P Value & T Score Calculator
Use this calculator to convert a t-score to a p-value, or find the critical t-score from a p-value. It supports one-tailed and two-tailed tests.
Tip: for a two-tailed test with p = 0.05 and df = 20, the critical t-score should be about ±2.086.
How to use this p value t score calculator
This tool is designed for common t-test workflows in statistics, research methods, and data analysis classes.
- Choose Find p-value from t-score when you already have a test statistic and want significance.
- Choose Find critical t-score from p-value when you are setting a rejection threshold.
- Enter the correct degrees of freedom (df). This matters a lot for small samples.
- Select one-tailed or two-tailed depending on your hypothesis.
What is a t-score?
A t-score (or t-statistic) tells you how far your sample result is from the null hypothesis value, measured in units of estimated standard error. Large absolute t-scores suggest stronger evidence against the null hypothesis.
In many tests, the t-score has this general form:
t = (estimate - null value) / standard error
Because the standard error is estimated from sample data, the t distribution (not normal) is used, especially with smaller sample sizes.
How p-values are computed from t-scores
The p-value is the probability of seeing a result at least as extreme as your observed t-score if the null hypothesis were true.
Two-tailed case
For two-tailed tests, extremeness in both directions counts. The calculator uses:
p = 2 × (1 - Ft,df(|t|))
One-tailed case
For one-tailed tests, only one direction is counted:
p = 1 - Ft,df(|t|)
Internally, the page computes the Student's t cumulative distribution using a stable numerical method based on the regularized incomplete beta function.
Going the other direction: p-value to t-score
If you already chose a significance level (like 0.05), you can find the critical t-score that marks your rejection boundary.
- Two-tailed: critical value is ±t* where each tail contains p/2.
- One-tailed: critical value is t* where upper tail contains p.
This is useful for planning hypothesis tests, creating decision rules, and checking table values quickly.
Interpreting your result
From t-score to p-value
If your p-value is below your significance level (for example p < 0.05), you reject the null hypothesis at that level.
From p-value to t-score
The critical t-score tells you the boundary. If your observed t-score is more extreme than that boundary (in absolute value for two-tailed tests), your result is statistically significant.
Common mistakes to avoid
- Using the wrong df (for many one-sample and paired t-tests, df = n - 1).
- Selecting one-tailed when your hypothesis is actually non-directional.
- Treating p-values as effect size (they are not).
- Ignoring practical significance even when statistical significance is present.
Quick FAQ
Does a lower p-value always mean a large effect?
No. Large sample sizes can produce tiny p-values for small effects. Always review confidence intervals and effect sizes.
Can I use this for z-tests?
This page is specifically for Student's t distribution. For known-population-variance z-tests, use a z calculator instead.
Why does df matter less when df is large?
As df increases, the t distribution approaches the standard normal distribution, so t critical values move closer to z critical values.