📐 Taper Calculator
Calculate taper dimensions and angles
How to Use This Calculator
Select Calculation Type
Choose to calculate from large and small diameters, from taper per foot, or from taper angle.
Enter Dimensions
Input large diameter, small diameter (or taper per foot/angle), and taper length in inches. Ensure large diameter is greater than small diameter.
Calculate and Review
Click "Calculate Taper" to see taper per foot, taper angle, taper ratio, and included angle. Use this for machining and design.
Use Results
Use taper per foot for machine setup, taper angle for tooling design, and included angle for inspection. Verify with measurements.
Formula
Taper per Foot = (D - d) / L × 12
Taper Angle = arctan((D - d) / (2 × L))
Small Diameter: d = D - (Taper per Foot × L / 12)
where: D = large diameter, d = small diameter, L = taper length
Example 1: From Diameters (D = 1.0", d = 0.5", L = 6")
Step 1: Taper per Foot = (D - d) / L × 12 = (1.0 - 0.5) / 6 × 12 = 1.0" per foot
Step 2: Taper Angle = arctan((D - d) / (2 × L)) = arctan(0.5 / 12) = 2.38° (half angle)
Step 3: Included Angle = 2 × 2.38° = 4.76° (full angle)
Example 2: From Taper per Foot (D = 1.0", Taper = 0.5" per foot, L = 6")
Step 1: Small Diameter = D - (Taper × L / 12) = 1.0 - (0.5 × 6 / 12) = 0.75"
Step 2: Taper per Foot = 0.5" per foot (given)
About Taper Calculator
The Taper Calculator is an essential tool for machinists, mechanical engineers, and tool designers who need to calculate taper dimensions and angles for machined tapers and conical shapes. This calculator implements standard taper formulas based on diameters, taper per foot, or taper angle, helping you determine taper specifications and machine setup.
When to Use This Calculator
- Machining Planning: Calculate taper dimensions for machining operations
- Tool Design: Determine taper specifications for tooling design
- Machine Setup: Calculate taper per foot for lathe and mill setup
- Inspection: Verify taper dimensions and angles
- Educational Use: Learn and understand taper calculations
Why Use Our Calculator?
- ✅ Multiple Calculation Modes: Supports diameter-based, taper-per-foot, and angle-based calculations
- ✅ Accurate Formulas: Uses standard taper equations
- ✅ Complete Analysis: Shows taper per foot, angle, ratio, and included angle
- ✅ Easy to Use: Simple inputs for dimensions and angles
- ✅ Time Savings: Instant calculations eliminate manual math
Understanding Tapers
Basic Principle: Taper is the gradual reduction in diameter along a length. Taper per foot is the change in diameter per foot of length. It's calculated as Taper per Foot = (D - d) / L × 12, where D is large diameter, d is small diameter, and L is taper length in inches.
Taper Angle: Taper angle is the half-angle of the taper cone. It's calculated as Taper Angle = arctan((D - d) / (2 × L)). Included angle is twice the taper angle (full angle of the cone). Taper angle determines tooling setup and inspection.
Standard Tapers: Common tapers: Morse taper (0.625" per foot), Jarno taper (0.600" per foot), Brown & Sharpe taper (0.500" per foot), Metric taper (1:10, 1:20, 1:50). Taper specifications vary by application and standard.
Tips for Best Results
- Accurate Measurements: Measure diameters and length accurately for precise calculations
- Correct Input: Ensure large diameter is greater than small diameter
- Check Taper Length: Measure taper length along the axis (not along the taper surface)
- Verify with Standards: Check taper standards (Morse, Jarno, etc.) for standard values
- Use for Setup: Use taper per foot for machine setup and tooling design
Frequently Asked Questions
How do I calculate taper per foot?
Taper per Foot = (Large Diameter - Small Diameter) / Taper Length × 12. For example, D = 1.0", d = 0.5", L = 6": Taper per Foot = (1.0 - 0.5) / 6 × 12 = 1.0" per foot. The calculator does this automatically.
How do I calculate taper angle?
Taper Angle (half angle) = arctan((D - d) / (2 × L)), where D is large diameter, d is small diameter, and L is taper length. For example, D = 1.0", d = 0.5", L = 6": Taper Angle = arctan(0.5 / 12) = 2.38°. Included angle = 2 × 2.38° = 4.76°.
What are standard taper values?
Common standard tapers: Morse taper = 0.625" per foot, Jarno taper = 0.600" per foot, Brown & Sharpe taper = 0.500" per foot, Metric taper = 1:10, 1:20, 1:50 (ratio). Taper specifications vary by application and standard. Use calculator to determine taper for your dimensions.
Can I calculate small diameter from taper per foot?
Yes, Small Diameter = Large Diameter - (Taper per Foot × Taper Length / 12). For example, D = 1.0", Taper = 0.5" per foot, L = 6": d = 1.0 - (0.5 × 6 / 12) = 0.75". The calculator supports this calculation mode.
What is the difference between taper angle and included angle?
Taper angle (half angle) is the angle from the centerline to the taper surface. Included angle (full angle) is twice the taper angle (angle between opposite taper surfaces). For example, 2.38° taper angle = 4.76° included angle. Both angles are used for tooling and inspection.