'decomposability' originates from Latin elements via English: the prefix 'de-' comes from Latin 'dē-' meaning 'away from, undoing', and the root 'compose' comes from Latin 'componere' (com- 'together' + ponere 'to place'); the suffix '-ability' comes from Latin '-abilitas' via Old French '-abilite' meaning 'ability or capacity'.

'compose' comes from Latin 'componere' which passed into Old French as 'composer' and then into Middle English as 'compose'; the verb 'decompose' formed by prefixing Latin 'de-' to 'compose' (Old French 'decomposer' / Middle English forms) and later the noun-forming suffix '-ability' was added in Modern English to create 'decomposability'.

Originally elements implied 'putting together' (from 'componere'); with the prefix 'de-' the meaning shifted to 'undoing or separating from a composite whole'; over time 'decomposability' came to mean the capacity to be broken down or expressed as parts in both physical and abstract contexts.