# True Position Formula?

#### DeKamp

##### Involved In Discussions
Hello,

I am currently discussing True Position with one of our suppliers. From my metrology experience, when calculating true position it is always using the following formula
A(Sqd) + B(Sqd) = SQR RT of C(Sqd) x 2. Our supplier is stating that due to the Print feature control frame, you do not have to times by 2!?? Is he correct? It is for Ballooned # 10 & 11. From my understanding you always follow the above formula.

Suppliers statement"engineer said the true position 1.0 has no symbol φ in front of it, so it's no need to times 2 after SQR RT of C2."

Super Moderator

#### DeKamp

##### Involved In Discussions
Hi Steve,

Thanks for the information. However, I am not completely understanding. Are they stating regardless if there is a Ø in front of the allowable tolerance you must always use the x2?

#### Cari Spears

##### Super Moderator
Super Moderator
Since there is not a diameter symbol in front of the tolerance zone size, it is a linear dimension. The formula for true position is not applicable.

You've got +/-0.5 in the direction indicated by the arrows.

#### DeKamp

##### Involved In Discussions
Since there is not a diameter symbol in front of the tolerance zone size, it is a linear dimension. The formula for true position is not applicable.

You've got +/-0.5 in the direction indicated by the arrows.
Thank you very much for this. This is something I did not know! can you please let me know, if I have a MMC with this tolerance and Both features for Datum B & C have a ±0.15 within there features, do I technically have a ±0.8 allowance in either direction?

#### John Predmore

Trusted Information Resource
A(Sqd) + B(Sqd) = SQR RT of C(Sqd) x 2

Geometric Dimensioning and Tolerancing is a matter of Geometry, not Algebra. It helps to bear in mind which geometry the notations refer to. The feature control frames refer to features, not dimensions per se. The formula you refer to, I think, is Pythagorean Theorem, that is C=Sqrt of (A-sq + B-sq), which can be used to find the distance between two points in a plane. The formula you typed is similar but not mathematically equivalent to Pythagorean Theorem.

The times 2 factor which I am thinking of is when people try to find the tolerance on a distance where both ends of the dimension are covered by a tolerance on the position of the endpoint. Both ends can be further apart by the tolerance, or both ends can be closer together by the tolerance. In that way, the distance between can vary by the sum of the positional tolerance of both ends, and if both ends have equivalent tolerances, the distance tolerance is 2 times the position tolerance of one end. In your drawing, the tolerance on dimensions 5 and 9 is given directly, and not determined by positional tolerance of the endpoints.

The supplier’s engineer points out lack of a diameter symbol in the tolerance of position feature control frame. Yet, the centerline of a hole is the feature controlled by a tolerance of position on a cylindrical feature (and I include an oval-shaped hole as a cylindrical feature). The tolerance of position on a centerline is interpreted as a diameter. There are different editions of the Y14.5 GD&T standard. I can't remember if all of them require the diameter symbol. If the diameter symbol does not explicitly appear, I can’t think of another interpretation which makes sense for this geometry.

Dimensions associated with balloons 10 and 11 also have bonus tolerance, indicated by the circled-M inside the feature control frame. Bonus tolerance is a more complicated explanation, that should be understood by the persons who machine or measure this part geometry.

#### Cari Spears

##### Super Moderator
Super Moderator
Calculating true position is the Pythagorean Theorem X 2. The Pythagorean Theorem finds the hypotenuse of the triangle, which you multiply times two to turn it into a diameter.

#### Cari Spears

##### Super Moderator
Super Moderator
Thank you very much for this. This is something I did not know! can you please let me know, if I have a MMC with this tolerance and Both features for Datum B & C have a ±0.15 within there features, do I technically have a ±0.8 allowance in either direction?
Calculating the bonus tolerance is the same. If you're at least material condition on all of the features that are called out at maximum condition, you get the full bonus of the feature size tolerances.