Free statistics tool · Bell curve + full z-table

Z-Score Calculator

Turn any raw score into a z-score, get the p-value and percentile, or work backwards from a probability to z. This z-score calculator shades the answer on a live bell curve and highlights it in a complete z-table, with every step shown.

Raw score → z
P-values & percentiles
Probability → z
Full z-table

Z-score calculator

Try:

z = 1.25

Z-score1.25

P(Z < z) left0.89435

P(Z > z) right0.10565

Two-tailed p0.21130

Middle area0.78870

Percentile89th89.44% of values are lower

How it was worked out

Normal distribution curve

Shade on the curve

LeftRightBoth tailsMiddle

The 68-95-99.7 rule

68%within ±1σ of the mean

95%within ±2σ of the mean

99.7%within ±3σ of the mean

Standard normal table

Z-Table (Standard Normal Distribution Table)

Each value is the area to the left of z, written P(Z < z). Find the row for the first decimal and the column for the second. Your current z-score is highlighted.

Positive z-table: area to the left of 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
3.5	0.9998	0.9998	0.9998	0.9998	0.9998	0.9998	0.9998	0.9998	0.9998	0.9998
3.6	0.9998	0.9998	0.9999	0.9999	0.9999	0.9999	0.9999	0.9999	0.9999	0.9999
3.7	0.9999	0.9999	0.9999	0.9999	0.9999	0.9999	0.9999	0.9999	0.9999	0.9999
3.8	0.9999	0.9999	0.9999	0.9999	0.9999	0.9999	0.9999	0.9999	0.9999	0.9999
3.9	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000

Negative z-table: area to the left of 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	0.4960	0.4920	0.4880	0.4840	0.4801	0.4761	0.4721	0.4681	0.4641
−0.1	0.4602	0.4562	0.4522	0.4483	0.4443	0.4404	0.4364	0.4325	0.4286	0.4247
−0.2	0.4207	0.4168	0.4129	0.4090	0.4052	0.4013	0.3974	0.3936	0.3897	0.3859
−0.3	0.3821	0.3783	0.3745	0.3707	0.3669	0.3632	0.3594	0.3557	0.3520	0.3483
−0.4	0.3446	0.3409	0.3372	0.3336	0.3300	0.3264	0.3228	0.3192	0.3156	0.3121
−0.5	0.3085	0.3050	0.3015	0.2981	0.2946	0.2912	0.2877	0.2843	0.2810	0.2776
−0.6	0.2743	0.2709	0.2676	0.2643	0.2611	0.2578	0.2546	0.2514	0.2483	0.2451
−0.7	0.2420	0.2389	0.2358	0.2327	0.2296	0.2266	0.2236	0.2206	0.2177	0.2148
−0.8	0.2119	0.2090	0.2061	0.2033	0.2005	0.1977	0.1949	0.1922	0.1894	0.1867
−0.9	0.1841	0.1814	0.1788	0.1762	0.1736	0.1711	0.1685	0.1660	0.1635	0.1611
−1.0	0.1587	0.1562	0.1539	0.1515	0.1492	0.1469	0.1446	0.1423	0.1401	0.1379
−1.1	0.1357	0.1335	0.1314	0.1292	0.1271	0.1251	0.1230	0.1210	0.1190	0.1170
−1.2	0.1151	0.1131	0.1112	0.1093	0.1075	0.1056	0.1038	0.1020	0.1003	0.0985
−1.3	0.0968	0.0951	0.0934	0.0918	0.0901	0.0885	0.0869	0.0853	0.0838	0.0823
−1.4	0.0808	0.0793	0.0778	0.0764	0.0749	0.0735	0.0721	0.0708	0.0694	0.0681
−1.5	0.0668	0.0655	0.0643	0.0630	0.0618	0.0606	0.0594	0.0582	0.0571	0.0559
−1.6	0.0548	0.0537	0.0526	0.0516	0.0505	0.0495	0.0485	0.0475	0.0465	0.0455
−1.7	0.0446	0.0436	0.0427	0.0418	0.0409	0.0401	0.0392	0.0384	0.0375	0.0367
−1.8	0.0359	0.0351	0.0344	0.0336	0.0329	0.0322	0.0314	0.0307	0.0301	0.0294
−1.9	0.0287	0.0281	0.0274	0.0268	0.0262	0.0256	0.0250	0.0244	0.0239	0.0233
−2.0	0.0228	0.0222	0.0217	0.0212	0.0207	0.0202	0.0197	0.0192	0.0188	0.0183
−2.1	0.0179	0.0174	0.0170	0.0166	0.0162	0.0158	0.0154	0.0150	0.0146	0.0143
−2.2	0.0139	0.0136	0.0132	0.0129	0.0125	0.0122	0.0119	0.0116	0.0113	0.0110
−2.3	0.0107	0.0104	0.0102	0.0099	0.0096	0.0094	0.0091	0.0089	0.0087	0.0084
−2.4	0.0082	0.0080	0.0078	0.0075	0.0073	0.0071	0.0069	0.0068	0.0066	0.0064
−2.5	0.0062	0.0060	0.0059	0.0057	0.0055	0.0054	0.0052	0.0051	0.0049	0.0048
−2.6	0.0047	0.0045	0.0044	0.0043	0.0041	0.0040	0.0039	0.0038	0.0037	0.0036
−2.7	0.0035	0.0034	0.0033	0.0032	0.0031	0.0030	0.0029	0.0028	0.0027	0.0026
−2.8	0.0026	0.0025	0.0024	0.0023	0.0023	0.0022	0.0021	0.0021	0.0020	0.0019
−2.9	0.0019	0.0018	0.0018	0.0017	0.0016	0.0016	0.0015	0.0015	0.0014	0.0014
−3.0	0.0013	0.0013	0.0013	0.0012	0.0012	0.0011	0.0011	0.0011	0.0010	0.0010
−3.1	0.0010	0.0009	0.0009	0.0009	0.0008	0.0008	0.0008	0.0008	0.0007	0.0007
−3.2	0.0007	0.0007	0.0006	0.0006	0.0006	0.0006	0.0006	0.0005	0.0005	0.0005
−3.3	0.0005	0.0005	0.0005	0.0004	0.0004	0.0004	0.0004	0.0004	0.0004	0.0003
−3.4	0.0003	0.0003	0.0003	0.0003	0.0003	0.0003	0.0003	0.0003	0.0003	0.0002
−3.5	0.0002	0.0002	0.0002	0.0002	0.0002	0.0002	0.0002	0.0002	0.0002	0.0002
−3.6	0.0002	0.0002	0.0001	0.0001	0.0001	0.0001	0.0001	0.0001	0.0001	0.0001
−3.7	0.0001	0.0001	0.0001	0.0001	0.0001	0.0001	0.0001	0.0001	0.0001	0.0001
−3.8	0.0001	0.0001	0.0001	0.0001	0.0001	0.0001	0.0001	0.0001	0.0001	0.0001
−3.9	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000

Example: for z = 1.96, go to row 1.9 and column 0.06 to read 0.9750. For the area to the right, subtract the table value from 1.

Why use this one

Why This Z-Score Calculator Is Different

Most tools answer only one question. This one covers the whole normal distribution workflow in a single place.

Three ways in

Start from a raw score, a z-score or a probability. The calculator works in every direction.

Live bell curve

Shade the left tail, right tail, both tails or the middle and watch the area update instantly.

Every probability at once

Left and right areas, two-tailed p-value, middle area and percentile appear together, so nothing gets missed.

Built-in z-table

A full positive and negative z-table sits on the page and highlights your exact row and column.

Steps and plain English

See the formula filled in with your numbers, plus a sentence that explains what the result means.

Accurate and private

High-precision math runs in your browser, so answers are instant and your data never leaves your device.

Quick start

How to Use the Z-Score Calculator

Pick what you know
Choose Raw score, Z-score or Probability at the top of the calculator.
Enter your numbers
For a raw score, add the value, the mean and the standard deviation. Otherwise, type the z-score or probability.
Read the results
Get z, both tail areas, the two-tailed p-value, the middle area and the percentile, all updated as you type.
Check the curve and table
Change the shaded area on the bell curve, then press Find in z-table to jump to your value.

The basics

What Is a Z-Score?

A z-score, also called a standard score, tells you how far a value is from the mean, measured in standard deviations.

z = (x − μ) ÷ σ

Here x is the value, μ is the mean and σ is the standard deviation. A z-score of 0 is exactly average. Positive scores are above the mean, while negative scores are below it.

Because z-scores put different measurements on the same scale, they let you compare things like an exam score and a height fairly. You can read more in this overview of standard scores.

Z-score calculator example on a bell curve: a score of 85 with mean 70 and standard deviation 12 gives z = 1.25 — A score of 85 is 1.25 standard deviations above the mean

Worked example

How to Calculate a Z-Score Step by Step

Suppose a class test has a mean of 70 and a standard deviation of 12, and you scored 85.

Subtract the mean from your score: 85 − 70 = 15.
Divide by the standard deviation: 15 ÷ 12 = 1.25.
So your z-score is 1.25, which is one and a quarter standard deviations above average.
Look up 1.25 in the z-table to get 0.8944. As a result, you scored higher than about 89% of the class.

Z-table guide

How to Read a Z-Table

A standard z-table lists the area to the left of each z-score. To use it, split your z-score into two parts.

Row: the whole number and first decimal, such as 1.9 for z = 1.96.
Column: the second decimal, such as 0.06.
Value: where the row and column meet, here 0.9750. That is the probability of a value below z.
Right tail: subtract from 1, so P(Z > 1.96) = 1 − 0.9750 = 0.0250.
Negative z: use the negative table, or use symmetry: P(Z < −z) = 1 − P(Z < z).

Percentiles and p-values

Z-Score to Percentile and P-Value

The area to the left of z, multiplied by 100, is the percentile. For hypothesis tests, however, you usually need a p-value instead. A one-tailed p-value is the area in one tail, and a two-tailed p-value doubles the smaller tail.

Going the other way, confidence levels map to fixed critical z-values:

Confidence level	Two-tailed α	Critical z
80%	0.20	1.282
90%	0.10	1.645
95%	0.05	1.960
98%	0.02	2.326
99%	0.01	2.576
99.9%	0.001	3.291

Rule of thumb

The 68-95-99.7 Rule

In a normal distribution, about 68% of values fall within one standard deviation of the mean, about 95% within two, and about 99.7% within three. Therefore, a z-score beyond ±2 is fairly unusual, and one beyond ±3 is rare. This quick rule helps you sanity-check any z-score before you look it up.

Benefits

Who Uses a Z-Score Calculator?

Statistics students

Check homework, understand the z-table and see how p-values connect to the bell curve.

Researchers

Find critical values and p-values for z-tests and confidence intervals in seconds.

Teachers

Compare scores across different tests fairly and explain grading on a curve.

Quality and finance

Spot outliers, set control limits and measure how unusual a result really is.

Questions

Z-Score Calculator FAQs

What is a z-score?

A z-score tells you how many standard deviations a value is from the mean. A z-score of 0 is exactly average, positive scores are above the mean and negative scores are below it.

How do you calculate a z-score?

Subtract the mean from the value, then divide by the standard deviation: z = (x − μ) ÷ σ. For a test score of 85 with a mean of 70 and a standard deviation of 12, z = (85 − 70) ÷ 12 = 1.25.

What is a good z-score?

It depends on the context. For test scores, a z-score above 1 beats about 84% of people and one above 2 beats about 98%. In quality control or finance, values beyond ±2 or ±3 are often flagged as unusual.

What does a negative z-score mean?

A negative z-score means the value is below the mean. For example, z = −1.5 is one and a half standard deviations below average, and only about 6.7% of values are lower.

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

Find the area to the left of the z-score using a z-table or this calculator, then multiply by 100. A z-score of 1.25 has an area of 0.8944, so it sits at about the 89th percentile.

What z-score is used for a 95% confidence interval?

The critical value is 1.96. That means 95% of a normal distribution lies between z = −1.96 and z = 1.96, leaving 2.5% in each tail.

How do you read a z-table?

Use the row for the whole number and first decimal of your z-score, and the column for the second decimal. Where they meet is the area to the left of z. For z = 1.96, row 1.9 and column 0.06 give 0.9750.

What is the difference between a z-score and a t-score?

Both measure distance from the mean. A z-score is used when the population standard deviation is known or the sample is large. A t-score is used for small samples with an estimated standard deviation, which gives the distribution fatter tails.

Try it now

Find Your Z-Score in Seconds

Enter a value, a z-score or a probability above and get every area, the percentile and the bell curve at once. It is free and works on any device.

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