Raw Score Calculator — Convert Z-Score to Original Value
Enter a z-score, the population mean and standard deviation to find the corresponding raw (original) score. Also shows the cumulative percentile under a normal distribution.
x = μ + z·σ = 70 + 1.5 × 10
- 1
Deviation from mean (z × σ)
1.5 × 10 = 15Multiply the z-score by the standard deviation to get the signed distance from the mean. - 2
Raw score (μ + z·σ)
70 + 15 = 85
How does this calculator work?
To recover a raw score from a z-score: x = μ + z·σ. Multiply z by the standard deviation to get the signed displacement from the mean, then add the mean. A z of 1.5 with mean 70 and SD 10 gives the raw score 85. Assumes normal distribution for the percentile estimate.
Formula
How this is calculated
A z-score expresses a value as the number of standard deviations it sits above or below the mean. The inverse operation — recovering the original (raw) value from a known z-score — is simply x = μ + z·σ. Multiply the z-score by the standard deviation to get the signed distance from the mean (the deviation), then add the mean to shift back to the original scale.
For example, if a test has a mean of 70 and a standard deviation of 10, a z-score of 1.5 corresponds to the raw score 70 + 1.5 × 10 = 85. A negative z-score (e.g. z = −1) gives a raw score below the mean (70 − 10 = 60 in the same example).
The calculator also reports the cumulative probability P(Z ≤ z) from the standard normal table, which equals the percentile rank — assuming the underlying population follows a normal distribution. This assumption is crucial: for non-normal data the z-score conversion still gives the correct raw value, but the percentile interpretation may not apply.
Frequently asked questions
A raw score is the original measurement in its natural unit (e.g. exam points, height in cm). A z-score rescales it to units of standard deviation from the mean, making it comparable across different distributions. This calculator reverses that rescaling.
Mathematically yes — the formula has no built-in ceiling. If the computed raw score exceeds the test maximum, check that the z-score, mean and SD are correct. In practice, z-scores beyond ±3 are rare in most populations.
T-scores are a rescaled z-score: T = 50 + 10·z. This calculator computes the raw score from the z directly using the original mean and SD — not the T-score scale.
Also known as
TG we-Calculate Editorial Team. (2026). Raw Score Calculator — Convert Z-Score to Original Value [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/raw-score-calculator
TG we-Calculate Editorial Team. "Raw Score Calculator — Convert Z-Score to Original Value." TG we-Calculate. 2026. https://we-calculate.com/calculator/raw-score-calculator.
TG we-Calculate Editorial Team, "Raw Score Calculator — Convert Z-Score to Original Value," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/raw-score-calculator
@misc{wecalculate_raw_score_calculator, title = {Raw Score Calculator — Convert Z-Score to Original Value}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/raw-score-calculator}}, year = {2026}, note = {TG we-Calculate} }
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