CNC Cutting Calculations

RMG TECH — 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 — metric and imperial units.
28+
Calculators
3
Operation Types
2
Unit Systems
17
Materials
Select →
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 — Cutting Time
Tc
—
seconds
Time (min)
—
RPM (calc)
—
Feed Speed vf
—
Formula: Tc = (60 × π × l × Dm) / (1000 × vc × f)
Tc [sec] = (60 × π × l [mm] × Dm [mm]) / (1000 × vc [m/min] × 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 — Power Requirements
Pc
—
kW
Net Power
—
HP (÷0.75)
—
kc selected
—
Formula: Pc = (vc × f × ap × kc) / (60,000 × η/100)
Pc [kW] = (vc [m/min] × f [mm/rev] × ap [mm] × kc [MPa]) / (60,000 × η/100)
vc
m/min

Cutting Speed vc [m/min]

Calculate cutting speed from spindle RPM and workpiece diameter. vc = (π × Dm × n) / 1000

min⁻¹ (RPM)
mm
Result — Cutting Speed
vc
—
m/min
m/s
—
sfm equiv.
—
Formula: vc = (π × Dm × n) / 1000
vc [m/min] = (π × Dm [mm] × n [min⁻¹]) / 1000
n
min⁻¹

Spindle Speed n [min⁻¹]

Required spindle speed from cutting speed and workpiece diameter. n = (1000 × vc) / (π × Dm)

m/min
mm
Result — Spindle Speed
n
—
min⁻¹
Rounded (×10)
—
rev/sec
—
Formula: n = (1000 × vc) / (π × Dm)
n [min⁻¹] = (1000 × vc [m/min]) / (π × 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 — Feed per Revolution
f
—
mm/rev
ipr equiv.
—
n (calc)
—
Formula: f = (vf × π × Dm) / (1000 × vc)
f [mm/rev] = (vf [mm/min] × π × Dm [mm]) / (1000 × vc [m/min])
h
μm

Surface Finish Rmax h [μm]

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

mm/rev
mm
Result — Surface Finish Rmax
h
—
μm
Ra est. (h/4)
—
Rz est. (×0.8)
—
Formula: h = f² / (8 × RE) × 1000 [μm]
h [μm] = (f [mm/rev]² / (8 × RE [mm])) × 1000
H
HP

Horsepower H [HP]

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

kW
Result — Horsepower
H
—
HP
Metric PS
—
kVA (≈)
—
Formula: H = Pc / 0.74569 [HP]
H [HP] = Pc [kW] / 0.74569    Metric PS = Pc / 0.7355
Q
cm³/min

Material Removal Rate Q [cm³/min]

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

m/min
mm/rev
mm
Result — Material Removal Rate
Q
—
cm³/min
mm³/min
—
in³/min equiv.
—
Formula: Q = (vc × f × ap) / 1000
Q [cm³/min] = (vc [m/min] × f [mm/rev] × ap [mm]) / 1000
P
kN

Cutting Force P [kN]

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

mm/rev
mm
MPa
Result — Cutting Force
P
—
kN
Newtons (N)
—
lbf
—
kgf
—
Formula: P = (f × ap × kc) / 1000
P [kN] = (f [mm/rev] × ap [mm] × kc [MPa]) / 1000
Select →
Tc
sec

Cutting Time Tc [sec] — Inch

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

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

Power Requirements Pc [kW] — Inch

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

sfm
ipr
in
MPa
% (70–85)
Result — Power (Inch)
Pc
—
kW
Net Power
—
HP (÷0.75)
—
Exact formula: Pc = vc × f × ap × kc / 60 / 1000 / η × 100
Pc [kW] = vc [sfm] × f [ipr] × ap [in] × kc [MPa] / 60 / 1000 / η × 100
vc
sfm

Cutting Speed vc [sfm]

vc = 0.262 × RPM × Dm (factor 0.262 = π/12)

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

RPM [rev/min] — Inch

RPM = 3.82 × vc / Dm (3.82 = 12/π)

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

Feed per Revolution f [ipr] — Inch

f = vf / 3.82 / vc × Dm

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

Feed Speed vf [ipm] — Inch

vf = 3.82 × vc / Dm × f

sfm
ipr
in
Result — Feed Speed (Inch)
vf
—
ipm
mm/min
—
in/sec
—
Exact formula: vf = 3.82 × vc / Dm × f
vf [ipm] = 3.82 × vc [sfm] / Dm [in] × f [ipr]
Ra
μin

Surface Finish Ra [μin] — Inch

Ra = 1,000,000 × f² / 24 / RE

ipr
in
Result — Surface Finish Ra
Ra
—
μin
Ra μm
—
RMS (×1.11)
—
Exact formula: Ra = 1,000,000 × f² / 24 / RE
Ra [μin] = 1,000,000 × f [ipr]² / 24 / RE [in]
RMS
μin

Surface Finish RMS [μin] — Inch

RMS = Ra × 1.11

μin
Result — RMS Roughness
RMS
—
μin
μm equiv.
—
Exact formula: RMS = Ra × 1.11
RMS [μin] = Ra [μin] × 1.11
H1
HPs

HP at Spindle H1 [HPs] — Inch

H1 = Q [in³/min] × K factor (material constant)

in³/min
HP per in³/min
Result — HP at Spindle
H1
—
HPs
kW equiv.
—
K used
—
Exact formula: H1 = Q × K
H1 [HPs] = Q [in³/min] × K (material constant)
H2
HPm

HP at Motor H2 [HPm] — Inch

H2 = H1 / η × 100

HPs
% (70–85)
Result — HP at Motor
H2
—
HPm
kW equiv.
—
Loss (H2−H1)
—
Exact formula: H2 = H1 / η × 100
H2 [HPm] = H1 [HPs] / η × 100
Mc
in·lb

Spindle Torque Mc [in·lb] — Inch

Mc = H1 × 63030 / 3.82 / vc × Dm

sfm
HPs
in
Result — Spindle Torque
Mc
—
in·lb
ft·lb
—
N·m
—
Exact formula: Mc = H1 × 63030 / 3.82 / vc × Dm
Mc [in·lb] = H1 [HPs] × 63030 / 3.82 / vc [sfm] × Dm [in]
Q
in³/min

Material Removal Rate Q [in³/min] — Inch

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

sfm
ipr
in
Result — MRR (Inch)
Q
—
in³/min
cm³/min
—
in³/sec
—
Exact formula: Q = 12 × vc × f × ap
Q [in³/min] = 12 × vc [sfm] × f [ipr] × ap [in]
P
kN

Cutting Force P [kN] — Inch

P = f × ap × kc / 1000

ipr
in
MPa
Result — Cutting Force (Inch)
P
—
kN
Newtons
—
lbf
—
kgf
—
Exact formula: P = f × ap × kc / 1000
P [kN] = f [ipr] × ap [in] × kc [MPa] / 1000
Select →
Tc
sec

Milling Cutting Time Tc [sec]

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

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

Milling Power Pc [kW]

Pc = (Q × kc) / (60,000 × η/100) where Q is MRR [cm³/min]

cm³/min
MPa
%
Result — Milling Power
Pc
—
kW
Net power
—
HP (÷0.75)
—
Formula: Pc = (Q [cm³/min] × kc) / (60,000 × η/100)
Pc [kW] = (Q [cm³/min] × kc [MPa]) / (60,000 × η/100)
vc
m/min

Milling Cutting Speed vc [m/min]

vc = (π × DC × n) / 1000

min⁻¹
mm
Result — Milling Cutting Speed
vc
—
m/min
sfm equiv.
—
m/s
—
Formula: vc = (π × DC × n) / 1000
vc [m/min] = (π × DC [mm] × n [min⁻¹]) / 1000
n
min⁻¹

Milling Spindle Speed n [min⁻¹]

n = (1000 × vc) / (π × DC)

m/min
mm
Result — Milling RPM
n
—
min⁻¹
Rounded (×10)
—
Formula: n = (1000 × vc) / (π × DC)
n [min⁻¹] = (1000 × vc [m/min]) / (π × DC [mm])
fz
mm/t

Feed per Tooth fz [mm/tooth]

fz = vf / (n × z)

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

Milling Feed Speed vf [mm/min]

vf = n × fz × z

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

Horsepower H [HP]

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

kW
Result — Horsepower
H
—
HP
Metric PS
—
kVA (≈)
—
Formula: H = Pc / 0.74569
H [HP] = Pc [kW] / 0.74569
Q
cm³/min

Milling MRR Q [cm³/min]

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

mm/min
mm
mm
Result — Milling MRR
Q
—
cm³/min
mm³/min
—
in³/min equiv.
—
Formula: Q = (vf × ap × ae) / 1000
Q [cm³/min] = (vf [mm/min] × ap [mm] × ae [mm]) / 1000
Scroll to Top