T-score to p-value calculator
Enter your t-statistic — also called a t-score — with its degrees of freedom for an exact p-value from the Student t-distribution. Fractional degrees of freedom from a Welch correction work exactly as they should.
Enter a test statistic to begin
Your p-value, a plain-English reading, and a shaded distribution chart appear here instantly.
Results
P-value
What this means
What it does not mean
Report it (APA)
Where this statistic comes from
You will typically be holding one of these:
- A one-sample, two-sample, or paired t-test
- Regression coefficients (every coefficient comes with a t and a p)
- A test of a Pearson correlation against zero
- Post-hoc comparisons after ANOVA
T-score or t-statistic? Same number
They are two names for one quantity. t-statistic is what statistical software and journals print; t-score is what most textbooks and courses call it. Whichever label your output carries, it is the number that goes in the box above, and it converts to a p-value the same way.
There is one genuine ambiguity worth clearing up. In psychometrics a "T-score" sometimes means a standardised score rescaled to a mean of 50 and a standard deviation of 10 — the scale used to report personality and clinical inventories. That is not a test statistic and does not belong here. If your number came out of a t-test, a regression coefficient table, or a test of a correlation, you are in the right place.
Finding your degrees of freedom
Degrees of freedom control the shape of the t-distribution, so getting them wrong changes your p-value. Which formula applies depends on the test:
| Test | Degrees of freedom |
|---|---|
| One-sample t-test | n − 1 |
| Paired t-test | number of pairs − 1 |
| Two-sample, pooled | n₁ + n₂ − 2 |
| Two-sample, Welch | Welch–Satterthwaite (usually fractional) |
| Regression coefficient | n − k − 1, for k predictors |
| Correlation | n − 2 |
If your statistics software reported something like df = 17.34, that is a
Welch correction and it is correct — enter it as-is. Rounding it to 17 changes your
p-value slightly, and there is no reason to.
Why the t-distribution is not the normal distribution
When you estimate the standard deviation from your sample rather than knowing it, you add a second source of uncertainty. The t-distribution accounts for it by having heavier tails than the normal — extreme values are more likely, so the same statistic yields a larger p-value.
The gap closes as the sample grows. At df = 5, a t of 2.0 gives p = 0.102; at df = 30 it gives p = 0.055; at df = 1000 it gives p = 0.046, almost exactly the normal answer. This is why the "use Z above n = 30" rule of thumb exists — but with a calculator there is no reason to approximate. If you estimated the SD, use t.
Reporting a t-test result
Journals expect the statistic, its degrees of freedom, and the p-value together, in the
form t(28) = 2.14, p = .041. The calculator produces this string for you —
note the APA conventions it follows: no leading zero on the p-value, three decimal
places, and p < .001 rather than a smaller number.
Report the effect size alongside it. A t-test tells you whether a difference is detectable; Cohen's d tells you whether it is large enough to matter. Our t-test calculator computes both from your raw data.
Frequently asked questions
Is a t-score the same as a t-statistic?
Yes. The two terms describe the same quantity — the difference you observed divided by its standard error. Software and journals tend to say t-statistic, textbooks and courses tend to say t-score, and this calculator accepts either. The one thing that is different is a psychometric "T-score" scaled to mean 50 and SD 10, which is a standardised score rather than a test statistic and should not be entered here.
How do you find the p-value from a t-score?
You need two numbers: the t-score itself and its degrees of freedom. The p-value is the area of the Student t-distribution with those degrees of freedom that lies beyond your t — both tails for a two-tailed test, one tail for a one-tailed test. Enter both above and the exact area is computed for you; a t of 2.14 with df = 28 gives a two-tailed p of 0.041.
What t-value is significant at p < 0.05?
It depends on your degrees of freedom, because the t-distribution changes shape with df. For a two-tailed test at α = 0.05 the critical value is 2.776 at df = 4, 2.228 at df = 10, 2.042 at df = 30, and 1.984 at df = 100. As df grows it converges on the normal value of 1.96.
Can degrees of freedom be a decimal?
Yes. A Welch two-sample t-test uses the Welch–Satterthwaite equation, which almost always produces a fractional value such as 17.34. This is correct and expected — enter it exactly as your software reported it rather than rounding.
Does a negative t-score matter?
For a two-tailed test, no: the t-distribution is symmetric, so −2.5 and +2.5 give the same p-value. For a one-tailed test the sign determines which tail you are testing and therefore changes the answer entirely.
What is the difference between a t-test and a Z-test?
Use a t-test when you estimate the standard deviation from your sample, which is the usual case. Use a Z-test when you know the population standard deviation, or when you are testing proportions. With small samples the t-test gives a larger, more honest p-value; with large samples the two agree closely.