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In [[crystallography]], the '''R-factor''' (sometimes called residual factor or reliability factor or the R-value or R<sub>Work</sub>) is a measure of the agreement between the crystallographic model and the experimental [[X-ray diffraction]] data. In other words, it is a measure of how well the refined structure predicts the observed data.<ref name="Morris1992">{{cite journal |author=Morris AL, MacArthur MW, Hutchinson EG, Thornton JM |title=Stereochemical quality of protein structure coordinates |journal=Proteins |volume=12 |issue=4 |pages=345–64 |date=April 1992 |pmid=1579569 |doi=10.1002/prot.340120407 |url=}}</ref> The value is also sometimes called the '''discrepancy index''', as it mathematically describes the difference between the experimental observations and the ideal calcluated values.<ref>{{cite web |url= http://reference.iucr.org/dictionary/R_factor |title= R factor |publisher= International Union of Crystallography |accessdate= 2013-12-13 }}</ref> It is defined by the following equation:

:<math>R = \frac{ \sum{||F_\text{obs}| - |F_\text{calc}|| } }{ \sum{ |F_\text{obs}|}}</math>

where ''F'' is the so-called [[structure factor]] and the sum extends over all the reflections measured and their calculated counterparts respectively. The structure factor is closely related to the intensity of the reflection it describes: 

:<math>I_{hkl} \propto |F(hkl)|^2</math>

The absolute range of values is zero to one, with a large R-factor indicating a poorly refined, low-resolution model or a disordered crystal. For large molecules, R-factor usually ranges between 0.6 (when comparing a random set of reflections with a given model) and 0.2 (for example for a well refined macro-molecular model at a resolution of 2.5 Ångström). Small molecules (up to 300 atoms) usually form more ordered crystals than large molecules, it is possible to attain lower R-factors. In the [[Cambridge Structural Database]] more than 95% of the 500,000+ crystals have an R-factor lower than 0.15 and 9.5% have an R-factor lower than 0.03.  

Crystallographers also use the Free R-Factor (<math>R_{Free}</math>) <ref name="Brunger1992">{{cite journal |author=Brunger AT |title=Free R value: a novel statistical quantity for assessing the accuracy of crystal structures |journal=Nature |volume=355 |pages=472–475 |date=January 1992 |pmid=18481394 |doi=10.1038/355472a0 |url=http://www.nature.com/nature/journal/v355/n6359/abs/355472a0.html |issue=6359|bibcode = 1992Natur.355..472B }}</ref> to describe the quality of a model. 

The quantities <math>R_\text{sym}</math> and <math>R_\text{merge}</math> are similarly used to describe the internal agreement of measurements in a crystallographic data set.

==References==
{{reflist}}

==See also==
* [[Patterson function]]

[[Category:Crystallography]]