How deep does a V-bit cut for a given width?

Depth = (width ÷ 2) ÷ tan(angle ÷ 2), where the angle is the bit’s full included angle. A 90° bit cuts 0.5 mm deep per 1 mm of width, a 60° bit about 0.866 mm and a 30° bit about 1.866 mm. A 6 mm wide line with a 90° bit is 3 mm deep.

Do I multiply or divide by tan for V-carve depth?

Divide. Width = 2 × depth × tan(angle ÷ 2), so depth = width ÷ (2 × tan(angle ÷ 2)). Multiplying by tan gives the wrong answer for every bit except 90°, where tan 45° = 1 and both happen to agree — so a 90° test won’t catch the mistake. Also check whether your bit is labelled with the full angle or the half angle.

What does Flat Depth do in V-carving?

Flat Depth limits how deep the V-bit goes. Areas narrow enough are carved as a V; wider areas reach the limit and get a flat bottom. Vectric lets you add a clearance tool such as an end mill to clear that floor, otherwise the V-bit clears it on its own.

How do I pick a ball-nose stepover for a smooth finish?

Decide the scallop height you can accept and solve for the stepover: s = 2√(h × (D − h)). With a 1/8" ball nose, a 0.5 mm stepover leaves a scallop of about 0.02 mm, thinner than most human hairs; halving the stepover cuts the scallop to about a quarter but doubles the passes.

Calculator · hobby CNC

V-bit depth & ball-nose scallop calculator

How deep a V-bit goes for a line of a given width, how Flat Depth and Start Depth change the cut, what your lettering will look like carved — and how tall the ridges between ball-nose passes are, next to a human hair.

1Your V-bit

Included angle (tip to tip)

The full angle of the V. Some bits are labelled with the half angle (one side to the centre line); double it.

Flat tip width (mm)

0 for a sharp point. Some engraving bits have a small flat at the tip.

2The line you carve

Width of the line (mm)

Flat Depth (mm, 0 = off)

Limits how deep the bit goes; wider areas get a flat bottom (Vectric).

Start Depth (mm)

Usually 0. Vectric uses it to V-carve on the floor of a pocket.

Depth

3mm

from the surface · 0.1181 in

Width at the surface

6mm

0.2362 in

Depth per 1 mm of width

0.5mm

1 ÷ (2 × tan 45°)

Flat bottom

none

3Lettering preview

Text

Letter style

Letter height (mm)

Section line

Top view: each point is carved as deep as the V fits there — the distance to the nearest edge ÷ tan(angle ÷ 2). Below: the cut along the orange line (depth stretched by the factor shown when it would be too thin to see). Orange = Flat Depth floor, red = narrower than the flat tip.

4Ball-nose finishing pass

Ball diameter (mm)

I know

the stepoverthe scallop I want

Stepover (mm)

Scallop height

0.0198mm

19.8 µm

Stepover

0.5mm

15.7 % of the diameter

Passes across 100 mm

201

both edges included

Halving the stepover cuts the scallop to about a quarter, but doubles the passes and the time.

The formulas

V-bit depth = (width − flat tip) ÷ 2 ÷ tan(angle ÷ 2) · width = flat tip + 2 × depth × tan(angle ÷ 2)

Depth per 1 mm of width: 30° ≈ 1.866 · 60° ≈ 0.866 · 90° = 0.5 · 120° ≈ 0.289

With Start Depth S: width at the surface = width + 2 × S × tan(angle ÷ 2)

Ball-nose scallop h = R − √(R² − (s ÷ 2)²) · stepover s = 2√(h × (D − h))

The angle is the bit’s full included angle. These are the formulas posted on the Easel forum (width = 2 × depth × tan(A/2)); the flat-tip term is the same geometry with the tip width taken off first, which is how we treat it. The scallop formula is the circle geometry Modern Machine Shop uses in its ballnose article: two ball passes a stepover apart leave a ridge between them.

Divide by tan, don’t multiply

On forums the V-carve formula is often written upside down. If you multiply the half-width by tan(angle ÷ 2), a 60° bit appears to cut a 6 mm line only 1.7 mm deep instead of 5.2 mm. The check is easy, but not with a 90° bit: tan 45° = 1, so the right and the wrong formula agree there. Try a 30° or 60° bit instead — a narrower bit must cut deeper than a 90° one, and the upside-down formula makes it shallower. One more trap from the same Easel thread: some bits are sold by the half angle (one side to the centre line). A “30°” bit could be 60° included.

How V-carving software uses depth

In a V-carve, the bit goes deeper where the design is wide and rises to the surface where lines narrow to a point, so one bit makes both bold strokes and fine serifs. Vectric describes exactly this. Flat Depth caps the depth: wider areas get a flat bottom, and you can add an end mill as a clearance tool to clear them faster. Start Depth is the level the carve is calculated from; Vectric uses it to V-carve on the floor of a pocket. Set it on a flat board by mistake and every line gets wider at the surface, as the calculator shows. Easel users report that its maximum depth works the same way as a cap: a thin line is cut only as deep as its width allows, whatever the depth setting.

Ball-nose stepover and scallops

A ball-nose finishing pass leaves small ridges between neighbouring passes. Their height depends on the ball radius and the stepover, and it falls fast as the stepover shrinks: halve the stepover and the scallop drops to about a quarter, but the job takes twice as many passes. For a sense of scale, a human hair is 17–181 µm thick and copy paper 0.05–0.10 mm; with a 1/8" ball, a 0.5 mm stepover leaves about 20 µm.

Feeds for the bits themselves are in the CNC chipload and feed rate calculator. All tools are on the tools page.

Before carving: check that the deepest point is well inside your board and the bit’s cutting length, run the toolpath once in the air or in scrap, wear eye protection and stay with the machine.

FAQ

How deep does a V-bit cut for a given width?: Depth = (width ÷ 2) ÷ tan(angle ÷ 2), where the angle is the bit’s full included angle. A 90° bit cuts 0.5 mm deep per 1 mm of width, a 60° bit about 0.866 mm and a 30° bit about 1.866 mm. A 6 mm wide line with a 90° bit is 3 mm deep.
Do I multiply or divide by tan for V-carve depth?: Divide. Width = 2 × depth × tan(angle ÷ 2), so depth = width ÷ (2 × tan(angle ÷ 2)). Multiplying by tan gives the wrong answer for every bit except 90°, where tan 45° = 1 and both happen to agree — so a 90° test won’t catch the mistake. Also check whether your bit is labelled with the full angle or the half angle.
What does Flat Depth do in V-carving?: Flat Depth limits how deep the V-bit goes. Areas narrow enough are carved as a V; wider areas reach the limit and get a flat bottom. Vectric lets you add a clearance tool such as an end mill to clear that floor, otherwise the V-bit clears it on its own.
How do I pick a ball-nose stepover for a smooth finish?: Decide the scallop height you can accept and solve for the stepover: s = 2√(h × (D − h)). With a 1/8" ball nose, a 0.5 mm stepover leaves a scallop of about 0.02 mm, thinner than most human hairs; halving the stepover cuts the scallop to about a quarter but doubles the passes.

Sources

Easel forum, V-carve depth control (width = 2 × depth × tan(A/2); half-angle labels; max depth behaviour).
Vectric, VCarve Toolpath (Spark) and V-Carve Toolpath (VCarve Pro 12) (Flat Depth, Start Depth, clearance tools).
Peter Zelinski, Basic Math For Ballnose Tools, Modern Machine Shop, 2003 (stepover and scallop height).
The Physics Factbook, Width of a human hair (17–181 µm) and Thickness of a piece of paper (0.05–0.10 mm).

Last checked 2026-11-01 · Calculated values; no CNC machine was used to make this page.