitta.

Why does a larger ball nose smooth the finish?

A larger radius flattens the arc between passes, so the same step-over leaves a shallower cusp. The scallop height falls as the radius rises.

CNC Machining calculator

Ball Nose Scallop (Cusp) Height Calculator

The cusp left between ball-nose passes sets the finish a mold or contoured surface can hold. This tool computes the scallop height from the step-over and the tool radius.

What this calculator does

Scallop (cusp) height a ball-nose step-over leaves between passes, in inches and microinches, against your finish limit.

Formula used

Scallop height = ball-nose radius minus the square root of (radius squared minus half step-over squared)
Scallop height in microinches = scallop height in inches × 1,000,000
Gap to limit = scallop limit minus scallop height in microinches

Inputs explained

Radial Step-Over: Distance between adjacent passes from the finish toolpath.
Ball-Nose Tool Radius: Tool radius, which is half the ball-nose diameter.
Scallop Limit: Maximum cusp height allowed, peak to valley; not the drawing Ra.

How to use the result

Best suited to choosing a step-over for a finish callout, checking a mold surface finish budget, comparing a half-inch and quarter-inch ball nose.
Tool runout and deflection can leave marks deeper than the theoretical cusp. Marks along the step direction add roughness that this height does not capture.

Current U.S. benchmarks

The producer price index for steel mill products stands at 381.162 (BLS, Aug 2026), up 23.4% from a year earlier. Quotes priced off last quarter's material cost miss this move.
The U.S. has 17,154 machine shops establishments employing about 223,303 workers (Census County Business Patterns, 2023).

Common questions

How does step-over drive the scallop height? The cusp is the sagitta of the ball radius. For small stepovers it grows with the square of the step-over, so halving the step-over cuts the scallop to about a quarter.
Which value is compared with the finish limit? The microinch row. Enter the cusp height limit in microinches. A drawing Ra is about 0.26 times the cusp height for a ball-nose pass, so divide an Ra callout by 0.26 first.
Can a flat end mill use this formula? No. A flat end mill leaves square steps rather than a curved cusp. This geometry belongs to the ball nose, whose round tip forms the sagitta.
Why does a larger ball nose smooth the finish? A larger radius flattens the arc between passes, so the same step-over leaves a shallower cusp. The scallop height falls as the radius rises.

Last reviewed 2026-10-01.