---
type: "calculator"
name: "True Position Calculator"
standard: "ASME Y14.5 · ISO 1101"
verified: "August 1, 2026"
url: https://shopmath.org/calculators/true-position
---

# True Position Calculator

A feature 0.15 off in X and 0.2 off in Y sits 0.2500 from true position, which is a position value of 0.5000 — inside a Ø0.5 tolerance, using 100.0% of the zone. Units are whatever you put in; nothing is converted.

## Inputs

| Input | Range | Notes |
| --- | --- | --- |
| Deviation in X and Y | any value, in millimetre or inch | Measured position minus the basic (theoretically exact) position, in the datum reference frame the feature control frame calls out. |
| Position tolerance | the diametral value from the feature control frame | Diametral, not ± per axis — position defines a cylindrical zone. |
| Material condition | RFS, MMC (Ⓜ) or LMC (Ⓛ) | MMC and LMC additionally take the feature type, its actual size and its two size limits, and pay the bonus tolerance that follows. |

## Worked example — Δx 0.15, Δy 0.2, tolerance Ø0.5

- **Deviation in X**: 0.15
- **Deviation in Y**: 0.2
- **Radial deviation**: 0.2500
- **True position (diametral)**: 0.5000
- **Stated tolerance**: Ø0.5
- **Allowed diameter**: 0.5000
- **Zone used**: 100.0%
- **Remaining**: 0.0000
- **Result**: pass

```text
true position  =  2 × √( 0.15² + 0.2² )
               =  2 × 0.2500
               =  0.5000
```

The factor of two is what makes it a diameter. Reporting the radius instead is the single most common error in position reporting.

## Round zone against the ± box it replaces

| Position tolerance (Ø) | Equivalent ± per axis | Zone radius |
| --- | --- | --- |
| 0.100 | 0.0354 | 0.0500 |
| 0.200 | 0.0707 | 0.1000 |
| 0.250 | 0.0884 | 0.1250 |
| 0.500 | 0.1768 | 0.2500 |
| 1.000 | 0.3536 | 0.5000 |

A round zone of diameter Ø has π ÷ 2 ≈ 1.5708 times the area of the largest square inscribed in it — the ~57% more tolerance that converting from coordinate to geometric tolerancing buys, at the same functional limit.

## Sources and Method for the True Position Calculator

### GD&T characteristics and modifiers

- **Source**: Unicode Character Database (Unicode License v3); characteristic list cross-checked against NASA MSFC GD&T Basics (public domain); descriptions written from scratch
- **Method**: compiled
- **Verified against**: gdt: 98 checks passed across 1 harness(es)

### Formulas

**True position from measured deviation**

```text
true position  =  2 × √( Δx² + Δy² )

  Δx, Δy = measured position minus basic (theoretically exact) position
```

_The factor of two makes it a diameter. Position defines a cylindrical zone centred on the true location, so the tolerance and the result are both diametral values._

**Bonus tolerance under Ⓜ or Ⓛ**

```text
hole at MMC  =  its smallest limit        pin at MMC  =  its largest limit
bonus        =  | actual size − stated-condition size |     (never negative)
allowed Ø    =  stated tolerance + bonus
```

_A feature outside its own size limits earns no bonus — it is a size reject before position is evaluated._

**Equivalent coordinate tolerance**

```text
± per axis  =  Ø ÷ (2 × √2)
area ratio  =  (π · Ø² ÷ 4) ÷ (ز ÷ 2)  =  π ÷ 2  ≈  1.5708
```

_The largest square inscribed in the round zone, and how much smaller it is. This is where the '57% more tolerance' figure comes from._

### Assumptions

- Δx and Δy are deviations from the BASIC dimensions, measured in the datum reference frame the feature control frame calls out. Establishing that frame correctly is a measurement question this calculator cannot check.
- The calculation is two-axis. A true position with three basic dimensions extends the same way — 2 × √(Δx² + Δy² + Δz²) — but a three-axis case usually involves a projected tolerance zone or a feature normal to a compound datum, which is not the same arithmetic.
- Everything is unit-agnostic and nothing is converted. Mixing millimetre deviations with an inch tolerance would give a plausible wrong answer, so the calculator never converts and the unit control only labels the output.
- Bonus tolerance is applied only when a material-condition modifier is selected. Since 1994 the default with no modifier is RFS: the tolerance applies at whatever size the feature was produced, with no bonus.
- Datum shift — the additional tolerance available when a datum feature of size is referenced at MMB — is a separate allowance and is NOT included here.
- No text from ASME Y14.5 or ISO 1101 is reproduced anywhere on this page. The standards are cited by number; every description is original prose written for this project.
- GD&T characteristics and modifiers scope: EXCLUDED: all ASME Y14.5 definitional text, worked examples and figures. Every description on this site is original prose.

**Data last verified**: August 1, 2026

## Related pages

- The symbol itself: [Position](https://shopmath.org/gdt/position.md)
- Material condition modifiers: [GD&T symbol reference](https://shopmath.org/gdt.md)
- All calculators: [Machining calculators](https://shopmath.org/calculators.md)

---

*Source: [ShopMath](https://shopmath.org/calculators/true-position) — data verified August 1, 2026. Reference data; verify against the governing standard before manufacture.*