The formula to calculate the true position variance is:
\[ TPV = 2 \times \sqrt{(mX - tX)^2 + (mY - tY)^2} \]
Where:
A true position is a type of geometric tolerance used to describe the true position of a feature with respect to one or more datums. For example, a hole position along the x-y plane.
Can a true position be negative? A true position cannot be negative. It is a measure of the absolute value of the variance of the position of a feature and can only be equal to 0 at the very least.
Does true position need a datum? A true position should use a datum when used properly. The datum is usually referenced with x and y coordinates as the basic dimensions.
Is a true position a radius or diameter? A true position is most often described as a circle around a point with a certain diameter. For example, a true position with a tolerance of .010 would be a circle around the point with a diameter of .010.
Does true position control perpendicularity? When a true position is called out with datums on the face and sides of a part, the perpendicularity is also controlled by the true position. So in short, yes, the true position does imply perpendicularity when applied properly.
Let's assume the following values:
Using the formula to calculate the true position variance:
\[ TPV = 2 \times \sqrt{(5 - 3)^2 + (7 - 4)^2} = 2 \times \sqrt{4 + 9} = 2 \times \sqrt{13} \approx 7.21 \]
The true position variance is approximately 7.21.