How to use this raw score calculator
Enter a z-score, the distribution's mean and its standard deviation. The calculator reverses the z-score formula to recover the original (raw) value, and shows the percentile the z-score came from.
Running the z-score backwards
The z-score formula strips a value down to "standard deviations from the mean". The raw score calculator is its inverse: given a position (z) and a distribution (μ, σ), rebuild the value. Teachers use it to set grade boundaries: "the top 10% get an A" becomes a z of 1.28, becomes an actual mark. Psychologists use it to convert standardised test results back into the units of age norms and scaled scores.
On a test with mean 70 and SD 10, what raw mark marks the 93rd percentile? The percentile is z = 1.5, so x = 70 + 1.5 × 10 = 85. A boundary at the 75th percentile (z ≈ 0.674) would be 70 + 6.74 ≈ 77, the arithmetic this calculator does instantly.
Frequently asked questions
What is a raw score?
The original, unstandardised value (marks on a test, centimetres on a ruler) before any conversion to z-scores or percentiles.
What is the formula for converting a z-score back to a raw score?
x = μ + zσ: multiply the z-score by the standard deviation and add the mean.
Why convert z-scores back to raw scores?
To turn standardised positions into practical values: grade boundaries, growth-chart measurements, scaled test results.