A magnitude estimation experiment was carried out to scale the extent of whiteness from a set of near white textile samples including fluorescent white agent. Each was assessed under 4 different CCTs, each having a high and a low level of UV energy. The results were used to test various existing whiteness formulae. Finally, by fitting to the present data, two new metrics were developed. One is based on CIECAM02, and the other is based on the present CIE whiteness formula by transforming the data to D65 chromaticity from the other white sources via CAT02 chromatic adaption transform with a proper incomplete adaptation factor (D). It was also tested using an independent set of data. Both formulae gave accurate prediction to the data. The former metric is proposed because it is based on a colour appearance model.