Flatness and Level

Flatness
The tolerance zone is defined by two parallel planes above and below the best fit plane through the measured data. The tolerance planes are separated by the tolerance t. As with the line above, if we have measured 20 points. The best fit plane is the plane where the sum of the errors (hills and valleys) is a minimum.
Don’t forget: The flatness of a plane makes no comment about how level (wrt gravity) a plane is.

Levelling
The Tolerance Zone is here, like flatness, defined by two parallel planes above and below the data. The difference here is that the planes must be orthogonal (at right angles) to gravity. In plain English: These measured points are described as level or “in water” when they lie within a given tolerance (t) to a supposed waterline drawn through the average height of the points.

Specification and mechanical Adaption

In engineering applications we measure and sometimes correct the flatness of machine components. In flatness and straightness measurements the mechanical adaptation has a dramatic effect on what we measure. It is important to consider the flatness specification in detail in order to choose an appropriate method.

A flatness can state that all points on the surface shall lie between two parallel planes separated by "X" distance, where "X" is the flatness tolerance. It can specify a tolerable wave over a specific area. Alternatively it can specify the variance of the deviation for a best fit plane. Often the specification will define explicitly or inexplicitly how the measurement must be performed.