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Standard Score Conversion Calculator

Work out standard score conversion instantly with clear inputs, formula shown and shareable results.

About Standard Score Conversion Calculator

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.

Formulas

To z score

z = (score - mean) / sd

To the target scale

new score = target mean + target sd x z

Worked example

With the default values below, Standard Score Conversion Calculator returns Converted Score of 63.33. Change any input above and every figure here is recalculated in your browser.

Inputs used

Score to convert
120
Current scale mean
100
Current scale standard deviationminimum 0
15
Convert toone of T score (mean 50, SD 10), Standard score (mean 100, SD 15), Scaled score (mean 10, SD 3), Stanine (mean 5, SD 2), z score
T score (mean 50, SD 10)

Results

Converted Score
63.33
Target Scale
T score
Underlying z Score
1.3333
Percentile Rank
90.88%

Step by step

  1. 1Values used
  2. 2To z score
  3. 3To the target scale
  4. 4Converted Score= 63.33
  5. 5Target Scale= T score
  6. 6Underlying z Score= 1.3333
  7. 7Percentile Rank= 90.88

Assumptions and limits

  • The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Why do so many scales exist?

Historical convention within test families. Wechsler subtests use mean 10 SD 3, full scales use 100 and 15, and education research favours T scores.

Is conversion lossless?

Linearly yes, but rounding to integers loses precision, and stanines especially compress the distribution into nine coarse bands.

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Standard Score Conversion Calculator | Calcrivo