True Position Calculator
Check a feature's true position. Enter the basic and measured X/Y, the stated position tolerance and material condition (RFS / MMC / LMC), and the feature size for bonus — get the true position diameter, the bonus and total allowed tolerance, the percent used and a pass/fail result, with a tolerance-zone diagram, a true-position-to-coordinate table and a downloadable PDF.
| Feature size | Bonus | Total allowed | Result |
|---|---|---|---|
| Enter values to compare | |||
| True position ⌀ | ± Coord. tol. | Square zone | vs yours |
|---|---|---|---|
| Enter values to compare | |||
How to use the true position calculator
Four quick steps turn a feature’s basic and measured coordinates into a GD&T true position check — the true position diameter, the bonus and total allowed tolerance, the percent used and a clear pass or fail.
Enter basic vs measured
The basic (drawing) X/Y and the actual measured X/Y of the feature.
Enter the tolerance
The stated position tolerance diameter from the feature control frame.
Pick the condition
RFS, MMC or LMC — and the feature size for any bonus.
Read results & save a PDF
Get the true position, allowed tolerance and pass/fail — then download a report.
The formulas behind true position
The true position comes from the X and Y deviations; the allowed tolerance is the stated value plus any bonus from the material condition.
▶ Worked example
A feature basic at X 2.000, Y 1.500, measured at X 2.004, Y 1.497, stated tolerance Ø0.014 at MMC, MMC size 0.250, actual size 0.256.
Deviations ΔX = 0.004, ΔY = -0.003; radial = 0.005; true position = 2 × 0.005 = Ø0.010.
Bonus = |0.256 − 0.250| = 0.006, so allowed = 0.014 + 0.006 = Ø0.020.
True position Ø0.010 · allowed Ø0.020 · 50% used · PASS
At RFS there would be no bonus, so the allowed stays Ø0.014 and the feature uses 71%.
True position quick reference
The core formulas, the true-position-to-coordinate conversion, and how bonus tolerance grows as a feature moves away from MMC.
| Quantity | Formula |
|---|---|
| X / Y deviation | measured − basic |
| True position | 2 × √(ΔX² + ΔY²) |
| Bonus tolerance | |actual size − MMC / LMC size| |
| Total allowed | stated + bonus |
| Percent used | true position ÷ total allowed |
| Coordinate equivalent | Ø ÷ (2√2) per axis |
| True position Ø | ± per axis | Square zone |
|---|---|---|
| Ø0.005 | ±0.0018 | 0.0035 × 0.0035 |
| Ø0.010 | ±0.0035 | 0.0071 × 0.0071 |
| Ø0.014 | ±0.0049 | 0.0099 × 0.0099 |
| Ø0.020 | ±0.0071 | 0.0141 × 0.0141 |
| Ø0.030 | ±0.0106 | 0.0212 × 0.0212 |
| Ø0.050 | ±0.0177 | 0.0354 × 0.0354 |
Divide the position diameter by 2√2 (about 2.83) for the equivalent per-axis tolerance. The round zone has about 57% more area than the square zone that fits inside it.
| Actual size | Bonus | Total allowed | At TP Ø0.010 |
|---|---|---|---|
| 0.250 (at MMC) | 0.000 | Ø0.014 | 71.4% used |
| 0.252 | 0.002 | Ø0.016 | 62.5% used |
| 0.254 | 0.004 | Ø0.018 | 55.6% used |
| 0.256 | 0.006 | Ø0.020 | 50.0% used |
| 0.258 | 0.008 | Ø0.022 | 45.5% used |
| 0.260 | 0.010 | Ø0.024 | 41.7% used |
Bonus = |actual − MMC size|. As the hole grows away from MMC, more bonus is earned, so the same true position uses a smaller share of the allowed tolerance.
Everything the calculator returns
One calculation gives the full position picture — the deviation, the true position, the bonus and a clear verdict.
True position at a glance
The core relationships, and the default result.
Built for the way you work
Whether you are inspecting a part, running the machine, or drawing the print, the true position check starts from the same inputs.
Verifying a feature against its position callout and need the true position, bonus and a clear pass or fail for the report.
- Enter measured X/Y straight from the CMM
- Add bonus for off-MMC size
- Record the percent used
A feature is close to the edge of tolerance and you need to know how much to correct and whether bonus saves it.
- See the deviation on each axis
- Check if size earns bonus
- Know exactly how much you’re over
Setting a position tolerance and want to compare it against a coordinate tolerance or see the bonus a feature will earn.
- Convert to or from coordinate tol
- Pick RFS, MMC or LMC
- Size the zone for assembly
Get true position right
Seven things that keep a GD&T position check accurate.
Basic dimensions are exact
The basic X/Y that locate the feature carry no tolerance. All the allowance lives in the position callout, not the locating dimensions.
Claim your bonus
At MMC or LMC, a feature made away from the stated size earns bonus tolerance. Don’t reject a part before checking the actual size.
Mind the round vs square gap
A round position zone has about 57% more area than the square coordinate box, so coordinate limits can reject good parts.
Measure from the datums
True position is relative to the datum reference frame. If the datums are set up wrong, a good feature can read as out of position.
Report it as a diameter
True position is always a diameter — twice the radial error. Reporting a radius halves the number and misstates the result.
RFS earns no bonus
Under regardless-of-feature-size the tolerance is fixed. Only MMC and LMC callouts add bonus as the size moves.
Read the feature control frame
The callout gives the tolerance, the modifier and the datums in order. Enter the stated tolerance and condition exactly as drawn.
Frequently asked questions
Common questions about true position, bonus tolerance, material conditions and coordinate conversion.
True position is the diameter of the smallest cylindrical zone, centered on the basic (theoretically exact) location, that contains the feature’s actual center. You find it from the X and Y deviations: subtract the basic coordinate from the measured coordinate on each axis, then the true position diameter is two times the square root of the X deviation squared plus the Y deviation squared.
The factor of two is because the result is a diameter — a zone around the true location — not a radius. You then compare it against the allowed tolerance from the drawing.
For example, a feature basic at X 2.000, Y 1.500 measured at X 2.004, Y 1.497 has deviations of 0.004 and -0.003, a radial error of 0.005, and a true position of 0.010 diameter. This calculator works it out and checks it against the tolerance, bonus included.
True position is a GD&T control that defines how far a feature — usually a hole or pin — may stray from its exact drawing location. Instead of a square plus-or-minus box on each axis, it allows a round cylindrical tolerance zone centered on the basic location, which better matches how a round feature is actually used.
The basic dimensions that locate the feature are exact and carry no tolerance of their own; all the allowance lives in the position tolerance in the feature control frame, measured relative to the datums.
A round zone is both fairer and more generous than coordinate tolerancing, because it does not penalize a feature that is off in two axes at once. This calculator reports the true position and whether it falls inside the allowed zone.
Bonus tolerance is extra position tolerance you earn when a feature is made away from its maximum (or least) material condition. When a position tolerance is called out at MMC, the stated tolerance applies at the smallest hole, or largest pin; as the hole grows, the surplus material becomes extra position tolerance.
The bonus is the absolute difference between the actual feature size and the MMC (or LMC) size, and it is added to the stated tolerance: total allowed = stated + bonus. At RFS there is no bonus — the tolerance is fixed regardless of size.
For example, a 0.014 stated tolerance at MMC with a 0.250 MMC size and a 0.256 actual size earns a 0.006 bonus, for a 0.020 total allowed. This calculator computes the bonus and the total for you.
A true position diameter and a plus-or-minus coordinate tolerance describe the same deviation two ways. To convert a round position tolerance to an equivalent per-axis coordinate tolerance, divide the diameter by two times the square root of two; to go the other way, multiply the per-axis tolerance by two times the square root of two.
So a round zone is a little under three and a half times the per-axis tolerance in diameter. The conversion lets you compare a GD&T position callout against an older coordinate-dimensioned drawing.
For example, a true position of 0.014 diameter is about plus-or-minus 0.005 per axis, and a plus-or-minus 0.005 square tolerance converts to a 0.014 diameter zone. This calculator shows the coordinate equivalents across a range of position tolerances.
They are the three material condition modifiers that decide whether a feature earns bonus tolerance. RFS — regardless of feature size — means the position tolerance is fixed and no bonus applies, whatever the feature’s actual size.
MMC — maximum material condition — applies the stated tolerance when the feature has the most material (the smallest hole or largest pin), and grants bonus as it moves away from that. LMC — least material condition — does the reverse, applying the stated tolerance at the least material and granting bonus toward the most.
MMC is the most common, because it matches assembly: a hole that is larger than its smallest size has room to spare, so it can be a little more out of position. This calculator handles all three and adds the right bonus.
Because a hole or pin can be off in any direction, its location error is naturally a radial distance, and the set of allowed locations is a circle around the basic point. Quoting that circle as a diameter describes the full round tolerance zone in one number.
A diameter zone is more honest than a square plus-or-minus box, which would allow more error in the diagonal corners than along the axes. The round zone treats every direction equally, matching how a round feature mates with its counterpart.
For example, a feature 0.005 off the basic location in a straight line is at a true position of 0.010 diameter — twice the radial deviation. This calculator always reports the position as a diameter, as the standard requires.
Because the two zones are different shapes. A coordinate tolerance is a square box — plus-or-minus on each axis — while a true position tolerance is a round zone. A round diameter zone has about 57% more area than the square zone that fits inside it, so it accepts features the square box would reject, especially those off in two axes at once.
A feature sitting near the corner of the square zone can be inside the equivalent round zone, so it passes true position while failing the tighter coordinate check. This is one reason GD&T position tolerancing is preferred — it does not throw away good parts.
This calculator evaluates the round true position zone and also shows the coordinate equivalent, so you can see how the two compare for your feature.
When a feature is out of position, you have a few options. The most direct is to reduce the deviation — adjust the machine offsets, fixture or program so the feature is cut closer to its basic location on the axes that are off.
You can also check whether you are owed more tolerance: confirm the material condition and the actual feature size, because a hole made further from MMC earns bonus that may bring it into spec. Verify the datums and the measurement setup too, since an error in the reference frame can make a good feature look bad.
If none of that closes the gap, the drawing tolerance itself may need review with the designer. This calculator shows exactly how much the feature is over, so you know how much you need to recover.
Disclaimer: GD&T position, two-axis (X/Y). True position Ø = 2 × √(ΔX² + ΔY²), where ΔX and ΔY are measured minus basic. Bonus = |actual feature size − MMC (or LMC) size|; total allowed = stated tolerance + bonus; RFS earns no bonus. Coordinate equivalent = Ø ÷ (2√2) per axis. This covers a single feature from its datum reference frame — it does not handle composite position, pattern/datum shift, projected tolerance zones or three-dimensional cases. A reference aid only — interpret the feature control frame and verify results against ASME Y14.5 and your inspection procedure.