Arrans is located some 6 km north of Montbard and 5 km south-east of Asnières-en-Montagne. Access to the commune is by the D5 road from Montbard in the south which passes through the heart of the commune and the village and continues north to Verdonnet. The D119 road also links the village to Asnières-en-Montagne in the north-west. The D5E branches off the D5 in the commune and goes south-west to Saint-Rémy. The commune is mostly forest with farmland around and east of the village.
In 2009 the commune had 66 inhabitants. The evolution of the number of inhabitants is known from the population censuses conducted in the commune since 1793. From the 21st century, a census of communes with fewer than 10,000 inhabitants is held every five years, unlike larger towns that have a sample survey every year.[Note 1]
^At the beginning of the 21st century, the methods of identification have been modified by Law No. 2002-276 of 27 February 2002, the so-called "law of local democracy" and in particular Title V "census operations" allows, after a transitional period running from 2004 to 2008, the annual publication of the legal population of the different French administrative districts. For communes with a population greater than 10,000 inhabitants, a sample survey is conducted annually, the entire territory of these communes is taken into account at the end of the period of five years. The first "legal population" after 1999 under this new law came into force in 1 January 2009 and was based on the census of 2006.