Tailstock taper geometry
Mistake: Using bed-projected center spacing with the true-distance formula.
Fix: Use the actual center-to-center distance along the work axis; the worksheet does not mix the two definitions.
Calculators · Free
Tailstock taper geometry
Compare exact tailstock offset with the common small-angle approximation.
01Enter your values
Runs in your browserRuns offline in your browser. Once the page and required files have loaded, processing needs no internet.
02Tailstock taper geometry
Runs in your browser
How it works
Compare exact tailstock offset with the common small-angle approximation.
q = (D−d)/(2l); s = C sin(atan(q))
Center distance is the true straight-line distance along the work axis, not its bed projection. Taper length cannot exceed center distance. Only external straight tapers between centers; no setup, center-contact, machine-travel or workholding approval. Works offline after loading.
Your data stays yours
Inputs are processed on this page and are never sent to a server.
About this tool
Use tool ↑Compare exact tailstock offset with the common small-angle approximation.
Let q=(large diameter−small diameter)/(2 × taper length along the work axis). The half-angle is atan(q). Exact lateral offset is true center-to-center distance × sin(atan(q)); the approximation is center distance × q.
How to use it
- Enter your values
Large end diameter · Small end diameter · Taper length · True center distance
- Calculate / generate
Compare exact tailstock offset with the common small-angle approximation.
- Result
Exact lateral offset: 14.981285 mm Small-angle estimate: 15 mm Taper half-angle: 2.8624052 °
Calculation method
- Let q=(large diameter−small diameter)/(2 × taper length along the work axis).
- The half-angle is atan(q).
- Exact lateral offset is true center-to-center distance × sin(atan(q)); the approximation is center distance × q.
q = (D−d)/(2l); s = C sin(atan(q))
Tailstock taper geometry
- Large end diameter
- 30 mm
- Small end diameter
- 20 mm
- Taper length
- 100 mm
- True center distance
- 300 mm
Result
Exact lateral offset: 14.981285 mm Small-angle estimate: 15 mm Taper half-angle: 2.8624052 °
Frequently asked questions
What does this result assume?
Center distance is the true straight-line distance along the work axis, not its bed projection. Taper length cannot exceed center distance. Only external straight tapers between centers; no setup, center-contact, machine-travel or workholding approval. Works offline after loading.
Where does my data go?
Calculations run on your device. Form inputs are not sent to a server.
Terms and definitions
Enter your values
- Measurement system
The initial choice follows your browser region. Your choice is remembered on this device. Gallons are US gallons. Switching units keeps your numbers unchanged and interprets them in the new unit.
Numbers stay unchanged. Check the new unit and enter the intended measurement, or select an example for that system.
- Large end diameter
Larger taper diameter; must be at least the small diameter.
Enter a numerical value for this quantity. Use the unit shown beside this field. mm / in
Minimum: 1e-9 · Maximum: 1000000000000 mm
- Small end diameter
Smaller positive taper diameter.
Enter a numerical value for this quantity. Use the unit shown beside this field. mm / in
Minimum: 1e-9 · Maximum: 1000000000000 mm
- Taper length
Length of the tapered portion measured along the workpiece axis.
Enter a numerical value for this quantity. Use the unit shown beside this field. mm / in
Minimum: 1e-9 · Maximum: 1000000000000 mm
- True center distance
Actual distance between center contact points along the work axis.
Enter a numerical value for this quantity. Use the unit shown beside this field. mm / in
Minimum: 1e-9 · Maximum: 1000000000000 mm
Result
- Result
Let q=(large diameter−small diameter)/(2 × taper length along the work axis). The half-angle is atan(q). Exact lateral offset is true center-to-center distance × sin(atan(q)); the approximation is center distance × q.
Calculated from your entries using the method below.
- Exact lateral offset
Center distance multiplied by the sine of the taper half-angle.
Calculated from your entries using the method below.
- Small-angle estimate
Center distance multiplied by the taper slope.
Calculated from your entries using the method below.
- Taper half-angle
Arctangent of half the diameter change divided by taper length.
Calculated from your entries using the method below.
- Value
Let q=(large diameter−small diameter)/(2 × taper length along the work axis). The half-angle is atan(q). Exact lateral offset is true center-to-center distance × sin(atan(q)); the approximation is center distance × q.
Calculated from your entries using the method below.
- Unit
Let q=(large diameter−small diameter)/(2 × taper length along the work axis). The half-angle is atan(q). Exact lateral offset is true center-to-center distance × sin(atan(q)); the approximation is center distance × q.
Calculated from your entries using the method below.
- Approximation excess
Small-angle estimate minus exact offset; not machine uncertainty.
Calculated from your entries using the method below.
Common mistakes and quick fixes
Limits and key assumptions
- Center distance is the true straight-line distance along the work axis, not its bed projection. Taper length cannot exceed center distance. Only external straight tapers between centers; no setup, center-contact, machine-travel or workholding approval. Works offline after loading.
- Displayed results may be rounded; rounding does not add measurement precision.