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Norm Referenced Score Calculator

Work out norm referenced score instantly with clear inputs, formula shown and shareable results.

About Norm Referenced Score Calculator

A norm-referenced score expresses performance relative to a reference group. A raw score of 68 against a mean of 55 and standard deviation of 9 is 1.44 standard deviations above the mean - the 92.6th percentile, a T score of 64.4 and a standard score of 121.7. All four express the same position on different scales.

Formulas

z score

z = (raw score - norm mean) / norm standard deviation

Score scales

T = 50 + 10z; standard score = 100 + 15z

Worked example

With the default values below, Norm Referenced Score Calculator returns Percentile Rank of 92.57%. Change any input above and every figure here is recalculated in your browser.

Inputs used

Raw score
68
Norm group mean
55
Norm group standard deviationminimum 0
9

Results

Percentile Rank
92.57%
z Score
1.4444
T Score
64.44
Standard Score (Mean 100, SD 15)
121.67

Step by step

  1. 1Values used
  2. 2z score
  3. 3Score scales
  4. 4Percentile Rank= 92.57
  5. 5z Score= 1.4444
  6. 6T Score= 64.44
  7. 7Standard Score (Mean 100, SD 15)= 121.67

Assumptions and limits

  • The result is derived only from the 3 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

Which scale should I report?

Whatever the test manual specifies, since norms are published on a particular scale. Reporting the percentile alongside makes it interpretable to non-specialists.

Do percentiles assume normality?

Converting z to a percentile does. If the norm distribution is skewed, empirical percentile tables from the norming sample are more accurate.

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