What is the p-value for z = 1.96?

The preset shows 0.024998 above 1.96, 0.975002 below it and 0.049996 in both tails. For a greater-than alternative the upper tail is the p-value. For a two-sided alternative the p-value is P(|Z| >= 1.96). These are rounded normal-curve areas.

What happens for a negative z score?

The lower and upper tails exchange roles. At z = -1.96 the lower tail is 0.024998 and the upper tail is 0.975002. The two-sided p-value stays 0.049996 because it uses the distance from zero in either direction.

Does this calculate a test statistic from my data?

No. Enter an already-computed z statistic with the appropriate standard normal null model. The mean and standard deviation fields describe a distribution for converting a score to a raw value; they are not a sample size, standard error or a test-selection workflow.

Is 1.96 the exact two-sided 5% cutoff?

It is a rounded cutoff. The exact cutoff is about 1.95996398454, while 1.96 leaves about 0.0499957903 in both tails. The result rounds to 0.049996 at the displayed precision. The page shows probabilities and makes no decision about a hypothesis.

Will this preset replace my main-page draft?

No. Opening it reads its own draft without saving. Your first visit starts from z = 1.96, mean 0 and standard deviation 1. Edits made here are remembered separately from the main page.

Z Score to P-Value Calculator

Enter a z statistic whose null distribution is standard normal. Use the upper tail for a greater-than alternative, the lower tail for a less-than alternative, or both tails for a two-sided alternative.

Z-score1.96x 1.96 · mean 0 · sd 1 · lower tail 0.975002

What you have

z score

Mean (optional)

Standard deviation (optional)

Start from a z and read the areas around it. Add a mean and a standard deviation to turn it back into a value, or leave both empty to stay in standard units.

1.96

Lower tail

0.975002

Upper tail

0.024998

Two-tailed

0.049996

Areas under the standard normal curve, computed to within 1e-12 and shown to six decimal places. The value is computed in floating-point arithmetic: the mean plus z times the standard deviation.

Valuemean + z × standard deviation
1.96
Percentilethe percentage of the curve below the value
97.5002
Between the mean and the valueP(0 ≤ X ≤ 1.96)
0.475002
Within the same distance either wayP(|Z| ≤ 1.96)
0.950004
The workingthe arithmetic in full
x = 0 + 1.96 × 1 = 1.96

Common z values

The lines a z table is usually opened for. Every figure here is computed by the same code as the answer above, so the table and the tool can never disagree. Load one to see the rest of its numbers.

z	Below	Above	Both tails	Often wanted for
0.50	0.691462	0.308538	0.617075	half a standard deviation
1.00	0.841345	0.158655	0.317311	one standard deviation
1.282	0.900079	0.099921	0.199843	about 10% above
1.645	0.950015	0.049985	0.099970	about 5% above
1.96	0.975002	0.024998	0.049996	the 95% two-sided line
2.00	0.977250	0.022750	0.045500	two standard deviations
2.326	0.989991	0.010009	0.020019	about 1% above
2.576	0.995002	0.004998	0.009995	the 99% two-sided line
3.00	0.998650	0.001350	0.002700	three standard deviations

Accuracy. z is calculated as the value minus the mean, divided by the standard deviation, using floating-point arithmetic. The tail probabilities come from a numerical approximation to the standard normal distribution, accurate to within 1e-12, which is stated on the page next to them. A standard deviation of zero is refused rather than returned as infinity. The areas assume a normal distribution: z is arithmetic about your own three numbers, while every probability beside it is an area under the standard normal curve.

Common questions

What is the p-value for z = 1.96?: The preset shows 0.024998 above 1.96, 0.975002 below it and 0.049996 in both tails. For a greater-than alternative the upper tail is the p-value. For a two-sided alternative the p-value is P(|Z| >= 1.96). These are rounded normal-curve areas.
What happens for a negative z score?: The lower and upper tails exchange roles. At z = -1.96 the lower tail is 0.024998 and the upper tail is 0.975002. The two-sided p-value stays 0.049996 because it uses the distance from zero in either direction.
Does this calculate a test statistic from my data?: No. Enter an already-computed z statistic with the appropriate standard normal null model. The mean and standard deviation fields describe a distribution for converting a score to a raw value; they are not a sample size, standard error or a test-selection workflow.
Is 1.96 the exact two-sided 5% cutoff?: It is a rounded cutoff. The exact cutoff is about 1.95996398454, while 1.96 leaves about 0.0499957903 in both tails. The result rounds to 0.049996 at the displayed precision. The page shows probabilities and makes no decision about a hypothesis.
Will this preset replace my main-page draft?: No. Opening it reads its own draft without saving. Your first visit starts from z = 1.96, mean 0 and standard deviation 1. Edits made here are remembered separately from the main page.

z is calculated as the value minus the mean, divided by the standard deviation, using floating-point arithmetic. The tail probabilities come from a numerical approximation to the standard normal distribution, accurate to within 1e-12, which is stated on the page next to them. A standard deviation of zero is refused rather than returned as infinity.