Machinist Formula Reference Table

Category	Formula	Abbreviation Meanings	Description
1. Speeds & Feeds
Spindle Speed (RPM)	`RPM = (SFM × 3.82) / D`	SFM = surface feet per minute D = tool diameter (inches)	Determines spindle speed based on SFM and tool diameter.
Feedrate (IPM)	`IPM = RPM × FPT × Z`	FPT = feed per tooth (chip load) Z = number of flutes	Linear feedrate in inches per minute.
Feed per Tooth (Chip Load)	`FPT = IPM / (RPM × Z)`	FPT = chip load per cutting edge.	Chip thickness removed per tooth.
Surface Speed (SFM)	`SFM = (π × D × RPM) / 12`	D = tool diameter	Surface cutting speed.
Surface Speed (m/min)	`V = (π × D × RPM) / 1000`	V = metric surface speed	Metric version of SFM.
2. Drilling Formulas
Drill RPM	`RPM = (SFM × 3.82) / D`	Same as milling RPM	Determines drill speed.
Drill Feedrate (IPM)	`IPM = IPR × RPM`	IPR = inches per revolution	Drilling feedrate.
Drilling Cycle Time	`T = L / IPM`	L = drill depth	Cycle time estimate.
3. Turning Formulas
Turning Surface Speed	`SFM = (π × D × RPM) / 12`	D = turning diameter	Lathe cutting speed.
Material Removal Rate (Turning)	`MRR = (π × (D² − d²) / 4) × f × V`	D = start dia d = final dia f = feed/rev V = rev/min	Volume removed per minute.
Turning Feedrate (IPM)	`IPM = f × RPM`	f = feed per revolution	Lathe linear feed.
Lathe Cycle Time	`T = L / IPM`	L = length	Turning time.
4. Milling Formulas
Material Removal Rate (MRR)	`MRR = WOC × DOC × IPM`	WOC = width of cut DOC = depth of cut	Milling material removal rate.
HP Required	`HP = MRR / (33000 × E)`	E = 0.70–0.85 efficiency	Machine horsepower requirement.
Chip Thinning	`FPT_adj = FPT / √(1 - (WOC/R)²)`	R = tool radius	Radial chip thinning adjustment.
5. Tapping Formulas
Tapping RPM	`RPM = (SFM × 3.82) / D`	D = tap diameter	Calculated tapping speed.
Tapping Feedrate	`IPM = RPM × Pitch`	Pitch = thread pitch	Feedrate for rigid tapping.
6. Threading (Lathe)
Thread Height (Unified)	`H = 0.6495 × P`	P = pitch	Unified thread height.
Pitch (Unified)	`P = 1 / TPI`	TPI = threads per inch	Converts thread pitch.
Major Diameter (Unified)	`OD = Nominal Size`	OD = major diameter	Standard OD.
Minor Diameter (Unified)	`MD = OD − (1.08253 × P)`	MD = minor diameter	Unified minor diameter.
Metric Thread Height	`H = 0.6134 × P`	P = metric pitch	ISO metric thread height.
G76 1st Line	`P = Thread Height × 10000`	P = input parameter	Defines thread depth.
G76 2nd Line	`F = P`	Pitch = feed	Thread feedrate.
7. Geometry & Trigonometry
Right Triangle	`C = √(A² + B²)`	A,B = legs	Pythagorean theorem.
Angle (Opp/Adj)	`θ = tan⁻¹(O/A)`	O = opposite A = adjacent	Inverse tangent angle.
Bolt Circle (X/Y)	`X = R cos(θ) Y = R sin(θ)`	R = radius	Hole placement.
Chamfer Offset (45°)	`Offset = Chamfer Size`	45° chamfer	Equal offset.
Chamfer Offset (Any Angle)	`Offset = C / tan(θ)`	C = chamfer length	Used for angled chamfers.
8. Bore, Ream, Counterbore
Minimum Bore	`Min Bore = Shank Diameter / 2`	Shank = tool shank dia	Minimum entry diameter.
Reamer Allowance	Steel: 0.005"–0.015" Aluminum: 0.002"–0.010"	N/A	Material removal for reaming.
Fit Calculation	`Fit = OD − ID`	OD = outer dia ID = inner dia	Interference or clearance fit.
9. CNC Feedrate Conversions
IPR → IPM	`IPM = IPR × RPM`	IPR = inches per rev	Converts feed units.
Metric Feedrate	`mm/min = mm/rev × RPM`	N/A	Metric feedrate.
Inches → mm	`mm = inch × 25.4`	N/A	Unit conversion.
mm → Inches	`inch = mm / 25.4`	N/A	Unit conversion.
10. Cutting Force Formulas
Horsepower	`HP = (Force × Speed) / 33,000`	Force = cutting load	Power required.
Torque	`T = (HP × 63025) / RPM`	HP = horsepower	Torque on spindle.
11. Coolant, Tool Life & Wear
Taylor Tool Life	`V × Tⁿ = C`	V = cutting speed T = tool life n,C = constants	Predicts tool life.
12. Shop Conversions
Degrees → Radians	`rad = deg × 0.0174533`	deg = degrees	Conversion formula.
Radians → Degrees	`deg = rad × 57.2958`	rad = radians	Conversion formula.
13. Thread Mill Programming
Helix Height	`H = P × Number of Turns`	P = pitch	Thread helix height.
Circular Interpolation Radius	`R = (D_hole − D_tool) / 2`	D_hole = hole diameter D_tool = tool diameter	Radius for thread milling.

Disclaimer

The calculations, data, and machining values provided by YanaMaDigital’s CNC Tools are intended for general reference and educational purposes only. Actual machining conditions can vary due to machine rigidity, tool wear, workholding stability, material variations, and operator technique.

Always verify speeds, feeds, thread dimensions, and cutting parameters against your machine manufacturer’s recommendations, tooling supplier data, and applicable engineering standards (ISO, ANSI, DIN, ASME).

YanaMaDigital assumes no responsibility or liability for tool damage, machine crashes, part scrap, measurement deviations, or any losses resulting from the use of these calculators or data.