First used on a large-scale commercial project in 1983, the F-number system for measuring floor flatness and levelness has been perhaps the most significant factor in enabling the construction of flatter and more level concrete floors. However, because the dimensionless F-numbers are derived by processing the data from a large number of measurements, it can be difficult to grasp exactly what the numbers tell us.

### Testing for flatness and levelness

Thanks to its rigorous statistical approach and the highly accurate instruments typically used to collect the data, the F-number system's effectiveness has been widely accepted, and since 1989, has been ACI 117's preferred method for floor profile control. ASTM E1155, Standard Test Method for Determining F_{F} Floor Flatness and F_{L} Floor Levelness Numbers, specifies both the data collection procedure and how to convert the raw data into the floor's F_{F} and F_{L} numbers. It provides methodology for selecting an appropriate number of random samples from various sizes and configurations of floors to meet the minimum sampling requirements for statistical significance.

The standard is available on the ASTM Web site www.astm.org. Helpful guidelines also are offered by manufacturers and others that explain how to set up and run an F-number test. One example is the “1155 Floor Layout Helper” offered on The Face Companies' Web site, www.faceco.com. It provides examples and step-by-step instructions to help you lay out the ASTM E1155 test on almost any floor.

Allen Face developed the method and authored the ASTM standard while he was president of the Norfolk, Va.-based Edward W. Face Co., which later became The Face Companies. His company's site, www.allenface.com, offers downloadable, fill-in-the-blank sample specifications and universal, Excel-based reporting forms.

### Flatness

Flatness is a measure of how bumpy the floor's finished surface is. To quantify floor flatness using F-numbers, you begin by measuring the elevation differences, *d*, between points on the floor that are 1 foot apart along a straight line. The differences, *q*, between all adjacent *d* values are then calculated, and the mean and standard deviation of these *q* values are the two statistics finally used to compute the F_{F} number.

It's common to collate one set of data with another by comparing their means and standard deviations. The mean tells you what the average difference from the design value is—how far off target you are—and the standard deviation characterizes how much variation there is among the measurements in a set of data.

In considering floor flatness, both of these things matter. The greater the average difference, the greater the typical dip or hump there is in the surface. A small standard deviation means the transition into and out of such a dip or hump is smoother than if the standard deviation is large. Taken to the extreme, a large standard deviation may indicate a washboard effect.

However, the small scale of the *q* measurements, commonly hundredths or thousandths of an inch, would require comparing very small numbers taken out to an inconvenient number of decimal places.

In developing the F-number system, Face wanted to come up with values that would be easier to compare directly. He began by adding the magnitude of the average variation in *q* values (the absolute value of the mean) to three times the standard deviation of the *q* values. The reason for adding three standard deviations is that it represents very nearly the maximum half-width of the normal probability distribution curve, also known as a bell curve. In other words, using three times the standard deviation accounts for the diversity of the data and what the maximum difference is between the design value and any measured value.

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