Raw Score Calculator

What This Raw Score Calculator Does

This tool converts between raw score, z-score, mean, and standard deviation. Pick the quantity you want to solve, enter the other three values, and the calculator rearranges the same formula instantly.

Raw Score Formula

$$z = \frac{X-\mu}{\sigma} \qquad \Longleftrightarrow \qquad X = z\sigma + \mu$$

Because the relationship is algebraic, you can isolate any one variable:

• $X = z\sigma + \mu$
• $z = \frac{X-\mu}{\sigma}$
• $\mu = X - z\sigma$
• $\sigma = \frac{X-\mu}{z}$

Why Raw Scores Matter

A raw score is the original observed value before standardization. Z-scores are useful for comparison across datasets, but the raw score tells you the actual number of points, measurements, or units. If you need the standardized side of the problem, also try our Z Score Calculator and Normal Distribution Calculator.