How to Use a Z-Score Calculator

Step 1: Enter Your Numbers

Raw Score (X): This is your actual result

• Example: You got 75 on a test

Mean (μ): This is the average of all scores

• Example: Class average was 70

Standard Deviation (σ): This shows how spread out the scores are

• Example: Most students scored within 5 points of average

Step 2: Calculate

Click the "Calculate Z-Score" button. The tool uses this formula: z = (X - μ) / σ

Using our example:

• z = (75 - 70) / 5 = 1.00

Step 3: Read Your Results

Z-Score: Shows how many standard deviations you are from average

• 0 = exactly average
• Positive = above average
• Negative = below average

Probability: Shows what percentage of people scored below you

• In our example: 15.87% means you did better than 84% of students

Real Examples

Test Scores

• Your score: 85
• Class average: 78
• Standard deviation: 6
• Z-score: +1.17 (above average)

Height Comparison

• Your height: 160 cm
• Average height: 165 cm
• Standard deviation: 8
• Z-score: -0.63 (slightly below average)

Salary Analysis

• Your salary: $55,000
• Average salary: $50,000
• Standard deviation: $10,000
• Z-score: +0.50 (moderately above average)

Understanding the Graph

The blue curve shows normal distribution. The red dot marks your position:

• Far left = much below average
• Center = average
• Far right = much above average

The Z-score tells how far your number is from the average:

Z-Score	Meaning
0	You are exactly average
+1	1 step above average
−1	1 step below average
+2	Much better than average
−2	Much lower than average

Z Score Table

Here is a standard Z-Score Table (Z-Table) that shows the area (probability) under the normal curve to the left of a given Z-score value. This is also called the cumulative probability.

How to Read This Table:

• The rows give the first digit and the first decimal of the Z-score (e.g., 1.2).
• The columns give the second decimal (e.g., .01, .02...).
• The value in the cell is the area to the left of the Z-score (i.e., the cumulative probability from −∞ to Z).

Partial Z-Score Table (Z from 0.00 to 3.09)

Z|Col	.00	.01	.02	.03	.04	.05	.06	.07	.08	.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
2.5	0.9938	0.9939	0.9940	0.9941	0.9942	0.9943	0.9944	0.9945	0.9946	0.9947
3.0	0.9987	0.9987	0.9987	0.9988	0.9988	0.9989	0.9989	0.9989	0.9990	0.9990