FREE MACHINIST TOOLS
Machining calculators & shop math
Calculate speeds, feeds, thread pitch and lead—then solve right triangles and taper angles. Imperial and Metric units, with clear formulas.
New guide: speeds and feeds, explained
Understand cutting speed versus RPM, chip load versus feed per revolution, and what to change when spindle speed is capped. Work through a milling example, then try the linked calculators.
Speeds, feeds & threading
Choose Milling, Drilling, Lathe, Tapping or Threading. Use the unit switch for Imperial or Metric. For angles and taper geometry, use the free calculator below.
Milling calculator
| THREAD VALUE | COMPUTED RESULT |
|---|---|
| Selected standard | |
| Pitch | |
| Lead | |
| Included angle / form | |
| Theoretical sharp-V height | |
| Basic external minor diameter | |
| Basic internal minor diameter | |
| Taper / specification note |
Educational starting point only. Verify against the cutting-tool manufacturer’s data, machine limits and a safe prove-out. Thread diameters are basic 60° geometry and do not include class or tolerance.
Two-line G76 program generator
Build a reviewable starting program. Confirm your exact control format and every value before running.
Mandatory verification: Fanuc G76 address meanings and integer scaling vary by control generation and machine builder. Confirm diameter/radius conventions, P/Q scaling, taper sign, tool orientation, clearance, spindle direction, insert data and the machine manual. Never run generated code without simulation, single-block and a safe prove-out.
Angle & taper calculator
Find angles, missing sides and taper geometry. All angles are measured in degrees.
Formulas and angle conventions
Right triangle: θ = atan(rise / run); travel = √(run² + rise²). With angle and run: rise = run × tan(θ); travel = run / cos(θ). The other acute angle is 90° − θ.
Find Z: Z = (major X − minor X) / (2 × tan θ). θ is the angle to the spindle axis. For a full included angle A, use θ = A / 2. Example: X2 to X1 at 30° to the axis gives Z = 0.866025 in. At a 30° included angle, Z = 1.866025 in.
Taper: radial change = (D − d) / 2; half-angle θ = atan((D − d) / (2L)); included angle = 2θ; diameter taper per unit length = (D − d) / L. Enter the axial length, not the sloping surface length. Values use one common length unit.
The diagram illustrates the angle convention and is not to scale. Confirm whether your drawing or machine setup specifies the half-angle or included angle.
Thread families
UNC · UNF · UNEF
UNIFIED THREADS
60° thread form. Use TPI to calculate pitch and single- or multi-start lead.
COARSE · FINE
ISO METRIC
60° metric form. Enter pitch directly in millimetres.
GENERAL · STUB
ACME THREADS
29° power-transmission thread families. Final dimensions require the applicable standard table.
NPT · NPTF
PIPE THREADS
Tapered 60° pipe threads. Confirm gauge planes, engagement lengths and tolerances.
CASING · TUBING
API 8-ROUND
Oilfield connection family. Use the applicable API 5B table and certified gauges.
SPECIFICATION CONTROLLED
API BUTTRESS / LINE PIPE
Pitch and feed can be calculated here; final form, taper and diameters require the controlled specification.
Core thread formulas
Imperial pitch
Pitch = 1 ÷ TPI
Example: 20 TPI = 0.0500 in pitch.
Thread lead
Lead = pitch × number of starts
Threading feed
Feed per minute = RPM × lead
On controls using feed per revolution, the programmed feed normally equals thread lead. Verify the control mode and machine manual.
Important
Calculator results are educational starting points. Thread class, allowance, truncation, taper, gauge plane and final diameters depend on the exact standard and drawing. API connections require the applicable controlled API specification and certified gauges.
Latest threading guides
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