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The Formless Realm or Ārūpyadhātu (Sanskrit) or Arūpaloka (Pāli) (Tib: gzugs med pa'i khams) is a realm in Buddhist cosmology. It would have no place in a purely physical cosmology, as none of the beings inhabiting it has either shape or location; and correspondingly, the realm has no location either. This realm belongs to those devas who attained and remained in the Four Formless Absorptions (catuḥ-samāpatti) of the arūpadhyānas in a previous life, and now enjoy the fruits (vipāka) of the good karma from that accomplishment. Bodhisattvas, however, are never born in the Ārūpyadhātu even when they have attained the arūpadhyānas.
There are four types of Ārūpyadhātu devas, corresponding to the four types of arūpadhyānas:
- Naivasaṃjñānāsaṃjñāyatana or Nevasaññānāsaññāyatana (Tib: 'du shes med 'du shes med min) "Sphere of neither perception nor non-perception". In this sphere the formless beings have gone beyond a mere negation of perception and have attained a liminal state where they do not engage in "perception" (saṃjñā, recognition of particulars by their marks) but are not wholly unconscious. This was the sphere reached by Udraka Rāmaputra (Pāli: Uddaka Rāmaputta), the second of the Buddha's two teachers, who considered it equivalent to enlightenment.
- Ākiṃcanyāyatana or Ākiñcaññāyatana (Tib: ci yang med) "Sphere of Nothingness" (literally "lacking anything"). In this sphere formless beings dwell contemplating upon the thought that "there is no thing". This is considered a form of perception, though a very subtle one. This was the sphere reached by Ārāḍa Kālāma (Pāli: Āḷāra Kālāma), the first of the Buddha's two teachers; he considered it to be equivalent to enlightenment.
- Vijñānānantyāyatana or Viññāṇānañcāyatana or more commonly the contracted form Viññāṇañcāyatana (Tib: rnam shes mtha' yas) "Sphere of Infinite Consciousness". In this sphere formless beings dwell meditating on their consciousness (vijñāna) as infinitely pervasive.
- Ākāśānantyāyatana or Ākāsānañcāyatana (Tib: nam mkha' mtha' yas) "Sphere of Infinite Space". In this sphere formless beings dwell meditating upon space or extension (ākāśa) as infinitely pervasive.
See also 
- Lopez, Donald. Buddhist Scriptures.