Apchon is located some 80 km south-west of Clermont-Ferrand, 25 km north-west of Murat, and 30 km south-east of Bort-les-Orgues. Access is by the D3 road from Riom-ès-Montagnes in the north-west passing through the north of the commune to Murat in the south-east. Access to the village is by the D49 which branches off the D3 north-east of the commune and passes through the village then south to Saint-Hippolyte. There is also the D249 from the village south-west to join the D263 south of Collandres. Apart from the village there are also the hamlets of La Ribeyre and La Vidal along the D3, and Brechailles on the north-east. Apart from some patches of forest in the north the commune is entirely farmland.
The Petite Rhue river flows from south to north through the commune and continues to join the Grande Rhue river at Coindre. The Ruisseau de Brechailles flows from the south-east to join the Petite Rhue north of the D3. The Ruisseau de Mazeyres rises in the south of the commune and flows into the Petite Rhue on the left bank. Several small streams rise in the west of the commune and flow north-west eventually joining and flowing into the Veronne.
In 2009 the commune had 210 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.