Cutting Formulas
This page introduces formulas for calculating basic parameters necessary for machine cutting. The figures obtained from the calculations are for reference only. The conditions for machining depend on the machine tool you are using. Use the optimal conditions according to your actual machining circumstances.
 Cutting Speed (vc)
 Feed (f)
 Machining Time (Tc)
 Theoretical Finished Surface Roughness (h)
 Net Power (Pc)
 Kc Values (Cutting)
Cutting Speed (vc)
 π (3.14): Circular constant
 Dm (mm): Diameter of workpiece
 n (min^{1}): Spindle speed
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This formula is used to calculate the cutting speed from the spindle speed and the diameter of the workpiece.
Example:
Diameter (Dm) = 60 mm
Spindle speed (n) = 500 min^{1}
In this case, the cutting speed (vc) is approximately 94 m/min.
Feed (f)
 l (mm/min): Machined length per minute
 n (min^{1}): Spindle speed
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This formula is used to calculate the feed rate per revolution from the spindle speed and the length cut per minute.
Example:
Machined length per minute (l) = 150 mm/min
Spindle speed (n) = 600 min^{1}
In this case, the feed rate per revolution (f) is 0.25 mm/rev.
Machining Time (Tc)
 lm (mm): Length of workpiece
 l (mm/min): Machined length per minute
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This formula is used to calculate the machining time from the length of the workpiece and the spindle speed.
Example:
Feed (f) = 0.2 mm/rev
Spindle speed (n) = 1100 min^{1}
Length of workpiece (lm) = 120 mm
First, the machined length per minute is calculated, in this case from the rotational speed and the feed amount.
Machined length per minute (l) = n × f
= 0.2 × 1100 = 220 mm/min
Substitute this into the formula:
Tc = lm ÷ l
= 120 ÷ 220
= 0.55 (min) × 60
= 33 (sec)
The machining time (Tc) is approximately 33 seconds.
Theoretical Finished Surface Roughness (h)
 f (mm/rev): Feed per revolution
 Re (mm): Insert’s corner radius
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This formula is used to calculate the theoretical finished surface roughness from the blade corner radius of the insert and the feed per revolution.
Example:
Feed per revolution (f) = 0.1 mm/rev
Insert’s blade corner radius (Re) = 0.5 mm
In this case, the theoretical finished surface roughness (h) is 2.5 µm.
Net Power (Pc)
 ap (mm): Depth of cut
 f (mm/rev): Feed per revolution
 vc (m/min): Cutting speed
 Kc (MPa): Specific cutting force
 η: Machine efficiency
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This formula is used to calculate the net power from the depth of cut, the feed per revolution, the cutting speed, the specific cutting force, and the machine efficiency.
Example:
Depth of cut (mild steel: ap) = 5 mm
Feed per revolution (f) = 0.1 mm/rev
Cutting speed (vc) = 140 m/min
Machine efficiency (η) = 80% (0.8)
Given:
Specific cutting force (Kc) = 3610 MPa
In this case, the net power for machining (Pc) is 5.26 kW.
Kc Values (Cutting)
Workpiece material  Tensile strength (MPa) and stiffness  Specific cutting force Kc (MPa) for each feed  

0.1 (mm/rev)  0.2 (mm/rev)  0.3 (mm/rev)  0.4 (mm/rev)  0.6 (mm/rev)  
Mild steel (SS400, S10C, etc.)  520  3610  3100  2720  2500  2280 
Medium steel (S45C, S50C, etc.)  620  3080  2700  2570  2450  2300 
Hard steel (S55C, S58C, etc.)  720  4050  3600  3250  2950  2640 
Tool steel (Carbon tool steel (SK), etc.)  670  3040  2800  2630  2500  2400 
Tool steel (Alloy tool steel (SKS), etc.)  770  3150  2850  2620  2450  2340 
Chromemanganese steel (Manganese carbide (MnC), etc.)  770  3830  3250  2900  2650  2400 
Chromemanganese steel (Manganese carbide (MnC), etc.)  630  4510  3900  3240  2900  2630 
Chrome molybdenum steel (SCM grades, etc.)  730  4500  3900  3400  3150  2850 
Chrome molybdenum steel (SCM grades, etc.)  600  3610  3200  2880  2700  2500 
Nickel chrome molybdenum steel (SNCM415, etc.)  900  3070  2650  2350  2200  1980 
Nickel chrome molybdenum steel (SNCM439, etc.)  352HB  3310  2900  2580  2400  2200 
Hard cast iron  46HRC  3190  2800  2600  2450  2270 
Meehanite cast iron (FC350, etc.)  360  2300  1930  1730  1600  1450 
Gray cast iron (FC250, etc.)  200HB  2110  1800  1600  1400  1330 