Taper Calculator — calculate taper, taper angle & solve for missing dimension
Instantly compute taper per inch/foot, taper angle, or solve for any missing taper dimension. Supports unit conversion and standard taper presets.
Calculator Inputs
Batch Mode
Process multiple taper calculations at once by pasting CSV data.
Results
How It Works
Basic Formulas
The taper calculator uses these fundamental formulas:
Where:
- T = Taper per unit (e.g., in/in or mm/mm)
- Dl = Large (major) diameter
- Ds = Small (minor) diameter
- L = Length of taper
The taper angle formula calculates the half-angle of the taper. The result is in radians; multiply by (180/π) to convert to degrees.
Worked Example
Problem: A machined part has a large diameter of 2.0 inches, small diameter of 1.5 inches, and taper length of 4.0 inches. Calculate the taper per unit, taper per foot, and taper angle.
Step 1: Calculate taper per unit
T = (2.0 - 1.5) / 4.0
T = 0.5 / 4.0
T = 0.125 in/in
Step 2: Convert to taper per foot
Tpf = 1.5 in/ft
Step 3: Calculate taper angle
θ = atan((2.0 - 1.5) / (2 × 4.0))
θ = atan(0.5 / 8.0)
θ = atan(0.0625)
θ = 0.0624 radians
θ = 3.576°
Answer: Taper = 0.125 in/in (or 1.5 in/ft), Angle = 3.576°
Solving for Unknown Values
The calculator can solve for any missing dimension when you provide the others:
Solve for Small Diameter: Ds = Dl - (T × L)
Solve for Length: L = (Dl - Ds) / T
Solve for Taper from Angle: T = 2 × tan(θ)
Frequently Asked Questions
What is taper?
Taper is the gradual decrease in diameter or width of an object along its length. It's expressed as the difference in diameters divided by the length, commonly measured as inches per foot or millimeters per millimeter. Tapers are used extensively in machining, manufacturing, and engineering for creating precise fits and mechanical advantages.
How do I convert taper per foot to degrees?
First convert taper per foot to taper per unit by dividing by 12 (for inches). Then use the formula: angle = atan((Dl - Ds) / (2L)) where Dl is large diameter, Ds is small diameter, and L is length. This gives the half-angle in radians; multiply by (180/π) to convert to degrees. Our calculator does this conversion automatically.
Can I solve for length if I know diameters and taper?
Yes! Select 'Length' in the 'Solve for' dropdown, enter your large diameter, small diameter, and desired taper per unit. The calculator will compute the required length using the formula: L = (Dl - Ds) / T. This is useful for designing parts to achieve a specific taper rate.
What are standard taper types?
Common standard tapers include Morse Taper (used in drill press spindles and lathe tailstocks), Jacobs Taper (for drill chucks), Brown & Sharpe Taper (milling machines), Jarno Taper (self-holding design), and NMTB (National Machine Tool Builders). Each has specific dimensions for different sizes and applications.
What's the difference between taper per inch and taper per foot?
Taper per inch (in/in) is the change in diameter per inch of length, while taper per foot (in/ft) is the change per foot of length. To convert: taper per foot = taper per inch × 12. In the imperial system, taper per foot is more commonly used in industry specifications.
How accurate are the calculations?
The calculator uses JavaScript's built-in math functions which provide double-precision floating-point accuracy (approximately 15-17 significant decimal digits). This is more than sufficient for virtually all engineering and machining applications. Always round results to the precision required by your manufacturing tolerances.
Example Calculations
| Large Ø | Small Ø | Length | Taper/Unit | Taper/Foot | Angle |
|---|---|---|---|---|---|
| 2.0 in | 1.5 in | 4.0 in | 0.125 in/in | 1.5 in/ft | 3.576° |
| 50 mm | 30 mm | 200 mm | 0.1 mm/mm | — | 2.862° |
| 3.0 in | 2.5 in | 10.0 in | 0.05 in/in | 0.6 in/ft | 1.432° |
| 100 mm | 80 mm | 150 mm | 0.133 mm/mm | — | 3.814° |