Taper Calculator
Calculate taper angles, dimensions, and machining parameters for conical workpieces
Calculate Taper Parameters
The diameter at the larger end of the tapered section
The diameter at the smaller end of the tapered section
The length of the tapered section (not including straight portions)
Taper Calculations
⚠️ Machining Safety Warning
• This calculator provides estimates for general taper machining operations
• Always verify calculations and consult machine manuals before machining
• Consider tool geometry, material properties, and machine limitations
• Ensure proper workholding and tool alignment for taper operations
• Start with shallow cuts and verify dimensions progressively
• Improper taper calculations can result in scrapped parts or tool damage
Example Calculation: Morse Taper #2
Taper Specifications
Application: Morse Taper #2 for drill chuck
Major Diameter: 17.780mm (0.700")
Minor Diameter: 14.907mm (0.587")
Taper Length: 56.5mm (2.224")
Standard TPI: 0.05083 in/in
Taper Calculation
• TPI = (Dl - Ds) / Tl = (17.780 - 14.907) / 56.5mm
• TPI = 2.873mm / 56.5mm = 0.05083 mm/mm
• Taper Angle = arctan(TPI/2) = arctan(0.02542) = 1.456°
• Half Angle = 1.456° / 2 = 0.728°
Result: 0.05083 in/in taper with 1.456° included angle
Standard Tapers
Morse Tapers (TPI)
Taper Applications
Tool Holders
Morse, R8, CAT, BT tapers for secure tool mounting
Drill Chucks
Jacobs tapers for drill bit retention
Machine Spindles
Self-holding tapers for automatic tool changing
Pipe Threads
NPT tapered threads for sealing connections
Key Formulas
Understanding Taper Calculations
What is a Taper?
A taper is a gradual reduction in cross-sectional dimensions along the length of a workpiece. Tapers are commonly used in machining for tool holders, drill chucks, pipe fittings, and many mechanical components where precise fit and easy assembly/disassembly are required.
Taper Classifications
- •Self-holding: Shallow tapers (TPI < 0.05) that lock in place
- •Quick-release: Steep tapers (TPI > 0.10) for easy removal
- •External: Taper on outside diameter (male taper)
- •Internal: Taper on inside diameter (female taper)
Taper Formulas
TPI = (Dl - Ds) / Tl
θ = arctan(TPI/2)
TPF = TPI × 12
- TPI: Taper per inch (in/in)
- TPF: Taper per foot (in/ft)
- Dl: Major diameter (larger end)
- Ds: Minor diameter (smaller end)
- Tl: Taper length
- θ: Full included angle
Machining Considerations
Tool Setup
Compound rest angle = half-angle for external tapers
Measurement
Use taper gauges, sine bars, or plug/ring gauges for verification
Tolerances
Standard tapers have tight tolerances (±0.0002" typical)