Skip to content
Calcumatix

True Position Calculator

Calculate two-axis GD&T true position from measured X and Y deviations, then compare the diametrical result with a stated tolerance.

Actual minus nominal, same unit as tolerance.

From the drawing's feature control frame, diameter value.

Result

0.01

A 0.003 x 0.004 deviation gives a true position of 0.01 (within tolerance)

Quick Answer

A true position calculator doubles the straight-line offset from the nominal point. Square the X and Y errors, add them, take the square root, then multiply by two. With errors of 0.003 and 0.004, the radial offset is 0.005 and true position is 0.010.

Understanding True Position From Two Axis Deviations

A true position calculator checks a measured point against its target point. The X and Y errors form a right triangle. Their direct distance gives the center offset. The formula doubles that distance. The result is then shown as a diameter. The tool can compare the result with a limit set by the user. The math is a quick check. A large miss is easy to spot. Machinists and CMM staff can also use the answer to check a report. A final pass call needs the right datum frame and part setup. The CMM frame must match the print. ASME Y14.5 rules still apply. Use the same unit on both axes. Keep full digits until the last round. A pass flag is only a basic check.

How True Position Is Calculated From Axis Deviations

The answer uses the same unit as the two errors. A basic pass means the answer does not exceed the entered limit.

  • True Position = 2 × √(Δx² + Δy²).

Δx: measured X minus nominal X.

Δy: measured Y minus nominal Y.

√(Δx² + Δy²): radial center offset.

True position: twice the radial offset.

Using A True Position Calculator In Five Clear Steps

Inputs

  • X deviation: measured X minus nominal X.
  • Y deviation: measured Y minus nominal Y.
  • Tolerance: allowed diametrical position value.

Steps

  1. Set the correct datum frame.
  2. Find both axis errors.
  3. Enter the X and Y values.
  4. Enter the position limit.
  5. Read the value and status.

True Position Calculation Example With Full Working

Δx is 0.003 in, Δy is 0.004 in, and tolerance is 0.012 in.

  1. Square the errors: 0.003² = 0.000009 and 0.004² = 0.000016.
  2. Sum the squares: 0.000009 + 0.000016 = 0.000025.
  3. Take the square root to find radial offset: √0.000025 = 0.005 in.
  4. Double the radial offset for true position: 2 × 0.005 = 0.010 in.

True position is 0.010 in. Since 0.010 ≤ 0.012, the basic check passes.

When True Position Math Fits A Basic Feature Check

Use the tool to check simple X and Y data or a CMM report value. Use full CMM software for datum shifts, bonus rules, and complex patterns. Read the print.

For other mechanical tolerances and coordinate checks, see the engineering calculators hub, and check the glossary for dimensional terms.

Assumptions

  • Both errors use the same unit.
  • Both errors use the right nominal point.
  • The axis frame matches the drawing datums.
  • The result is diametrical.
  • The limit uses the same unit.

Limitations

  • The tool covers two-axis math only.
  • MMC and LMC bonus are not added.
  • Datum alignment is not built by the tool.
  • Composite and projected zones need full review.
  • Measure error is not included.

In Practice

Inspectors often enter measured points instead of target errors, so find each axis error first. Use the same unit on both axes. Keep full digits until the last step, then check the datum setup and print. Check the math twice.

Related Calculators

SFM Calculator

Calculate machining surface speed, spindle RPM, or cutting diameter from the other two values, with a metres-per-minute result.

Open the Calculator

Planar Density Calculator

Find atomic planar density from the effective atoms on a crystal plane and the matching two-dimensional area in square nanometres.

Open the Calculator

Cycles Per Instruction Calculator

Find CPU cycles per instruction, IPC, and optional run time from a cycle count, an instruction count, and the chip clock rate.

Open the Calculator

Bolt Circle Calculator

Find the angle between bolt holes and the chord distance between adjacent holes on any bolt circle. Enter the radius and number of holes for instant results.

Open the Calculator

Related Guides

Frequently Asked Questions About Position Tolerance

Why Is The Center Offset Multiplied By Two?

The straight line from the target to the measured center is a radial offset. The position limit is shown as a diameter, so the calculator doubles that offset. The point did not move twice as far.

Do Negative X Or Y Errors Change The Result?

Negative X or Y signs do not change the final size because each error is squared. Direction still matters during the check, so keep the original signs in the report. Use those signs to review the setup and datum frame.

Does This Tool Add MMC Bonus Tolerance?

This calculator does not add MMC or LMC bonus to the entered limit. Read the size and datum rules on the print, then add any valid bonus before the final pass call. Use full inspection software when modifiers apply.

Can This Replace A Full CMM Position Report?

This calculator cannot replace a full CMM position report for final part acceptance. The simple pass flag checks two-axis math and an entered limit only. CMM software also applies datums, feature fits, bonus rules, and report settings.

Sources

Last updated: . Reviewed for accuracy against the formula shown above.