Work out standard score conversion instantly with clear inputs, formula shown and shareable results.
All standard score scales are linear transformations of z, so converting between them means going through z first. A score of 120 on a mean 100, SD 15 scale is z = 1.33, which becomes a T score of 63.3, a scaled score of 14 or a stanine of 7.67 - the same performance in different clothing.
To z score
z = (score - mean) / sd
To the target scale
new score = target mean + target sd x z
Historical convention within test families. Wechsler subtests use mean 10 SD 3, full scales use 100 and 15, and education research favours T scores.
Linearly yes, but rounding to integers loses precision, and stanines especially compress the distribution into nine coarse bands.