Tool Nose Radius Compensation Calculator
Enter the nose radius and the angle, and this calculates the compensated X/Z coordinates your lathe program needs. Chamfers, tapers and corner radii. No sign-up, no install, free.
This page runs as an app. Tap the Safari share button [↑] → Add to Home Screen, and it will launch and calculate even where there is no signal on the shop floor.
LATHE-NCCAMOffset — from nose radius and face angle
The basic case. When you program the imaginary tool tip, a face at angle θ shifts as a whole line. This is by how much.
Chamfer — Ø with a chamfer
The shape you meet most often, with real numbers. C is a sharp chamfer, R is a corner radius.
Four points — three lines and two corner radii
| Ø (dia. mm) | Z (mm) | Corner R (mm) | Angle θ (deg) | |
|---|---|---|---|---|
| P1 | — | — | ||
| P2 | — | |||
| P3 | ||||
| P4 | — | — |
Open LATHE-NC
How this calculator works
When you program the imaginary tool tip (orientation 3), for every face of the profile at angle θ from the Z axis, the line the imaginary tool tip draws is the drawing line shifted by this much.
The corner coordinate you put in the program is the intersection of the two shifted lines. The result you meet most often: at a cylinder running into a 45 degree chamfer, the point moves along Z by R × (1 − tan 22.5°) ≈ 0.586R (0.469 for a 0.8 nose radius). That is where the 0.47 everyone quotes on the shop floor comes from.
When the corner has a radius
If the corner on the drawing is not sharp but has a radius, an intersection will not give you the answer. You are cutting the arc itself, so the radius and the centre of the arc need compensating too. The rules are just these.
Concave corner: radius = corner R − nose R
Centre: shifts by −nose R in both Z and X (radius)
The tangent points are where the shifted arc meets the shifted lines. On a concave corner, if corner R ≤ nose R the insert cannot reach in and that radius cannot be cut (this calculator warns you).
For example, cutting Ø100 with the face at Z0, a 45 degree C10 chamfer and R5 at both corners, with a 0.8 nose radius: the corner radius becomes R5 → R5.8, and the tangent points are X74.258/Z0 → X82.460/Z−1.699 → X96.602/Z−8.770 → X100/Z−12.871.
What actually removes the metal is the arc of the yellow insert, and the two are never in the same place. This calculation closes that gap.
For the reasoning in full, see the article Tool nose radius compensation: why sizes come out wrong.
FAQ
Why is tool nose radius compensation needed?
Because the point your program actually moves is the imaginary tool tip, which does not physically exist. What removes the metal is the round nose of the insert. On a straight OD or on a face the two coincide, so nothing goes wrong, but on tapers, chamfers and radii the insert either leaves material or gouges. Nose radius compensation closes that gap.
Should I use G41 or G42?
Looking along the direction of travel, G41 is tool-left of the profile and G42 is tool-right. On a rear turret lathe, ordinary OD turning from right to left is usually G42 and boring is usually G41, but the sense flips between a front and a rear turret, so confirm it on your machine.
What does tool tip orientation 3 mean?
It is the 0 to 9 number that tells the control which corner of the insert is the imaginary tool tip. On a rear turret lathe an OD turning tool is normally 3 and a boring bar is normally 2, though it changes with turret position and tool hand. This calculator assumes orientation 3 (OD).
Where does the 0.47 that machinists quote come from?
It is the Z shift at the corner where a cylinder runs into a 45 degree chamfer: R x (1 - tan 22.5 deg), which is about 0.586R. For a 0.8 mm nose radius that is 0.469 mm. It only holds at 45 degrees, so for any other angle enter the angle here instead.
What happens if the corner radius is smaller than the nose radius?
On a concave corner, when the corner radius is less than or equal to the nose radius the insert cannot reach into it, because the compensated arc radius (corner radius minus nose radius) goes negative. This calculator warns you when you enter that combination.
Can I skip G41 and G42 and just program compensated coordinates?
Yes, and often that is safer, for example where the control compensation is unavailable, or where the lead-in and lead-out of compensation leave a witness mark. This calculator gives you exactly those compensated X/Z coordinates and the compensated arc radii.
Does it work offline? Can I put it on my home screen?
Yes. Open it once, add it to the home screen of your phone, and after that it launches as an app and calculates even where there is no signal on the shop floor. No sign-up and no app store install, and it is free.