ConverterHub

Z-Score to Raw Score Calculator

Enter the z-score, mean and standard deviation to get the raw score.

How it is calculated

The raw score is found with x = mean + z × sd, where z is the z-score (a unitless count of standard deviations, positive above the mean and negative below), mean is the distribution's average and sd is its standard deviation. The result is in the same unit as the mean and sd, for example test points, kilograms or centimetres. The standard deviation must be greater than zero: if it is zero, negative or left empty, the tool gives no result. The answer is rounded to two decimal places for display.

Worked example

An IQ-style scale has a mean of 100 and a standard deviation of 15, and you want the score for z = 1.5. First multiply: 1.5 × 15 = 22.5. Then add the mean: 100 + 22.5 = 122.5. The tool shows a raw score of 122.50, which sits one and a half standard deviations above the average.

Try this example →

Common mistakes

  • Entering the variance instead of the standard deviation. If a paper reports variance (σ²), take the square root first, otherwise the raw score is far too spread out.
  • Dropping the minus sign on a below-average z-score. A z of −1.5 gives 77.50 on the same scale, not 122.50.
  • Using a mean and sd from a different group or test version than the one the z-score was computed against. The same z maps to different raw scores on different scales.
  • Typing a percentile (such as 93) into the z field. A percentile is not a z-score; z = 1.5 corresponds to roughly the 93rd percentile only in a normal distribution, and the tool does not convert between them.
  • Entering 0 as the standard deviation for a group where everyone scored the same. The tool requires a positive sd and returns nothing.

About this calculator

This calculator reverses the standardisation process: given a z-score (how many standard deviations a value sits from the mean) along with a distribution's mean μ and standard deviation σ, it returns the original raw score using x = μ + zσ.

Standardising a raw score to a z-score (z = (x − μ) ⁄ σ) makes values from different scales directly comparable — but reports, test norms and research papers often quote results only as z-scores, so converting back to the raw, real-world unit is exactly what this calculator does. It's used across statistics, psychometrics and standardized testing wherever someone needs to translate “how many standard deviations above average” back into an actual score, weight, height or other measured quantity.

Was this helpful?

You can pick up to 3 reactions.

Be the first to comment.

Popular calculators

Loan Calculator

Monthly payment, total interest and full amortization schedule.

Percentage Calculator

Percent change, percent of, and ratio calculations.

Discount Calculator

Calculate final price, savings, and discount amount.

BMI Calculator

Body mass index from height and weight (metric or imperial).

Age Calculator

Compute your exact age in years, months and days from a birth date.

Compound Interest Calculator

Calculate the final amount and interest earned with compounding.

All Calculators