'metrizable' originates from Greek and English formation, specifically from the Greek word 'metron' where the root 'metr-' meant 'measure', combined with the English/Latinizing suffixes '-ize' (to make) and '-able' (capable of).

'metrizable' developed as a modern technical formation in English from verbs like 'metrize' (to endow with a metric) or related coinages (occasionally 'metricize'), eventually producing the adjective 'metrizable' in mathematical usage.

Initially related to the idea of 'measure' (from Greek 'metron'), it was later used in technical English to mean 'able to be given a metric'; this specialized sense is now standard in topology.