CNC Cutting Calculations

RMG TECH β€” CNC Cutting Calculators
RMGTECH
CNC Cutting Calculators
Engineering Reference Tool

CNC Cutting Calculations

All-in-one calculator suite for CNC turning and milling operations. Formulas verified β€” metric and imperial units.
28+
Calculators
3
Operation Types
2
Unit Systems
17
Materials
Select β†’
Tc
sec

Cutting Time Tc [sec]

Time to complete one turning pass. Derived from the relationship between workpiece circumference, cutting speed, feed rate and length of cut.

m/min
mm/rev
mm
mm
Result β€” Cutting Time
Tc
β€”
seconds
Time (min)
β€”
RPM (calc)
β€”
Feed Speed vf
β€”
Formula: Tc = (60 Γ— Ο€ Γ— l Γ— Dm) / (1000 Γ— vc Γ— f)
Tc [sec] = (60 Γ— Ο€ Γ— l [mm] Γ— Dm [mm]) / (1000 Γ— vc [m/min] Γ— f [mm/rev])
Pc
kW

Power Requirements Pc [kW]

Machine power required for the cut. Inputs: cutting speed, feed, depth of cut, specific cutting force (kc) and machine efficiency.

m/min
mm/rev
mm
MPa
% (70–85)
Result β€” Power Requirements
Pc
β€”
kW
Net Power
β€”
HP (Γ·0.75)
β€”
kc selected
β€”
Formula: Pc = (vc Γ— f Γ— ap Γ— kc) / (60,000 Γ— Ξ·/100)
Pc [kW] = (vc [m/min] Γ— f [mm/rev] Γ— ap [mm] Γ— kc [MPa]) / (60,000 Γ— Ξ·/100)
vc
m/min

Cutting Speed vc [m/min]

Calculate cutting speed from spindle RPM and workpiece diameter. vc = (Ο€ Γ— Dm Γ— n) / 1000

min⁻¹ (RPM)
mm
Result β€” Cutting Speed
vc
β€”
m/min
m/s
β€”
sfm equiv.
β€”
Formula: vc = (Ο€ Γ— Dm Γ— n) / 1000
vc [m/min] = (Ο€ Γ— Dm [mm] Γ— n [min⁻¹]) / 1000
n
min⁻¹

Spindle Speed n [min⁻¹]

Required spindle speed from cutting speed and workpiece diameter. n = (1000 Γ— vc) / (Ο€ Γ— Dm)

m/min
mm
Result β€” Spindle Speed
n
β€”
min⁻¹
Rounded (Γ—10)
β€”
rev/sec
β€”
Formula: n = (1000 Γ— vc) / (Ο€ Γ— Dm)
n [min⁻¹] = (1000 Γ— vc [m/min]) / (Ο€ Γ— Dm [mm])
f
mm/rev

Feed per Revolution f [mm/rev]

Feed rate per revolution from cutting speed, feed speed (vf) and diameter.

m/min
mm/min
mm
Result β€” Feed per Revolution
f
β€”
mm/rev
ipr equiv.
β€”
n (calc)
β€”
Formula: f = (vf Γ— Ο€ Γ— Dm) / (1000 Γ— vc)
f [mm/rev] = (vf [mm/min] Γ— Ο€ Γ— Dm [mm]) / (1000 Γ— vc [m/min])
h
ΞΌm

Surface Finish Rmax h [ΞΌm]

Theoretical maximum peak-to-valley roughness from feed rate (mm/rev) and insert nose radius (mm).

mm/rev
mm
Result β€” Surface Finish Rmax
h
β€”
ΞΌm
Ra est. (h/4)
β€”
Rz est. (Γ—0.8)
β€”
Formula: h = fΒ² / (8 Γ— RE) Γ— 1000 [ΞΌm]
h [ΞΌm] = (f [mm/rev]Β² / (8 Γ— RE [mm])) Γ— 1000
H
HP

Horsepower H [HP]

Convert power in kW to horsepower. Also shows metric PS and kVA equivalent for motor selection.

kW
Result β€” Horsepower
H
β€”
HP
Metric PS
β€”
kVA (β‰ˆ)
β€”
Formula: H = Pc / 0.74569 [HP]
H [HP] = Pc [kW] / 0.74569    Metric PS = Pc / 0.7355
Q
cmΒ³/min

Material Removal Rate Q [cmΒ³/min]

Volume of material removed per minute. Q = (vc Γ— f Γ— ap) / 1000

m/min
mm/rev
mm
Result β€” Material Removal Rate
Q
β€”
cmΒ³/min
mmΒ³/min
β€”
inΒ³/min equiv.
β€”
Formula: Q = (vc Γ— f Γ— ap) / 1000
Q [cmΒ³/min] = (vc [m/min] Γ— f [mm/rev] Γ— ap [mm]) / 1000
P
kN

Cutting Force P [kN]

Tangential cutting force on the insert. P = (f Γ— ap Γ— kc) / 1000

mm/rev
mm
MPa
Result β€” Cutting Force
P
β€”
kN
Newtons (N)
β€”
lbf
β€”
kgf
β€”
Formula: P = (f Γ— ap Γ— kc) / 1000
P [kN] = (f [mm/rev] Γ— ap [mm] Γ— kc [MPa]) / 1000
Select β†’
Tc
sec

Cutting Time Tc [sec] β€” Inch

Time for one pass. Formula: Tc = 60 Γ— L / 3.82 / vc Γ— Dm / f

sfm
ipr
in
in
Result β€” Cutting Time (Inch)
Tc
β€”
seconds
Time (min)
β€”
RPM (calc)
β€”
Feed Speed vf
β€”
Exact formula: Tc = 60 Γ— L / 3.82 / vc Γ— Dm / f
Tc [sec] = 60 Γ— L [in] / 3.82 / vc [sfm] Γ— Dm [in] / f [ipr]
Pc
kW

Power Requirements Pc [kW] β€” Inch

Machine power from vc [sfm], f [ipr], ap [in], kc [MPa] and efficiency Ξ·%.

sfm
ipr
in
MPa
% (70–85)
Result β€” Power (Inch)
Pc
β€”
kW
Net Power
β€”
HP (Γ·0.75)
β€”
Exact formula: Pc = vc Γ— f Γ— ap Γ— kc / 60 / 1000 / Ξ· Γ— 100
Pc [kW] = vc [sfm] Γ— f [ipr] Γ— ap [in] Γ— kc [MPa] / 60 / 1000 / Ξ· Γ— 100
vc
sfm

Cutting Speed vc [sfm]

vc = 0.262 Γ— RPM Γ— Dm (factor 0.262 = Ο€/12)

rev/min
in
Result β€” Cutting Speed (Inch)
vc
β€”
sfm
m/min
β€”
ft/sec
β€”
Exact formula: vc = 0.262 Γ— RPM Γ— Dm
vc [sfm] = 0.262 Γ— RPM Γ— Dm [in]
RPM
rev/min

RPM [rev/min] β€” Inch

RPM = 3.82 Γ— vc / Dm (3.82 = 12/Ο€)

sfm
in
Result β€” RPM (Inch)
RPM
β€”
rev/min
Rounded (Γ—10)
β€”
rev/sec
β€”
Exact formula: RPM = 3.82 Γ— vc / Dm
RPM = 3.82 Γ— vc [sfm] / Dm [in]
f
ipr

Feed per Revolution f [ipr] β€” Inch

f = vf / 3.82 / vc Γ— Dm

sfm
ipm
in
Result β€” Feed/Rev (Inch)
f
β€”
ipr
mm/rev
β€”
RPM (calc)
β€”
Exact formula: f = vf / 3.82 / vc Γ— Dm
f [ipr] = vf [ipm] / 3.82 / vc [sfm] Γ— Dm [in]
vf
ipm

Feed Speed vf [ipm] β€” Inch

vf = 3.82 Γ— vc / Dm Γ— f

sfm
ipr
in
Result β€” Feed Speed (Inch)
vf
β€”
ipm
mm/min
β€”
in/sec
β€”
Exact formula: vf = 3.82 Γ— vc / Dm Γ— f
vf [ipm] = 3.82 Γ— vc [sfm] / Dm [in] Γ— f [ipr]
Ra
ΞΌin

Surface Finish Ra [ΞΌin] β€” Inch

Ra = 1,000,000 Γ— fΒ² / 24 / RE

ipr
in
Result β€” Surface Finish Ra
Ra
β€”
ΞΌin
Ra ΞΌm
β€”
RMS (Γ—1.11)
β€”
Exact formula: Ra = 1,000,000 Γ— fΒ² / 24 / RE
Ra [ΞΌin] = 1,000,000 Γ— f [ipr]Β² / 24 / RE [in]
RMS
ΞΌin

Surface Finish RMS [ΞΌin] β€” Inch

RMS = Ra Γ— 1.11

ΞΌin
Result β€” RMS Roughness
RMS
β€”
ΞΌin
ΞΌm equiv.
β€”
Exact formula: RMS = Ra Γ— 1.11
RMS [ΞΌin] = Ra [ΞΌin] Γ— 1.11
H1
HPs

HP at Spindle H1 [HPs] β€” Inch

H1 = Q [inΒ³/min] Γ— K factor (material constant)

inΒ³/min
HP per inΒ³/min
Result β€” HP at Spindle
H1
β€”
HPs
kW equiv.
β€”
K used
β€”
Exact formula: H1 = Q Γ— K
H1 [HPs] = Q [inΒ³/min] Γ— K (material constant)
H2
HPm

HP at Motor H2 [HPm] β€” Inch

H2 = H1 / Ξ· Γ— 100

HPs
% (70–85)
Result β€” HP at Motor
H2
β€”
HPm
kW equiv.
β€”
Loss (H2βˆ’H1)
β€”
Exact formula: H2 = H1 / Ξ· Γ— 100
H2 [HPm] = H1 [HPs] / Ξ· Γ— 100
Mc
inΒ·lb

Spindle Torque Mc [inΒ·lb] β€” Inch

Mc = H1 Γ— 63030 / 3.82 / vc Γ— Dm

sfm
HPs
in
Result β€” Spindle Torque
Mc
β€”
inΒ·lb
ftΒ·lb
β€”
NΒ·m
β€”
Exact formula: Mc = H1 Γ— 63030 / 3.82 / vc Γ— Dm
Mc [inΒ·lb] = H1 [HPs] Γ— 63030 / 3.82 / vc [sfm] Γ— Dm [in]
Q
inΒ³/min

Material Removal Rate Q [inΒ³/min] β€” Inch

Q = 12 × vc × f × ap (12 converts ft→in)

sfm
ipr
in
Result β€” MRR (Inch)
Q
β€”
inΒ³/min
cmΒ³/min
β€”
inΒ³/sec
β€”
Exact formula: Q = 12 Γ— vc Γ— f Γ— ap
Q [inΒ³/min] = 12 Γ— vc [sfm] Γ— f [ipr] Γ— ap [in]
P
kN

Cutting Force P [kN] β€” Inch

P = f Γ— ap Γ— kc / 1000

ipr
in
MPa
Result β€” Cutting Force (Inch)
P
β€”
kN
Newtons
β€”
lbf
β€”
kgf
β€”
Exact formula: P = f Γ— ap Γ— kc / 1000
P [kN] = f [ipr] Γ— ap [in] Γ— kc [MPa] / 1000
Select β†’
Tc
sec

Milling Cutting Time Tc [sec]

Tc = (60 Γ— L) / vf   where vf = n Γ— fz Γ— z (from Sumitool milling reference)

m/min
mm/tooth
mm
mm
teeth
Result β€” Milling Cutting Time
Tc
β€”
seconds
Time (min)
β€”
n (RPM)
β€”
vf (mm/min)
β€”
Formula: n = (1000Γ—vc)/(π×DC), vf = nΓ—fzΓ—z, Tc = (60Γ—L)/vf
Tc [sec] = (60 Γ— L) / vf   vf = n Γ— fz Γ— z   n = (1000 Γ— vc) / (Ο€ Γ— DC)
Pc
kW

Milling Power Pc [kW]

Pc = (Q Γ— kc) / (60,000 Γ— Ξ·/100) where Q is MRR [cmΒ³/min]

cmΒ³/min
MPa
%
Result β€” Milling Power
Pc
β€”
kW
Net power
β€”
HP (Γ·0.75)
β€”
Formula: Pc = (Q [cmΒ³/min] Γ— kc) / (60,000 Γ— Ξ·/100)
Pc [kW] = (Q [cmΒ³/min] Γ— kc [MPa]) / (60,000 Γ— Ξ·/100)
vc
m/min

Milling Cutting Speed vc [m/min]

vc = (Ο€ Γ— DC Γ— n) / 1000

min⁻¹
mm
Result β€” Milling Cutting Speed
vc
β€”
m/min
sfm equiv.
β€”
m/s
β€”
Formula: vc = (Ο€ Γ— DC Γ— n) / 1000
vc [m/min] = (Ο€ Γ— DC [mm] Γ— n [min⁻¹]) / 1000
n
min⁻¹

Milling Spindle Speed n [min⁻¹]

n = (1000 Γ— vc) / (Ο€ Γ— DC)

m/min
mm
Result β€” Milling RPM
n
β€”
min⁻¹
Rounded (Γ—10)
β€”
Formula: n = (1000 Γ— vc) / (Ο€ Γ— DC)
n [min⁻¹] = (1000 Γ— vc [m/min]) / (Ο€ Γ— DC [mm])
fz
mm/t

Feed per Tooth fz [mm/tooth]

fz = vf / (n Γ— z)

mm/min
min⁻¹
teeth
Result β€” Feed per Tooth
fz
β€”
mm/t
in/tooth equiv.
β€”
Formula: fz = vf / (n Γ— z)
fz [mm/tooth] = vf [mm/min] / (n [min⁻¹] Γ— z [teeth])
vf
mm/min

Milling Feed Speed vf [mm/min]

vf = n Γ— fz Γ— z

min⁻¹
mm/tooth
teeth
Result β€” Milling Feed Speed
vf
β€”
mm/min
mm/sec
β€”
ipm equiv.
β€”
Formula: vf = n Γ— fz Γ— z
vf [mm/min] = n [min⁻¹] Γ— fz [mm/tooth] Γ— z [teeth]
H
HP

Horsepower H [HP]

Convert power in kW to horsepower. H = Pc / 0.74569

kW
Result β€” Horsepower
H
β€”
HP
Metric PS
β€”
kVA (β‰ˆ)
β€”
Formula: H = Pc / 0.74569
H [HP] = Pc [kW] / 0.74569
Q
cmΒ³/min

Milling MRR Q [cmΒ³/min]

Q = (vf Γ— ap Γ— ae) / 1000 where ae = radial depth of cut

mm/min
mm
mm
Result β€” Milling MRR
Q
β€”
cmΒ³/min
mmΒ³/min
β€”
inΒ³/min equiv.
β€”
Formula: Q = (vf Γ— ap Γ— ae) / 1000
Q [cmΒ³/min] = (vf [mm/min] Γ— ap [mm] Γ— ae [mm]) / 1000
Engineering Calculators
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