True Position Calculator
Convert measured X and Y deviations into a diametral true position, with optional MMC bonus tolerance and a pass/fail against your feature control frame.
- Rev
- 2026-08-01
- Formulas
- 3
- Assumptions
- 4
Position tolerance in ASME Y14.5 is a diametral zone: the axis of the produced feature must lie inside a cylinder of diameter Ⓣ centered on the theoretically exact (basic) location. Measurement gives you a radial deviation; the tolerance is stated as a diameter. That factor of two is where most of the confusion lives.
Enter the deviation of the actual feature axis from its basic location, resolved into two perpendicular directions in the datum reference frame.
From the basic location.
Perpendicular to X.
Diametral, from the feature control frame.
Regardless of feature size: the tolerance applies as written and there is no bonus. Switch to MMC only when the feature control frame carries the Ⓜ modifier.
True position
0.2884⌀ mm
Radial deviation
0.1442mm
Bonus tolerance
0mm
RFS — no bonus
Total allowed
0.3500⌀ mm
Stated tolerance plus any bonus.
Substitution
TP = 2 × √(0.1200² + 0.0800²) = 0.2884 mm
allowed = 0.3500 + 0.0000 = 0.3500 mm
0.2884 ≤ 0.3500 → within tolerance
Assumptions
A number without its assumptions is not citable. These are the conditions the result is valid under.
- ΔX and ΔY are perpendicular and expressed in the datum reference frame called out by the feature control frame — not in machine coordinates.
- Bonus tolerance is available only with the Ⓜ (MMC) modifier applied to the tolerance. Without a modifier the tolerance applies regardless of feature size (RFS) and the bonus is zero.
- MMC of an internal feature (a hole) is its smallest allowed size; MMC of an external feature (a pin or boss) is its largest allowed size.
- The result is a two-dimensional position. Features toleranced over a length may also need perpendicularity or a projected tolerance zone, which this does not cover.
Formulas
What the tool computes, written out. Every symbol is defined.
True position
TP = 2 × √(ΔX² + ΔY²)
- TP
- true position — the diameter of the zone the axis lies in
- ΔX
- deviation from basic location along the first axis
- ΔY
- deviation from basic location along the second axis
Bonus tolerance at MMC
bonus = |actual size − MMC size|
Only applies when the Ⓜ modifier follows the tolerance in the feature control frame.
Acceptance
pass if TP ≤ tolerance + bonus
Questions
6 questionsWhy is true position multiplied by two?
Because the tolerance zone is a cylinder specified by its diameter, while your measurement gives the radius of the offset. √(ΔX² + ΔY²) is how far the axis has moved from the basic location; the smallest cylinder centered on the basic location that still contains it has twice that diameter.
What is bonus tolerance at MMC?
When a feature is produced away from its maximum material condition — a hole bigger than its smallest allowed size, a pin smaller than its largest — there is extra material clearance available, and Y14.5 lets you spend it as additional position tolerance. The bonus equals the departure from MMC and is added to the stated tolerance before the pass/fail check.
How do I find MMC for a hole and for a pin?
MMC is the condition containing the most material. For a hole, that is the smallest diameter in the size tolerance; for a pin or shaft, the largest. So a Ø10.0–10.2 hole has MMC = 10.0, and a Ø9.8–10.0 pin has MMC = 10.0.
Does position apply at MMC by default?
No. Under ASME Y14.5 all geometric tolerances apply RFS — regardless of feature size — unless a material condition modifier is shown in the feature control frame. If there is no Ⓜ, there is no bonus.
What if my hole is measured at an angle?
Then the axis is not parallel to the datum and a single X/Y pair is not sufficient. Either evaluate position at the worst-case section, or specify a projected tolerance zone so the tolerance is evaluated over the mating length rather than at the surface.
Can true position ever be negative?
No. It is a diameter derived from a square root, so it is always zero or positive. A result of exactly zero means the feature axis is at its basic location.
Standards and references
- ASME Y14.5-2018, Dimensioning and Tolerancing — position tolerance, material condition modifiers, bonus tolerance.
- ISO 1101 / ISO 5458 use the same diametral-zone convention with different modifier syntax.