Z-Score Calculator

It depends on context. A z-score of 0 is exactly average, +1 is higher than about 84% of values and +2 is higher than about 97.7%.

Yes. A negative z-score means the value is below the mean. For example, z = −1 is lower than about 84% of values.

Enter a value, the mean and the standard deviation to get the z-score and percentile, or turn a z-score back into a value.

What do you want to find?

Value (x)

Mean (μ)

Standard deviation (σ)

Z-score

1.5

93.32% of values fall below this value (percentile)

Step-by-step solution

Worked out with your numbers. Change any value above and the steps update.

1
z = (x − μ) ÷ σ
(85 − 70) ÷ 10 = 1.5
2
Area to the left of z (standard normal table): the percentile
P(Z < 1.5) = 93.32%
3
Area to the right: 1 − area to the left
1 − 0.933193 = 0.066807

Z-score: z = (x − μ) ÷ σ, the number of standard deviations a value is from the mean.
To go back from a z-score: x = μ + z × σ.
The percentile is the area under the standard normal curve to the left of z, the same as looking it up in a z-table.
Probabilities assume the data follows a normal (bell-shaped) distribution.

What is a good z-score?

It depends on context. A z-score of 0 is exactly average, +1 is higher than about 84% of values and +2 is higher than about 97.7%.

Can a z-score be negative?

Yes. A negative z-score means the value is below the mean. For example, z = −1 is lower than about 84% of values.

Results are estimates for general information and are not financial, medical or professional advice.