Z-Score Calculator: Raw Score to Z-Score, Percentile and P-Value

Convert a raw score to a z-score with z = (x − μ) / σ, turn a z-score back into a raw score, and get percentiles, tail probabilities and the probability between two z-scores.

Raw score (x)Mean (μ)Standard deviation (σ)

z = (x − μ) / σ

z = 1.5

The value is 1.5 standard deviations above the mean.

P(Z < z) · percentile: 0.933193 (93.3193%)
P(Z > z): 0.066807
Two-tailed P(|Z| > |z|): 0.133614

Probabilities assume the values follow a normal distribution.

What is a z-score?

A z-score (standard score) tells you how many standard deviations a value is above or below the mean. z = 2 means two standard deviations above the mean; z = −0.5 means half a standard deviation below it. Because it removes the original units, it lets you compare values from different scales.

Z-score formula

z = (x − μ) / σ

x is the value, μ the mean and σ the standard deviation. Turn it around to get a raw score from a z-score: x = μ + z × σ. If you only have a sample, you can use its mean x̄ and standard deviation s; the percentile and tail probabilities are then estimates under a normal model, not exact test p-values.

How to use the z-score calculator

Choose Raw score → z-score to standardize a value, or Z-score → raw score to find the value at a given z, and enter the mean and standard deviation (greater than 0).
Choose Between two z-scores for the probability that Z falls between a and b, or Percentile → z-score to find z for a percentile such as 0.9.
Read the result with the percentile P(Z < z), the right tail P(Z > z) and the two-tailed probability. Results update as you type; a decimal comma (1,5) also works, but do not use thousands separators.

Worked z-score examples

Computed with this calculator on 2026-11-02 from illustrative numbers. Each button loads the same inputs above.

Test score above the class mean

Inputs: x = 85, μ = 70, σ = 10
Result: z = 1.5
Percentile P(Z < z): 93.3193%

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Measurement below the process mean

Inputs: x = 9.82, μ = 10, σ = 0.06
Result: z = -3
Percentile P(Z < z): 0.1350%

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Score needed for z = 1.96 (top 2.5%)

Inputs: z = 1.96, μ = 100, σ = 15
Result: x = 129.4
Percentile P(Z < z): 97.5002%

Load this example

90th percentile height

Inputs: z = 1.281552, μ = 175, σ = 7
Result: x = 183.970861
Percentile P(Z < z): 90.0000%

Load this example

Example	Inputs	Result	Percentile P(Z < z)	Calculator
Test score above the class mean	x = 85, μ = 70, σ = 10	z = 1.5	93.3193%	Load
Measurement below the process mean	x = 9.82, μ = 10, σ = 0.06	z = -3	0.1350%	Load
Score needed for z = 1.96 (top 2.5%)	z = 1.96, μ = 100, σ = 15	x = 129.4	97.5002%	Load
90th percentile height	z = 1.281552, μ = 175, σ = 7	x = 183.970861	90.0000%	Load

Z-table: common z-scores and percentiles

Areas under the standard normal curve, computed by the same code as the calculator and rounded to 6 decimals.

z	P(Z < z)	P(Z > z)	Two-tailed
-3	0.001350	0.998650	0.002700
-2.576	0.004998	0.995002	0.009995
-2	0.022750	0.977250	0.045500
-1.96	0.024998	0.975002	0.049996
-1.645	0.049985	0.950015	0.099970
-1	0.158655	0.841345	0.317311
0	0.500000	0.500000	1.000000
1	0.841345	0.158655	0.317311
1.282	0.900079	0.099921	0.199843
1.645	0.950015	0.049985	0.099970
1.96	0.975002	0.024998	0.049996
2	0.977250	0.022750	0.045500
2.576	0.995002	0.004998	0.009995
3	0.998650	0.001350	0.002700

Probability between two z-scores

P(a < Z < b) = Φ(b) − Φ(a)

Subtract the two left-tail areas. Between z = −1 and z = 1 the probability is 68.2689%; between −1.96 and 1.96 it is 95.0004%; between 0 and 1.5 it is 43.3193%. Use the Between two z-scores mode above for any other pair.

How to interpret a z-score

z = 0 is exactly the mean; positive z is above it and negative z below it.
In a normal distribution, 4.5500% of values are more than 2 standard deviations from the mean and 0.2700% are more than 3, which is why |z| > 3 is a common outlier flag.
A z-score compares values measured on different scales, such as two exams with different means and spreads.

Need the mean and standard deviation first?

Paste your raw data into the standard deviation calculator to get the mean and the sample or population standard deviation, then enter them here. The z-score from standard deviation guide walks through the whole process.

Z-score FAQ

Can a z-score be negative?

Yes. A negative z-score means the value is below the mean; z = −1 is one standard deviation below it. Only the sign shows the direction, so z = −1.5 and z = 1.5 are equally far from the mean.

What is the z-score for the 90th percentile?

About 1.281552. Ninety percent of a normal distribution lies below z = 1.281552; for the 95th percentile it is about 1.644854.

How do you get a p-value from a z-score?

For a one-tailed test use the tail in the direction of your hypothesis: P(Z > z) for "greater than" or P(Z < z) for "less than". For a two-tailed test double the smaller tail. The calculator shows all three.

Is this a z-test?

No. This page standardizes a single value against a mean and standard deviation. A one-sample z-test compares a sample mean with a hypothesized mean using the standard error σ/√n, not σ. When σ is unknown and estimated from the sample, the usual test is a t-test with n − 1 degrees of freedom.