Polar True Position Calculator

Add one or more calculated positions, then export the table to CSV or PDF for reporting and traceability.

The following example shows typical values for polar true position analysis using millimetres and degrees.

The calculator works in polar coordinates. Nominal and actual feature positions are given as radius and angle, then converted to Cartesian coordinates.

• Nominal point: xn = rn cos θn,  yn = rn sin θn
• Actual point: xa = ra cos θa,  ya = ra sin θa
• Linear deviation: d = √[(xa − xn)² + (ya − yn)²]
• True position (diameter zone): TP = 2 · d
• Radial error: Δr = ra − rn
• Angular error: Δθ = θa − θn (normalized between −180° and +180°)
• Tangential error: et ≈ rn · Δθ (with Δθ in radians)
• Approximate true position from components: d ≈ √[Δr² + et²],  TP ≈ 2 · d

The calculator reports both the exact distance from coordinates and the component-based approximation from radial and tangential errors.

1. Choose the radius unit (millimetres or inches) for your inspection data.
2. Enter the nominal radius and nominal angle of the theoretical feature position.
3. Enter the actual measured radius and angle obtained from your coordinate measurement system.
4. Optionally, enter the specified positional tolerance diameter from the drawing.
5. Click “Calculate True Position” to compute deviation, true position, and component errors.
6. Review the status badge to see whether the measured position meets the specified tolerance.
7. Click “Add current result to table” to store the calculation in the history grid.
8. After adding all relevant points, use “Download CSV” or “Download PDF” for reporting or archiving.

You can repeat calculations with different measured points, building a complete inspection record per part or feature pattern.

Polar true position combines radial and angular deviation into one cylindrical tolerance zone. It is ideal for checking drilled holes, machined bosses, and pins where position affects fit, sealing, or load transfer between mating components.

In structural steelwork, accurate position helps ensure bolt groups share loads correctly and avoid prying or unintended eccentricity under service conditions.

The calculator reports both radial and tangential components. Radial error shows how far a feature shifts in or out from the datum origin. Tangential error indicates rotation around the origin, driven by angle error multiplied by nominal radius.

Large tangential error is common on big bolt circles where even small angle differences convert into substantial linear offsets along the circumference.

Position error directly influences the clearance needed between fastener and hole. You can pair this tool with the Clearance Hole Calculator to confirm that the selected hole diameter still accommodates worst-case misalignment.

Combining tolerance and hole size checks reduces the risk of field reaming, slotted holes, or fasteners that will not fit during installation.

Many construction and fabrication details rely on arcs: curved balustrades, segmental arches, flanges, and rolled sections. When locating points along an arc, polar coordinates are natural, using radius and included angle to define each feature position.

For arc geometry itself, you can reference the Arc Circumference Calculator to relate angle, radius, and developed length while still using polar true position for inspection.

In heavy steel work, clearance holes often follow standard tables while true position is specified on shop drawings. Using this calculator together with the Steel Clearance Hole Calculator allows you to balance practical drill sizes against achievable positioning accuracy.

This approach helps fabricators decide when oversize holes or slotted holes are justified versus improving setup and fixturing to tighten position variation.

After calculating several features, you can build a compact inspection table using the “Add current result to table” button. The CSV export is ideal for spreadsheets, while the print-friendly PDF view is convenient for attaching to inspection or welding records.

Keeping consistent datasets helps quality teams correlate position trends with tooling changes, process adjustments, or environmental conditions across multiple projects.

What is polar true position?

Polar true position is a geometric tolerance that defines a cylindrical zone around the nominal feature location. The actual feature axis or center must lie inside this zone, regardless of direction, combining radial and angular deviations together.

When should I use polar instead of Cartesian position?

Use polar position when your drawing or inspection equipment naturally references radius and angle, such as hole patterns on bolt circles. It is especially convenient when angles are critical, or when comparing several features around the same datum origin.

How do I choose an appropriate tolerance diameter?

Start from part function and fit. Consider clearance between mating parts, manufacturing capability, and gage resolution. Many shops begin with a conservative tolerance, then adjust values based on process capability and inspection data collected over several production runs.

Can I use this calculator for bolt circle inspection?

Yes. Enter the nominal radius and angle for each hole on a bolt circle, then input the measured polar coordinates from your CMM. The calculator reports true position for every feature, helping you quickly identify misaligned or shifted holes.

Why might my CMM software show slightly different values?

CMM or inspection software may use different conventions for angle normalization and rounding. Ensure your angle direction, units, and datum origin match this calculator. Small numeric differences are usually rounding; large differences often indicate a coordinate-system mismatch.

Does changing angle units affect the final result?

Angle unit affects only how you type data. Internally, angles are converted to radians for trig functions, then optionally reported in degrees for readability. Switching between degrees and radians will not change geometry, only the numeric values you input.

Which related tools should I use with this calculator?

You can pair this tool with the Clearance Hole Calculator to validate hole sizes against position error, and the Arc Circumference Calculator when dealing with curved features in construction or fabrication layouts.