# R factor

The term ** R factor** in crystallography is commonly taken to refer to the 'conventional'

*R*factor

,

a measure of agreement between the amplitudes of the structure factors calculated from a crystallographic model and those from the original X-ray diffraction data. The *R* factor is calculated during each cycle of least-squares structure refinement to assess progress. The final *R* factor is one measure of model quality.

More generally, a variety of *R* factors may be determined to measure analogous residuals during least-squares optimization procedures. Where the refinement attempts to minimize the deviates of the squares of the structure factors (refinement against *F*^{2}), the *R* factor based on *F*^{2} is used to monitor the progress of refinement:

.

Likewise, refinement against *I* can be tracked using the Bragg *R* factor

.

Even for refinement against *F*^{2} or *I*, the 'conventional' *R* factor may be calculated and quoted as a measure of model quality, in order to compare the resulting quality of models calculated at different times and with different refinement strategies.

The *R* factor is sometimes described as the **discrepancy index**.

*R* factor as a measure of structure quality

Theoretical values of *R* range from zero (perfect agreement of calculated and observed intensities) to about 0.6 for a set of measured intensities compared against a set of random intensities. *R* factors greater than 0.5 indicate very poor agreement between observed and calculated intensities, and many models with will not respond to attempts at improvement. An early model with can usually be improved during refinement. A desirable target *R* factor for a protein model refined with data to 2.5 Å is considered to be . Small organic molecules commonly refine to *R* < 0.05. However, the *R* factor must always be treated with caution, as an indicator of precision and not accuracy. Partially incorrect structures have been reported with *R *values below 0.1; many imprecise but essentially correct structures have been reported with higher *R* values.

### Weighted *R* factors

In practice, *weighted* *R* factors are more often used to track least-squares refinement, since the functions minimized are weighted according to estimates of the precision of the measured quantity *Y*: (*Y *being *F*, *F*^{2} or *I*). The general term for a weighted residual is

The sum is usually computed over all reflections measured in the experiment. However, occasionally reflections are omitted from the calculation, either because they are believed to result from a systematic experimental error or are recorded with an intensity small compared with background noise. Any such selection may introduce statistical artifacts, and must always be described when reporting *R* factors.