The Field Citation Ratio (FCR) is a citation-based measure of scientific influence of one or more articles. It is calculated by dividing the number of citations a paper has received by the average number received by documents published in the same year and in the same Fields of Research (FoR) category.

The FCR is calculated for all publications in Dimensions which are at least 2 years old and were published in 2000 or later. Values are centered around 1.0 so that a publication with an FCR of 1.0 has received exactly the same number of citations as the average, while a paper with an FCR of 2.0 has received twice as many citations as the average for the Fields of Research code(s).

Compared to the Relative Citation Ratio (RCR), the FCR uses a more tangible definition of a field, i.e. you can get a list of all articles in a specific FoR code - the same is not possible for RCR where the a field is relative to the publication in question.

Fields of Research (FoR) is a classification system covering all areas of research from Arts and Humanities to Science and Engineering. Assigning FoR codes to publications in Dimensions is done automatically using machine learning emulations of the categorisation processes. The FCR indicates how a publication has been cited relative to other publications with the same Fields of Research code(s).

## FCR Mean / Mean per Year

FCR Mean is the average Field Citation Ratio (FCR), which indicates the relative citation performance of an article, when compared to similarly-aged articles in its Fields of Research (FoR) category. The values per year are the years in which the publications were published. As with other calculations involving the FCR, the average calculated is the geometric mean, which reduces the effect of outlier publications with extreme citation rates.

## How we calculate the geometric mean

To calculate the geometric mean, we use the following approach, as documented in Thelwall & Fairclough (2015):

- For a set of documents, all citation counts are incremented by 1.
- We calculate the natural log of the citations counts.
- We add these values together, and divide by the number of documents.
- We calculate the exponential of this value (reversing the log effect).
- We reduce the final value by 1.