Z-Score to P-Value Table
Two-tailed p-value at every hundredth of a z-score from 0 to 4, computed rather than transcribed from a printed table. The classic cuts fall at 1.645 (p = 0.10), 1.96 (p = 0.05) and 2.576 (p = 0.01).
Source data and formula checked · How we check
Z-Score to P-Value Table reads p-value straight off z-score, for 76 values from 0 to 4. Every row is computed from the same formula the calculator uses, not measured or copied from another table, so a value between two rows can be worked out the same way. The formula is the one published by NIST/SEMATECH e-Handbook of Statistical Methods.
Standard normal, two-tailed. Halve any value for a one-tailed test.
| Z-score | P-value | Percentile |
|---|---|---|
| 0 | 1 | 50 % |
| 0.05 | 0.960122 | 51.99 % |
| 0.1 | 0.920344 | 53.98 % |
| 0.15 | 0.880765 | 55.96 % |
| 0.2 | 0.841481 | 57.93 % |
| 0.25 | 0.802587 | 59.87 % |
| 0.3 | 0.764177 | 61.79 % |
| 0.35 | 0.726339 | 63.68 % |
| 0.4 | 0.689157 | 65.54 % |
| 0.45 | 0.65271 | 67.36 % |
| 0.5 | 0.617075 | 69.15 % |
| 0.55 | 0.582319 | 70.88 % |
| 0.6 | 0.548506 | 72.57 % |
| 0.65 | 0.515692 | 74.22 % |
| 0.7 | 0.483927 | 75.8 % |
| 0.75 | 0.453255 | 77.34 % |
| 0.8 | 0.423711 | 78.81 % |
| 0.85 | 0.395325 | 80.23 % |
| 0.9 | 0.36812 | 81.59 % |
| 0.95 | 0.342112 | 82.89 % |
| 1 | 0.317311 | 84.13 % |
| 1.05 | 0.293718 | 85.31 % |
| 1.1 | 0.271332 | 86.43 % |
| 1.15 | 0.250144 | 87.49 % |
| 1.2 | 0.230139 | 88.49 % |
| 1.25 | 0.2113 | 89.44 % |
| 1.3 | 0.193601 | 90.32 % |
| 1.35 | 0.177016 | 91.15 % |
| 1.4 | 0.161513 | 91.92 % |
| 1.45 | 0.147059 | 92.65 % |
| 1.5 | 0.133614 | 93.32 % |
| 1.55 | 0.121142 | 93.94 % |
| 1.6 | 0.109599 | 94.52 % |
| 1.645 | 0.0999698 | 95 % |
| 1.65 | 0.0989429 | 95.05 % |
| 1.7 | 0.0891309 | 95.54 % |
| 1.75 | 0.0801183 | 95.99 % |
| 1.8 | 0.0718606 | 96.41 % |
| 1.85 | 0.0643135 | 96.78 % |
| 1.9 | 0.0574331 | 97.13 % |
| 1.95 | 0.0511761 | 97.44 % |
| 1.96 | 0.0499958 | 97.5 % |
| 2 | 0.0455003 | 97.72 % |
| 2.05 | 0.0403644 | 97.98 % |
| 2.1 | 0.0357288 | 98.21 % |
| 2.15 | 0.0315552 | 98.42 % |
| 2.2 | 0.0278069 | 98.61 % |
| 2.25 | 0.0244489 | 98.78 % |
| 2.3 | 0.0214482 | 98.93 % |
| 2.33 | 0.0198062 | 99.01 % |
| 2.35 | 0.0187734 | 99.06 % |
| 2.4 | 0.0163951 | 99.18 % |
| 2.45 | 0.0142856 | 99.29 % |
| 2.5 | 0.0124193 | 99.38 % |
| 2.55 | 0.0107723 | 99.46 % |
| 2.576 | 0.00999506 | 99.5 % |
| 2.6 | 0.00932238 | 99.53 % |
| 2.65 | 0.00804918 | 99.6 % |
| 2.7 | 0.00693395 | 99.65 % |
| 2.75 | 0.00595953 | 99.7 % |
| 2.8 | 0.00511026 | 99.74 % |
| 2.85 | 0.00437192 | 99.78 % |
| 2.9 | 0.00373163 | 99.81 % |
| 2.95 | 0.00317774 | 99.84 % |
| 3 | 0.0026998 | 99.87 % |
| 3.1 | 0.00193521 | 99.9 % |
| 3.2 | 0.00137428 | 99.93 % |
| 3.291 | 0.000998319 | 99.95 % |
| 3.3 | 0.000966848 | 99.95 % |
| 3.4 | 0.000673859 | 99.97 % |
| 3.5 | 0.000465258 | 99.98 % |
| 3.6 | 0.000318217 | 99.98 % |
| 3.7 | 0.000215599 | 99.99 % |
| 3.8 | 0.000144696 | 99.99 % |
| 3.9 | 9.61927e-5 | 100 % |
| 4 | 6.33425e-5 | 100 % |
Questions people actually ask
- How do I read the Z-Score to P-Value Table chart?
- Find your z-score in the first column and read across. At 0 the p-value is 1; at 4 it is 6.33425e-5. The table runs from 0 to 4 in 76 rows.
- How much does the p-value change per row?
- By 0 for every 0.05 of z-score, and by the same amount everywhere in the table — the relationship is a straight line, so halfway between two rows is halfway between their two answers. That is what makes reading between the rows safe here.
- What if my z-score is outside the table?
- The chart covers 0 to 4, which is the range people actually look up. Anything above or below goes into the calculator, which takes any figure and shows each step of the working rather than only the result. Open the z-score to p-value calculator.
- Where do these numbers come from?
- Every row is computed at build time from the formula published by NIST/SEMATECH e-Handbook of Statistical Methods, by the same code behind the calculator — not transcribed from another table, which is how a rounding error in one chart ends up in twenty.
Need a different number?
The chart covers the common values. For anything between the rows, the z-score to p-value calculator takes any figure and shows the working.
Source: NIST/SEMATECH e-Handbook of Statistical Methods — cumulative distribution function of the standard normal, American Statistical Association — statement on p-values