Machining formulas

Area from radius.

Circumference from radius.

Area of an ellipse with semi-axes a, b.

Classic base × height / 2.

Circular sector - proportion φ of the full circle.

Height of the circular segment from radius R and chord C.

X of a bore on the bolt circle with radius R.

Y of a bore on the bolt circle with radius R.

vc from workpiece Ø and spindle speed.

n from target vc and workpiece Ø.

Material removal per minute.

Pure cutting time for one cut.

Theoretical roughness depth from feed and corner radius.

Table feed from fz, number of teeth, spindle speed.

Actual cutting Ø when plunge depth < radius.

Correction of fz when ae < D/2.

Material removal per minute.

Drive-wheel speed from SFM and wheel Ø.

Depth of the drill point - important for the hole depth.

Pure feed time at full depth.

Typical allowance for the reamer.

Theoretical core diameter per ISO.

Depth of the theoretical 60° profile.

Wire diameter for the 3-wire method on UN/M threads.

Depth of cut for ACME standard profile 29°.

Ratio of pitch circle to number of teeth.

Tooth tip above the pitch circle.

Tooth root below pitch circle (with tip clearance 0,25·m).

Base circle for the involute form.

Half the apex angle of the bevel gear.

Simplified formula: F from T with friction coefficient K (≈ 0.2 unlubricated).

Change in length of a tensioned bolt.

Change in length with change in temperature.

Maximum load without permanent deformation.

Load-bearing cross-section of a metric/UN thread per DIN 13.

Feed per tooth as load control.

Ratio of chip thickness to cut thickness (Merchant model).

Stiffness ratio. Above 4:1 it becomes prone to vibration.

Z depth until reaching a counterbore Ø D at point angle θ.

Estimated cutting force per stroke.

Total feed path over the strokes.

Required pulling force on the broach incl. safety factor.

Number of strokes until full depth is reached.

Center distance of two externally toothed spur gears.

Tooth pitch on the pitch circle in the inch system.

Tooth pitch on the pitch circle in the metric system.

Dimensional difference bore/shaft - positive = clearance, negative = interference.

Convert linear path feed (mm/min) to C-axis feed (deg/min).

Deflection of a compression spring under load.

Simplified stress estimate (without Wahl correction factor).

Stiffness of a helical compression spring made of round wire.

Stiffness with square wire.

Maximum compression - all coils are in contact.

Potential energy stored in the spring.

Required torque delivered by a torsion spring.

Steifigkeit einer Torsionsfeder, je UMDREHUNG.

Stress correction for curved spring wires.

Circumference from diameter.

Volume of a right circular cylinder.

Volume of a right circular cone.

Volume of a sphere.

Hypotenuse of a right triangle.

Third side from two sides and included angle.

Angle conversion.

Length of a circular arc.

Sheet metal diameter for a cylindrical cup (equal volume).

Inch variant: 3,82 = 12/π.

Cutting speed in the inch system.

Duration of a turning pass.

Facing/grooving from outer to inner radius.

Classic tool life relationship (Frederick Taylor).

Pressure per unit area on the chip.

Power from torque and spindle speed (imperial world: 5252 = 33000/(2π)).

convert lb·ft to lb·in.

Tool tangential force from spindle power.

Taper angle from Ø difference and length.

Inch measure: Ø change per foot of length.

Removal volume per minute.

Simplified scallop approximation at small stepover.

Exact scallop height by Pythagoras.

Feed adjustment at the outer edge of a contour.

Feed adjustment for internal milling.

Time for one face milling pass incl. overrun.

Duration of one full circular path.

Kehrwert der Spanverdünnung für beliebigen WOC. Algebraisch dasselbe wie der RCTF darüber, nur in der Schreibweise, die Werkzeughersteller drucken. Bis zum 02.10.2026 fehlte hier die 2 im Zähler des Klammerausdrucks: bei aₑ = 25 % von D kamen 1,51 heraus statt der bekannten 1,15.

Static deflection at the free end. Tip: carbide ≈ 90 GPa, HSS ≈ 30 GPa.

Shorter point for hard materials.

Direct drilling, without peck cycle.

Drilling time with chip breaking (retracts at rapid traverse).

Reaming feed typically 2× drill.

Reaming speed typically 0.66× drill.

Drill penetration rate.

Z depth from target Ø and point angle.

Z depth from outer and inner diameter.

Half the target chamfer as Z depth.

Synchronous feed during tapping.

Angle of the thread flank relative to the transverse.

Effective lead with n starts.

Number of cuts to target depth.

Load-bearing lateral surface in the screw-in section.

Force until the thread profile strips.

Recommended pilot drill diameter in the inch system.

Rough rule of thumb - for actual values see /kernloch.

Three-wire measurement on the UN/M thread.

Ratio of the numbers of teeth.

Resulting spindle speed from the gear ratio.

Torque scales with gear ratio.

Addendum circle Ø from number of teeth and diametral pitch.

Pitch circle from number of teeth and pitch.

Inch system: teeth per inch of pitch diameter.

Conversion metric ↔ US system.

Standard gear: addendum + dedendum = 2,25/P.

Helical-gear pitch circle from normal pitch.

Transverse pitch from normal pitch and angle.

Pitch circle of the worm wheel.

Axial travel per worm revolution.

Lead angle of the worm.

Pitch circle Ø of a sprocket.

Geometric angle of the involute.

Four-bar linkage synthesis (central term).

Link length between two sprockets (round up to a whole link).

Sichere Spindeldrehzahl aus Umfangsgeschwindigkeit. Rechnet in SFM und Zoll; der Reiter auf /schleifen rechnet dieselbe Groesse metrisch in m/s.

From the gauge-block stack on the sine-bar tab.

Required stack height for a target angle.

Dimension over two measuring pins on the external dovetail.

Dimension between two measuring pins on the internal dovetail.

Circle radius from chord length c and sagitta b.

Outside radius with micrometer + two rollers.

Positional deviation as a diameter tolerance value.

Smallest effective opening at MMC.

Largest effective pin Ø at MMC.

Share of active pulse on-time in the total cycle.

Volume per unit time, K material-dependent.

Mean cutting speed in planing/shaping.

Position of the neutral fiber in the sheet metal cross-section.

Neutral axis radius in the bend zone.

Elongation of the neutral fiber in the bend arc.

Distance from start of bend → theoretical outer corner.

Deduction value for the developed length calculation.

Developed length of the sheet metal before bending.

Press force for bending sheet metal.

Required cutting force for a round hole.

Force for a straight cut-off.

Contact length between roll and sheet metal.

Thickness difference before/after rolling.

Peripheral speed of the wheel.

Volume per minute in external cylindrical grinding.

Power from material removal rate and material-specific value.

Ungeklärt: die angegebene Beziehung ist die Rauheit aus Vorschub und Eckenradius (Drehen/Fräsen), nicht aus dem Werkstückradius und nicht fürs Schleifen. Vor Gebrauch gegen das Tabellenbuch prüfen - deshalb ohne Rechner.

Heating ΔT so that the bore grows by δ.

Rule-of-thumb conversion of averaged roughness values.