Z-score calculator
Convert a raw value into a z-score using the population mean and population standard deviation.
What this calculator covers
Use this calculator when you need to compare a raw value against a known distribution on a standard-deviation scale.
A z-score is often the bridge between raw measurements and other probability tools because it turns unlike units into a common standardized position.
Frequently asked questions
- What does a z-score of 2 mean?
- A z-score of 2 means the raw value sits 2 standard deviations above the population mean. A z-score of −1.5 means the value is 1.5 standard deviations below the mean. The sign indicates direction and the number indicates distance in standard-deviation units.
- What inputs does the calculator require?
- You need the raw value you want to standardize, the population mean, and the population standard deviation. All three must be known values — this calculator does not estimate them from a dataset.
- What is the difference between a population z-score and a sample z-score?
- This calculator uses the population formula z = (x − μ) / σ, which assumes the mean and standard deviation entered are known population parameters. When those values are estimated from a sample, the same formula is still commonly used, but confidence intervals and hypothesis tests may apply t-distributions for small samples.
- Can I use a z-score to find a probability?
- Not directly here. A z-score gives you a standardized position on the normal distribution, but converting that position to a cumulative probability requires a z-table or a separate normal-distribution tool.
Tool
Run the calculation
Result
RESULT · Z-SCORE
â„–160
Primary result
1.5
A raw value of 85 sits 1.5 standard deviations from the mean of 70.
- Raw value
- 85
- Population mean
- 70
- Population SD
- 10
- Difference from mean
- 15
- Z-score
- 1.5
Step-by-step solution
- 1.Subtract the population mean from the raw value: 85 - 70 = 15.
- 2.Scale that difference by the population standard deviation 10.
- 3.The standardized result is z = 1.5, so the value is above the mean.
Walkthrough
Visual walkthrough
A z-score converts a raw measurement into a standardized distance from the mean.
01
Anchor the raw value to the mean
85 - 70 = 15
The first move is to measure how far the raw value sits from the population average.
02
Scale by the population spread
15 / 10
Dividing by the population standard deviation turns the raw-unit gap into a standardized distance.
03
Read the standardized position
Positive z-scores land above the mean and negative z-scores land below it.
z = 1.5