Calculator Inputs
Formula used
When an angular requirement is applied via a linear offset over a known length, the equivalent angular tolerance can be estimated as:
Limits are then: LSL = nominal - theta and USL = nominal + theta. For direct tolerances: LSL = nominal + lower, USL = nominal + upper.
How to use this calculator
- Select a tolerance method that matches your drawing.
- Choose angle units, then enter the nominal angle.
- Enter direct tolerances or the offset and length.
- Optionally add one measured angle for quick status.
- Paste batch readings to compute yield, Cp, and Cpk.
- Download CSV or PDF for your inspection record.
Example data table
| Nominal (deg) | Feature length (mm) | Linear tol (mm) | Computed tol (deg, per side) | Sample readings (deg) |
|---|---|---|---|---|
| 90.000 | 100 | 0.200 | ~ 0.1146 | 89.96, 90.01, 90.07, 90.10, 90.12 |
Notes for quality control
- Cp and Cpk are meaningful when data is stable and approximately normal.
- Use a consistent datum and measurement approach for angles.
- For small angles, arctan(delta/L) is close to delta/L.
- Record the unit and method on your inspection report.
Professional guidance
Operational guidance for angle control
Angular requirements often fail due to setup variation rather than machining error. Stabilize datums, clamp force, and probe approach before collecting data. For small offsets, the linear method links an allowed shift δ over length L to an angle band near δ/L. Use this to communicate what the drawing really permits.
Reading interpretation and pass criteria
The calculator evaluates a measured angle against LSL and USL and returns PASS or FAIL. For example, a nominal 90.000 deg with a per-side tolerance of 0.1146 deg yields limits near 89.8854 to 90.1146 deg. Use a consistent reporting unit to avoid transcription errors.
Batch statistics for inspection lots
Paste multiple readings to compute mean, sample standard deviation, and yield. A lot of 25 parts with 24 in spec gives a 96.00% yield. If the mean drifts toward a limit, corrective action may be needed even when yield remains high. Review the trend chart for shifts.
Capability metrics and practical thresholds
Cp estimates potential capability from spread: Cp = (USL − LSL)/(6σ). Cpk adds centering: Cpk = min((USL − μ)/(3σ), (μ − LSL)/(3σ)). Many teams target Cpk ≥ 1.33 for stable production, but interpret values carefully when sample sizes are small.
Method selection for drawings and GD&T
Use the direct angular tolerance option when limits are specified explicitly on the print. Use the linear option when an angle is controlled by an offset or runout measured over a defined length. Always keep δ and L in the same unit system; changing units changes the ratio if mixed.
Report export for audits and traceability
CSV export captures limits, readings, and statuses for quick SPC uploads. PDF export creates a single inspection record that can be attached to work orders. Include the method, units, and any fixture notes in your quality file to preserve traceability across shifts.
FAQs
1) When should I use the linear-to-angle method?
Use it when an angle is verified by measuring an offset over a known length, such as height difference across a span. It converts the offset band into an equivalent angular band for clear limits.
2) Why does the calculator use arctan(delta/L)?
The tangent of an angle equals opposite over adjacent. With a small offset delta across length L, the angle is arctan(delta/L). This matches common inspection geometry for angular deviation.
3) What does Cp tell me in practice?
Cp compares tolerance width to process spread. Cp above 1.0 suggests the spread fits inside limits, but it does not confirm centering. Use it alongside Cpk and a trend review.
4) What does Cpk add beyond Cp?
Cpk accounts for both spread and centering. A high Cp with a low Cpk indicates the process is capable but shifted toward one limit. Correct the mean before defects increase.
5) How many readings are enough for capability?
More is better. As a practical start, 25 to 50 stable readings can produce a clearer estimate of sigma and Cpk. If the process is drifting, capability numbers can be misleading.
6) Can I mix degrees and radians in the same dataset?
No. Choose one angle unit for entry and keep all batch readings in that unit. The tool converts internally, but mixed-unit inputs will distort mean, sigma, and your pass/fail decisions.