Cutting speed, spindle speed and feed calculation: the Vc, n, fz and vf formulas
How are spindle speed and feed calculated in milling? The Vc, n, fz and vf formulas, cutting speed and feed per tooth tables by material group, the chip thinning correction and two worked examples.
Short answer
- The spindle speed is calculated from n = (Vc × 1000) / (π × D) and the feed from vf = fz × Z × n.
- When the radial engagement ae is smaller than half the diameter, the chip thinning correction is mandatory; otherwise the tool rubs instead of cutting.
- The chip thinning factor is found from RCTF = 1 / (2 × √((ae/D)(1 − ae/D))) and fz is multiplied by this factor.
- Table values are starting values; on the first trial it is advisable to hold the spindle speed constant and raise the feed gradually.
In milling, two numbers have to be determined correctly: the spindle speed (n) and the table feed (vf). In this guide both are calculated step by step, tables are given and the most frequently omitted correction, chip thinning, is explained.
Short answer
n = (Vc × 1000) / (π × D) spindle speed [rpm]
vf = fz × Z × n table feed [mm/min]
Vc is the cutting speed (m/min), D the cutting diameter (mm), fz the feed per tooth
(mm/tooth) and Z the number of flutes. Vc and fz are selected from the tables according to
the material. When the radial engagement ae is smaller than half the diameter, the fz value is
multiplied by the chip thinning factor.
Formulas
| Quantity | Formula | Unit |
|---|---|---|
| Spindle speed | n = (Vc × 1000) / (π × D) | rpm |
| Cutting speed | Vc = (π × D × n) / 1000 | m/min |
| Table feed | vf = fz × Z × n | mm/min |
| Feed per tooth | fz = vf / (Z × n) | mm/tooth |
| Chip thinning correction | RCTF = 1 / (2 × √((ae/D)(1 − ae/D))) | – |
| Average chip thickness | hex = fz × 2 × √((ae/D)(1 − ae/D)) | mm |
| Metal removal rate | Q = (ap × ae × vf) / 1000 | cm³/min |
| Spindle power | P = (ap × ae × vf × kc) / (60 × 10⁶ × η) | kW |
ap is the axial depth of cut (mm) · ae the radial width of cut (mm) ·
kc the specific cutting force (N/mm²) · η the machine efficiency (≈ 0.80).
Cutting speed Vc table (carbide tool, suitable coating)
| ISO group | Material | Vc (m/min) | kc (N/mm²) |
|---|---|---|---|
| P | Structural steel (S235, St37) | 120–200 | 1,500 |
| P | Carbon steel (C45) | 100–180 | 1,700 |
| P | Alloy steel (42CrMo4) | 80–150 | 1,900 |
| P | Pre-hardened mould steel (1.2312, 1.2738 · 28–34 HRC) | 70–130 | 2,000 |
| M | Austenitic stainless (304, 316) | 60–110 | 2,000 |
| M | Duplex stainless (2205) | 45–85 | 2,300 |
| K | Grey cast iron (GG25) | 120–220 | 1,100 |
| K | Ductile iron (GGG50) | 100–180 | 1,400 |
| N | Wrought aluminium (6061, 7075) | 300–800 | 700 |
| N | Cast aluminium (Si > 10%) | 200–500 | 800 |
| N | Copper, brass, bronze | 200–500 | 900 |
| S | Titanium (Ti6Al4V) | 40–80 | 2,100 |
| S | Nickel-based (Inconel 718) | 20–45 | 2,600 |
| H | Hardened steel 45–55 HRC | 60–110 | 2,600 |
| H | Hardened steel 55–65 HRC | 40–80 | 3,100 |
The lower end of the range means long tool life, the upper end high productivity. If the machine is not rigid or the tool runout is excessive, starting from the lower end is advisable.
Feed per tooth fz table (mm/tooth)
The values refer to ae = D/2 (half engagement).
| Diameter D1 | P: Steel | M: Stainless | K: Cast iron | N: Aluminium | S: Superalloy | H: Hardened steel |
|---|---|---|---|---|---|---|
| 1 mm | 0.004–0.008 | 0.003–0.006 | 0.005–0.009 | 0.008–0.015 | 0.003–0.005 | 0.002–0.004 |
| 2 mm | 0.008–0.015 | 0.006–0.012 | 0.010–0.018 | 0.015–0.030 | 0.006–0.010 | 0.004–0.008 |
| 3 mm | 0.012–0.022 | 0.010–0.018 | 0.015–0.026 | 0.022–0.045 | 0.009–0.015 | 0.006–0.012 |
| 4 mm | 0.016–0.030 | 0.013–0.024 | 0.020–0.034 | 0.030–0.060 | 0.012–0.020 | 0.008–0.016 |
| 6 mm | 0.025–0.045 | 0.020–0.036 | 0.030–0.050 | 0.045–0.090 | 0.018–0.030 | 0.012–0.024 |
| 8 mm | 0.035–0.058 | 0.028–0.046 | 0.040–0.065 | 0.060–0.120 | 0.024–0.038 | 0.016–0.030 |
| 10 mm | 0.045–0.072 | 0.036–0.058 | 0.050–0.080 | 0.075–0.150 | 0.030–0.048 | 0.020–0.038 |
| 12 mm | 0.055–0.088 | 0.044–0.070 | 0.060–0.095 | 0.090–0.180 | 0.036–0.058 | 0.024–0.046 |
| 16 mm | 0.070–0.110 | 0.056–0.088 | 0.078–0.120 | 0.115–0.230 | 0.046–0.072 | 0.030–0.058 |
| 20 mm | 0.090–0.140 | 0.072–0.112 | 0.100–0.155 | 0.145–0.290 | 0.058–0.092 | 0.038–0.074 |
Chip thinning: the most frequently omitted correction
In milling the cutting edge enters the workpiece along a circular arc. As the radial engagement
ae becomes smaller this arc shortens and the actual chip thickness remains below the fz value
that has been set.
The result: the tool rubs instead of cutting. Rubbing generates far more heat than cutting; the edge wears rapidly, the surface deteriorates and the cycle time grows.
The solution: when ae < D/2, the fz value has to be multiplied by a correction factor.
RCTF = 1 / (2 × √((ae/D) × (1 − ae/D)))
fz_corrected = fz_table × RCTF
| ae / D | RCTF | Comment |
|---|---|---|
| 1.00 (full slot) | — | No chip thinning, force at maximum |
| 0.50 | 1.00 | Reference case |
| 0.40 | 1.02 | Negligible |
| 0.30 | 1.09 | Slight correction |
| 0.25 | 1.15 | Correction begins |
| 0.20 | 1.25 | Noticeable |
| 0.15 | 1.40 | Significant |
| 0.10 | 1.67 | Critical |
| 0.05 | 2.29 | Trochoidal milling range |
This is precisely why trochoidal milling (ae ≈ 0.05–0.1 × D) is efficient: the small engagement
allows ap to be increased greatly, and fz is raised by a factor of 1.7–2.3 through the
correction.
Worked example 1: pocketing in 42CrMo4 steel
Data: Ø10 mm, 4 flute, AlTiN coated carbide end mill. The material is 42CrMo4 (alloy steel).
A pocket is to be milled: ap = 5 mm, ae = 5 mm (half engagement).
1. Vc selection. From the table, alloy steel: 80–150 m/min. Mid-range value Vc = 110 m/min.
2. Spindle speed.
n = (110 × 1000) / (π × 10) = 110,000 / 31.42 ≈ 3,501 rpm
3. fz selection. From the table, Ø10 / group P: 0.045–0.072. Mid-range value fz = 0.058 mm/tooth.
4. Chip thinning. ae/D = 5/10 = 0.50 → RCTF = 1.00, no correction.
5. Feed.
vf = 0.058 × 4 × 3,501 ≈ 812 mm/min
6. Metal removal rate.
Q = (5 × 5 × 812) / 1000 ≈ 20.3 cm³/min
7. Power.
P = (5 × 5 × 812 × 1,900) / (60 × 10⁶ × 0.80) ≈ 0.80 kW
Result: n ≈ 3,500 rpm, vf ≈ 810 mm/min, and a spindle power of ≈ 0.8 kW is sufficient.
Worked example 2: the same tool in trochoidal milling
With the same Ø10 mm tool the aim is to increase productivity. ae is reduced and ap increased:
ap = 20 mm (2 × D), ae = 1 mm (0.1 × D).
Steps 1–3 are the same: Vc = 110 → n ≈ 3,501 rpm, fz_table = 0.058 mm/tooth.
4. Chip thinning. ae/D = 0.10:
RCTF = 1 / (2 × √(0.10 × 0.90)) = 1 / (2 × 0.3) = 1.67
fz = 0.058 × 1.67 ≈ 0.097 mm/tooth
5. Feed.
vf = 0.097 × 4 × 3,501 ≈ 1,358 mm/min
6. Metal removal rate.
Q = (20 × 1 × 1,358) / 1000 ≈ 27.2 cm³/min
Comparison:
| Conventional (ap 5 / ae 5) | Trochoidal (ap 20 / ae 1) | |
|---|---|---|
| Spindle speed | 3,501 | 3,501 |
| fz | 0.058 | 0.097 |
| Feed vf | 812 mm/min | 1,358 mm/min |
| Metal removal rate Q | 20.3 cm³/min | 27.2 cm³/min |
| Cutting edge contact time | long | short (cooling interval available) |
The trochoidal strategy removes 34% more material while also extending tool life, because it reduces the engagement angle of the cutting edge. The price of this is a longer toolpath and the need for CAM support.
Application sequence on the shop floor
- The
Vcandfzvalues are taken from the middle of the range in the table. - If
ae < D/2, thefzvalue is multiplied by RCTF. - The spindle speed is calculated and entered into the machine.
- The feed is started at 70% of the calculated value.
- The feed is raised gradually to 100% while the sound of the cut and the chips are monitored.
- If tool life is short, Vc is reduced first, not the feed. Tool life is governed by heat, not by force.
Critical point: reducing the feed when a problem arises is a common mistake. This thins the chip, increases rubbing and makes the situation worse. The correct approach is to reduce Vc (the spindle speed).
Instead of working the calculation out by hand, the cutting parameter calculator can also be used; it applies the chip thinning correction automatically and links directly from the result to the tools held in stock.
Frequently Asked Questions
How is the spindle speed calculated in milling?
Short answer: n = (Vc × 1000) / (π × D). Vc is the cutting speed (m/min) and D the cutting diameter (mm). Example: for Vc = 120 m/min and D = 8 mm, n = (120 × 1000) / (3.1416 × 8) ≈ 4,775 rpm.
How is the table feed found?
Short answer: vf = fz × Z × n. fz is the feed per tooth (mm/tooth), Z the number of flutes and n the spindle speed. The fz value is selected from the table according to material group and diameter, and multiplied by the chip thinning factor where this is required.
What is chip thinning?
When the radial engagement ae drops below D/2, the actual chip thickness becomes smaller than fz. Without a correction the tool rubs instead of cutting; the heat rises, the edge wears rapidly and the surface deteriorates. The fz value is corrected by multiplying it by the RCTF factor.
Where is the Vc value obtained from?
Vc depends on the ISO group of the material being machined (P/M/K/N/S/H), on the tool material and on the coating. The table on this page assumes a carbide tool with a suitable coating. As hardness increases Vc falls, and in non-ferrous materials it rises considerably.
Can the calculated values be entered directly into the machine?
The values are starting values. Machine rigidity, holder runout, workholding and cooling all change the result. On the first trial it is advisable to hold the spindle speed and raise the feed gradually, while the chip colour and the sound of the cut are monitored.
Related Products
Tools covered by this topic; order directly from the size table.
Square Carbide End Mill WDN (standard length)
16 sizes
$9.90 – $382.00
Size tableSquare Carbide End Mill NDN (standard length)
18 sizes
$13.65 – $309.40
Size tableSquare Carbide End Mill SDN (standard length)
15 sizes
$15.02 – $340.34
Size tableBall Nose Carbide End Mill WKN (standard length)
16 sizes
$10.90 – $388.50
Size tableBall Nose Carbide End Mill NKN (standard length)
19 sizes
$13.65 – $318.50
Size tableCorner Radius Carbide End Mill WRN (standard length)
16 sizes
$12.00 – $319.00
Size tableRelated Products
Other Guides
Surface Roughness (Ra, Rz) and Finish Milling: Theoretical Calculation, Stepover Selection and Measurement
What Ra, Rz and Rmax actually measure, the changes brought by the ISO 21920 series, theoretical roughness calculated from nose radius and feed, scallop height and stepover selection in ball nose milling, and the cut-off rules.
Trochoidal Milling and High Efficiency Machining (HEM/HSM): Engagement Angle, Parameters and MRR Calculation
The low radial, high axial engagement principle; engagement angle and chip thinning correction, material removal rate compared against full slotting, CAM naming conventions and machine tool requirements.
Milling Titanium and Heat-Resistant Alloys (ISO S): Parameters, Cooling and Safety
In ISO S materials such as Ti-6Al-4V and Inconel 718, heat builds up on the cutting edge instead of leaving with the chip. Cutting speed limits, high-pressure coolant, trochoidal engagement control, notch wear and the risk of chip fire are covered together.
Chip thinning: radial, axial and feed correction
At small radial engagements and with ball nose or corner radius cutters, the actual chip thickness falls below the programmed fz. Correction factors, effective diameter calculation and the minimum chip thickness limit are explained through worked examples.