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P-Value From Z Calculator | Convert Z-Score To P-Value

Convert a z-score into a p-value for one- and two-tailed hypothesis tests, with the standard normal curve explained. The quick significance check for statistics coursework and research.

Last updated: June 2026 · Free · No sign-up required

Results

Enter values above and click Calculate to see your result instantly.

Quick reference

z-scoreTwo-tailed p
1.6450.10
1.960.05
2.5760.01
3.2910.001

info P-Value from Z-Score Calculator

Free math calculator — enter your numbers and get an instant, accurate result.

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Everything runs locally in your browser. No uploads, no accounts, no tracking.

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Fully responsive and mobile-friendly — calculate on any device, any time.

info Educational

Includes the formula and step-by-step explanation so you understand the math, not just the answer.

Interpretation guide

p-valueConventional reading
p < 0.01Strong evidence against H₀
0.01 ≤ p < 0.05Significant at the 5% level
0.05 ≤ p < 0.10Marginal — often called suggestive
p ≥ 0.10No evidence against H₀ at usual levels

lightbulb Worked example

Let's say you are using the P-Value from Z-Score Calculator. Converts a z-score into its p-value for statistical significance testing. Enter your z-score and choose a one-tailed or two-tailed test, and the tool computes the corresponding p-value from the Enter the values that match your situation into the input fields and press calculate — using realistic numbers makes the result directly useful for you.

Result: The calculator instantly applies the formula Left: p = Φ(z); Right: p = 1 − Φ(z); Two-tailed: p = 2 × min(Φ(z), 1 − Φ(z)) and returns the result with appropriate precision.

What this means: Read the result in the context of what you are measuring. The step-by-step breakdown lets you confirm the math and understand which input most affects the outcome.

Formula & methodology

Formula: Left: p = Φ(z); Right: p = 1 − Φ(z); Two-tailed: p = 2 × min(Φ(z), 1 − Φ(z))

The P-Value from Z-Score Calculator is built on a well-established calculation method. It uses the formula Left: p = Φ(z); Right: p = 1 − Φ(z); Two-tailed: p = 2 × min(Φ(z), 1 − Φ(z)) to turn your inputs into a reliable result. Converts a z-score into its p-value for statistical significance testing. Enter your z-score and choose a one-tailed or two-tailed test, and the tool computes the corresponding p-value from the standard normal The steps are shown on the page so you can follow the reasoning from input to output.

  1. Enter the z-score from your test statistic.
  2. Choose the tail that matches your alternative hypothesis.
  3. The standard normal CDF Φ gives the tail area — the p-value — compared against α = 0.05 and 0.01.

Worked example: z = 1.96, two-tailed → p = 2 × (1 − 0.975) = 0.05 — right at the classic significance threshold. z = −2.5 left-tailed → p = 0.0062.

Authoritative source: Wolfram MathWorld

Frequently asked questions

How do I find the p-value from a z-score?
Enter the required values into the input fields and press the calculate button. The tool applies the formula Left: p = Φ(z); Right: p = 1 − Φ(z); Two-tailed: p = 2 × min(Φ(z), 1 − Φ(z)) and returns the result with a short explanation of each step, so you can check the working yourself.
What is the p-value for z = 1.96?
The P-Value from Z-Score Calculator is free, private, and accurate: it runs entirely in your browser (no uploads, no accounts), applies the standard calculation, and explains each step so you can verify the result. Converts a z-score into its p-value for statistical significance testing. Enter your z-score and choose a one-tailed or two-tailed test, and the tool computes the corresponding p-value from the standard normal distribution, helping you decide whether to There is no limit on usage, and it works on any device.
When do I use one-tailed vs two-tailed?
Use a two-tailed test when your hypothesis is simply 'different from' — the direction does not matter. Use one-tailed when the hypothesis predicts a specific direction, like 'greater than' or 'less than'. Two-tailed is the conservative default and is required in most published research; one-tailed doubles the sensitivity in one direction but misses surprises in the other.
Is my result significant?
Your result is statistically significant if the p-value is below your pre-chosen significance level, conventionally 0.05. A p-value of 0.03 means the observed result has a 3% probability under the null hypothesis — below 5%, so it is significant. Report the actual p-value and the level rather than just 'significant' or 'not', and remember significance is not the same as importance.
Can a z-score be negative?
Yes — a negative z-score means the value is below the mean, and it carries the same magnitude information as a positive one: z = −1.5 is 1.5 standard deviations below the mean. In hypothesis testing, the sign matters for one-tailed tests (which tail you check) but not for two-tailed p-values, which use the absolute value.
What does the P-Value from Z-Score Calculator do?
Converts a z-score into its p-value for statistical significance testing. Enter your z-score and choose a one-tailed or two-tailed test, and the tool computes the corresponding p-value from the standard normal distribution, helping you decide whether to. The calculator takes your inputs, applies the standard calculation, and returns a clear result so you can make an informed decision without doing the math by hand.
What formula does the P-Value from Z-Score Calculator use?
The P-Value from Z-Score Calculator applies the standard formula: Left: p = Φ(z); Right: p = 1 − Φ(z); Two-tailed: p = 2 × min(Φ(z), 1 − Φ(z)). The tool walks through each step of the calculation so you can verify the numbers yourself.
Is the P-Value from Z-Score Calculator free and private?
Yes — the P-Value from Z-Score Calculator. There is no sign-up, no paywall, no trial, and no limit on how many calculations you can run. CalcaTools covers its costs with non-intrusive display advertising, so the calculator itself never asks for payment or restricts any feature.
How accurate is the P-Value from Z-Score Calculator?
The P-Value from Z-Score Calculator applies the standard formula: Left: p = Φ(z); Right: p = 1 − Φ(z); Two-tailed: p = 2 × min(Φ(z), 1 − Φ(z)). It is tested against published worked examples before launch and uses native double-precision arithmetic, so results are accurate to typical precision for the values you enter — with no intermediate rounding that could distort the answer.

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