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Engineering Calculations

Use these formulas and the interactive calculators to size clamping and fasteners for your operation. Values are practical handbook figures — confirm with cutting tool data when available.

Cutting Force (Turning)

The main cutting force in turning is the specific cutting force of the work material times the chip cross-section:

Fc = kc · ap · f

Fc — main cutting force (N)
kc — specific cutting force of the material (N/mm², see table)
ap — depth of cut (mm)
f — feed per revolution (mm/rev)

Required Clamp Force

Fcl = K · Fc / μ

Where K = 2…3 (safety factor) and μ = friction coefficient between workpiece and locator (0.1…0.3). For drilling, base Fc on the thrust and torque; for milling, on the tangential cutting force.

Screw Clamp Force from Torque

F = T / (Kt · d)

For a standard metric steel bolt or stud: Kt ≈ 0.2 (thread friction included, dry). T is applied torque (N·mm) and d the nominal diameter (mm).

Interactive Calculator

Cutting force & required clamp force

Enter cutting parameters to estimate main cutting force and the clamp force needed to hold the part.

Specific cutting force kc (N/mm²) N/mm²

Depth of cut ap (mm) mm

Feed f (mm/rev) mm/rev

Friction coefficient μ —

Safety factor K —

Screw clamp force from applied torque

Estimate the clamp force generated by tightening a bolt or stud with a given torque.

Applied torque T (N·m) N·m

Bolt diameter d (mm) mm

Unit converter

Convert force, length and pressure between common engineering units.

Type —

Value —

From →

To —

Spindle speed from cutting speed

Convert a cutting speed to spindle speed for a given diameter.

Cutting speed v (m/min) m/min

Diameter D (mm) mm

Spindle power for milling

Estimate the power required at the spindle for a milling operation.

Cutting force Fc (N) N

Cutting speed v (m/min) m/min

Machine efficiency η (0.7 – 0.9) —

Drilling torque & thrust

Estimate torque and thrust for drilling with an HSS twist drill.

Drill diameter d (mm) mm

Feed f (mm/rev) mm/rev

Specific cutting force kc (N/mm²) N/mm²

Moment coefficient Mt (≈ 0.35 for HSS) —

Positioning error

Estimate the positioning error of a locator system from datum, locator and clearance tolerances (flat or V-block).

Workpiece datum tolerance δd (mm) mm

Locator tolerance δD (mm) mm

Minimum clearance δw (mm) mm

V-block angle (90/120/180°) °

Hydraulic / pneumatic clamp force

Force from a piston actuator: pressure times net piston area, times number of cylinders and efficiency.

Pressure p (MPa) MPa

Piston diameter D (mm) mm

Rod diameter d (mm) mm

Number of cylinders —

Efficiency η (0.85 – 0.95) —

Vacuum clamping force

Force from a vacuum chuck: vacuum pressure times the sealed area of the vacuum zone.

Vacuum pressure Pv (kPa, 60 – 80) kPa

Sealed area A (mm²) mm²

Indexing accuracy

Angular error of a single-pin indexing mechanism from pin clearance and index radius.

Number of index positions N —

Pin clearance / positioning error e (mm) mm

Index radius R (mm) mm

ISO fit & tolerance lookup

Find hole and shaft deviations and the resulting fit type (clearance / transition / interference) for an ISO 286 nominal size up to 250 mm.

Nominal size D (mm, 1 – 250) mm

Hole tolerance —

Hole IT grade —

Shaft tolerance —

Shaft IT grade —

Hardness conversion

Convert between HRC, HRB, HV, HB and HS scales using common steel conversion references.

Input scale —

Hardness value —

Surface roughness conversion

Convert between Ra, Rz and RMS using approximate engineering rules.

Convert from µm

Roughness value µm

Metric thread geometry

Compute pitch diameter, minor diameter, stress area, tap drill size and thread height for a 60° ISO metric thread.

Nominal diameter D (mm) mm

Pitch P (mm) mm

Dimension chain & tolerance stack-up

Sum a chain of signed dimensions and stack their tolerances by worst case and by root-sum-square (RSS) to check the closing dimension.

Link 1 ± mm

Link 2 ± mm

Link 3 ± mm

Link 4 ± mm

Clamping force requirement

Find the clamp force needed to hold a part against cutting force and torque with a given friction coefficient and safety factor.

Cutting force Fc (N) N

Cutting torque M (N·m) N·m

Clamp radius r (mm) mm

Friction coefficient μ —

Safety factor K —

Number of clamps n —

Typical specific cutting force kc (N/mm²)

Material	kc (N/mm²)
Aluminium alloys	700 – 900
Carbon steel (C45)	1800 – 2200
Alloy steel (40Cr)	2200 – 2600
Cast iron	1200 – 1600
Stainless steel	2000 – 2500

Worked example

Turning C45 steel, ap = 2 mm, f = 0.25 mm/rev, kc = 2000 N/mm², μ = 0.2, K = 2.5. Fc = 2000 × 2 × 0.25 = 1000 N. Fcl = 2.5 × 1000 / 0.2 = 12 500 N ≈ 1.27 t. Tighten the clamp to hold well above this value.

Fc = 1000 N · Fcl ≈ 12 500 N (1.27 t)