Cutting Force Formula

The tangential cutting force is what the spindle pushes against and what tries to deflect the tool. It follows directly from horsepower and cutting speed.

Force (lbf) = (33,000 × HP) / SFM

What the variables mean

Symbol Meaning
Force Tangential cutting force (pounds)
HP Spindle horsepower at the cut
SFM Cutting speed (surface feet per minute)
33,000 ft·lbf per minute in one horsepower

Worked example

3.75 HP at 300 SFM: Force = 33,000 × 3.75 / 300 = 413 lbf. Lower SFM at the same power means higher force.

FAQ

Why does cutting force matter beyond just tool wear? Cutting force directly affects workpiece deflection, fixture design requirements, and machine spindle loading, so understanding expected force helps predict whether a thin-walled part will deflect or a lightweight fixture will hold securely.

Does cutting force scale linearly with depth of cut? Roughly yes for a fixed feed and speed, cutting force scales close to linearly with depth of cut and width of cut, which is part of why material removal rate is a useful proxy for expected cutting force.

Run it instantly with the Cutting Force calculator in Material & Weight.

Scroll to Top

The calculators and tools on Formula Factory are provided for general guidance and informational purposes only. Results are estimates based on standard formulas and the values you enter — they do not constitute professional engineering, electrical, or architectural advice. Always verify calculations with a qualified professional before making decisions for any safety-critical, code-compliance, or commercial application. Formula Factory makes no representations or warranties as to the accuracy or completeness of any result, and accepts no liability for errors, omissions, or any outcomes arising from reliance on this information.