What does a z-score mean?

It says how many standard deviations a value sits from the mean. z = 2 is two standard deviations above the mean, z = −1.5 is one and a half below it.

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

The one-tailed p-value is P(Z > |z|); the two-tailed one is twice that. For z = 1.96 they are 0.025 and 0.05. The right-tail and two-tail modes of this calculator give each of them.

How do I convert a z-score to a percentile?

The percentile is Φ(z) × 100. z = 1 is the 84.13th percentile and z = 0 is exactly the 50th.

How do I read a z table?

Find z to one decimal in the row, the second decimal in the column, and the cell where they meet is Φ(z) = P(Z ≤ z). Negative z is not listed, so use Φ(−z) = 1 − Φ(z). The table below highlights the cell for the z-score you are currently looking at.

Z-Score Calculator

μ = 0, σ = 1 · type a z-score or a p-value — either one solves the other

The standard normal curve with μ = 0 and σ = 1. Type a z-score to get its p-value and percentile, or type a p-value to get the z-score — the conversion runs both ways.

See other distributions →

Real-world presets:

P(X ≥ 1.96) = 0.024998

μ = 0, σ = 1

What to calculate

Value x

Probability

Type in either box — the other one is solved for you.

Decimal places

Result

P(X ≥ 1.96)

0.024998 P(X ≥ 1.96) = 1 − Φ(1.96) = 0.0249979

Related probabilities

P(X ≤ x)

0.975002

P(X ≥ x)

0.024998

P(−|z| ≤ Z ≤ |z|)

0.950004

Two-tail probability

0.049996

z-score

1.960000

Percentile

97.50th percentile

Distribution summary

Mean

Variance

Standard deviation

Median

Mode

Skewness

Excess kurtosis

Empirical rule (68–95–99.7)

Region	Range	P
Within ±1σ	-1 – 1	0.682689
Within ±2σ	-2 – 2	0.954500
Within ±3σ	-3 – 3	0.997300

Critical values

Click a row to jump the graph to that value.

Significance level α	One-tailed	Two-tailed
0.1
0.05
0.025
0.01
0.005
0.001

Convert a raw score

Raw score x

Mean (μ)

Standard deviation (σ)

z = (x − μ) / σ

—

Standard normal (z) table

Row = first decimal of z, column = second decimal. Values are Φ(z) = P(Z ≤ z). For negative z use Φ(−z) = 1 − Φ(z).

z	0.00	0.01	0.02	0.03	0.04	0.05	0.06	0.07	0.08	0.09
0.0	0.5000	0.5040	0.5080	0.5120	0.5160	0.5199	0.5239	0.5279	0.5319	0.5359
0.1	0.5398	0.5438	0.5478	0.5517	0.5557	0.5596	0.5636	0.5675	0.5714	0.5753
0.2	0.5793	0.5832	0.5871	0.5910	0.5948	0.5987	0.6026	0.6064	0.6103	0.6141
0.3	0.6179	0.6217	0.6255	0.6293	0.6331	0.6368	0.6406	0.6443	0.6480	0.6517
0.4	0.6554	0.6591	0.6628	0.6664	0.6700	0.6736	0.6772	0.6808	0.6844	0.6879
0.5	0.6915	0.6950	0.6985	0.7019	0.7054	0.7088	0.7123	0.7157	0.7190	0.7224
0.6	0.7257	0.7291	0.7324	0.7357	0.7389	0.7422	0.7454	0.7486	0.7517	0.7549
0.7	0.7580	0.7611	0.7642	0.7673	0.7704	0.7734	0.7764	0.7794	0.7823	0.7852
0.8	0.7881	0.7910	0.7939	0.7967	0.7995	0.8023	0.8051	0.8078	0.8106	0.8133
0.9	0.8159	0.8186	0.8212	0.8238	0.8264	0.8289	0.8315	0.8340	0.8365	0.8389
1.0	0.8413	0.8438	0.8461	0.8485	0.8508	0.8531	0.8554	0.8577	0.8599	0.8621
1.1	0.8643	0.8665	0.8686	0.8708	0.8729	0.8749	0.8770	0.8790	0.8810	0.8830
1.2	0.8849	0.8869	0.8888	0.8907	0.8925	0.8944	0.8962	0.8980	0.8997	0.9015
1.3	0.9032	0.9049	0.9066	0.9082	0.9099	0.9115	0.9131	0.9147	0.9162	0.9177
1.4	0.9192	0.9207	0.9222	0.9236	0.9251	0.9265	0.9279	0.9292	0.9306	0.9319
1.5	0.9332	0.9345	0.9357	0.9370	0.9382	0.9394	0.9406	0.9418	0.9429	0.9441
1.6	0.9452	0.9463	0.9474	0.9484	0.9495	0.9505	0.9515	0.9525	0.9535	0.9545
1.7	0.9554	0.9564	0.9573	0.9582	0.9591	0.9599	0.9608	0.9616	0.9625	0.9633
1.8	0.9641	0.9649	0.9656	0.9664	0.9671	0.9678	0.9686	0.9693	0.9699	0.9706
1.9	0.9713	0.9719	0.9726	0.9732	0.9738	0.9744	0.9750	0.9756	0.9761	0.9767
2.0	0.9772	0.9778	0.9783	0.9788	0.9793	0.9798	0.9803	0.9808	0.9812	0.9817
2.1	0.9821	0.9826	0.9830	0.9834	0.9838	0.9842	0.9846	0.9850	0.9854	0.9857
2.2	0.9861	0.9864	0.9868	0.9871	0.9875	0.9878	0.9881	0.9884	0.9887	0.9890
2.3	0.9893	0.9896	0.9898	0.9901	0.9904	0.9906	0.9909	0.9911	0.9913	0.9916
2.4	0.9918	0.9920	0.9922	0.9925	0.9927	0.9929	0.9931	0.9932	0.9934	0.9936
2.5	0.9938	0.9940	0.9941	0.9943	0.9945	0.9946	0.9948	0.9949	0.9951	0.9952
2.6	0.9953	0.9955	0.9956	0.9957	0.9959	0.9960	0.9961	0.9962	0.9963	0.9964
2.7	0.9965	0.9966	0.9967	0.9968	0.9969	0.9970	0.9971	0.9972	0.9973	0.9974
2.8	0.9974	0.9975	0.9976	0.9977	0.9977	0.9978	0.9979	0.9979	0.9980	0.9981
2.9	0.9981	0.9982	0.9982	0.9983	0.9984	0.9984	0.9985	0.9985	0.9986	0.9986
3.0	0.9987	0.9987	0.9987	0.9988	0.9988	0.9989	0.9989	0.9989	0.9990	0.9990
3.1	0.9990	0.9991	0.9991	0.9991	0.9992	0.9992	0.9992	0.9992	0.9993	0.9993
3.2	0.9993	0.9993	0.9994	0.9994	0.9994	0.9994	0.9994	0.9995	0.9995	0.9995
3.3	0.9995	0.9995	0.9995	0.9996	0.9996	0.9996	0.9996	0.9996	0.9996	0.9997
3.4	0.9997	0.9997	0.9997	0.9997	0.9997	0.9997	0.9997	0.9997	0.9997	0.9998

Same calculation in code

from scipy.stats import norm
norm.cdf(1.96, loc=0, scale=1)  # 0.02499789514822045

The full z table below highlights the cell for the z-score you are looking at, and every critical-value row jumps the graph to that threshold.

Z-Score Calculator

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