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Disponible vs. à disposition

While both disponible and the phrase à disposition translate to available in English, they are not always interchangeable. The choice depends on what is available and the context, with disponible describing a state and à disposition implying an action of providing something for someone's use.

Disponible

A2
This is an adjective that describes the state of a person, place, or thing being free, not in use, or obtainable. It agrees in gender and number with the noun it modifies (disponible for masculine/feminine singular, disponibles for plural). It is the most common and general way to say available.
Le médecin n'est pas disponible avant la semaine prochaine.
(The doctor is not available before next week.)
Ce livre est-il disponible à la bibliothèque ?
(Is this book available at the library?)
La salle de réunion sera disponible dans dix minutes.
(The meeting room will be available in ten minutes.)
Tous les billets pour le concert de ce soir sont déjà vendus, il n'y en a plus de disponibles.
(All tickets for tonight's concert are already sold, there are no more available.)
Je suis disponible si tu as besoin de parler.
(I'm available if you need to talk.)
Les nouvelles fonctionnalités seront disponibles dans la prochaine mise à jour.
(The new features will be available in the next update.)

À disposition

B1
This is a prepositional phrase that means something is put 'at someone's disposal' or made available for use. It emphasizes the action of providing a resource or service for a specific person or group. It is often used with verbs like mettre (to put/place) or être (to be). It is invariable.
Je reste à votre entière disposition pour toute information complémentaire.
(I remain at your entire disposal for any further information.)
L'hôtel met des vélos à la disposition de ses clients.
(The hotel puts bicycles at the disposal of its guests.)
Un service de navette est à la disposition des voyageurs.
(A shuttle service is available for travelers.)
Toute la documentation nécessaire a été mise à votre disposition.
(All the necessary documentation has been made available to you.)
Le budget est à la disposition du chef de projet.
(The budget is at the disposal of the project manager.)
L'entreprise met un coach à ma disposition pour m'aider à progresser.
(The company is providing me with a coach to help me progress.)

Summary

In short, use disponible as a simple adjective to state that a person or thing is free or in stock. Use à disposition when you want to emphasize that something is actively being provided for someone's use or service, often translated as 'at someone's disposal'. If you can say at your disposal in English, à disposition is the correct choice. Otherwise, disponible is usually the safer bet.