Quick Calculator: p-value from t-statistic
Enter your t value and degrees of freedom to get the p value for a one-tailed or two-tailed t test.
What this p value from t test calculator does
This calculator converts a t-statistic and degrees of freedom into a p-value. It is useful when you already ran a t test in software, a spreadsheet, or by hand and now want to quickly interpret significance.
You can compute:
- Two-tailed p-value (tests whether the effect is different in either direction)
- Right-tailed p-value (tests whether the effect is greater than a reference value)
- Left-tailed p-value (tests whether the effect is less than a reference value)
How to use it
Step 1: Enter your t-statistic
The t-statistic can be positive or negative. Keep the sign exactly as reported by your analysis.
Step 2: Enter degrees of freedom
Degrees of freedom depend on the kind of t test:
- One-sample t test: df = n - 1
- Paired t test: df = number of pairs - 1
- Independent samples t test (equal variances): df = n1 + n2 - 2
Step 3: Choose one-tailed or two-tailed
If your research hypothesis was directional before looking at data, one-tailed may be appropriate. Otherwise, use two-tailed.
Step 4: Set alpha and interpret
The calculator compares p to alpha (default 0.05) and tells you if the result is statistically significant.
Formula and statistical background
The p-value is computed from the cumulative distribution function (CDF) of the Student's t distribution with your specified degrees of freedom.
Right-tailed: p = 1 - F(t)
Left-tailed: p = F(t)
Where F(t) is the t-distribution CDF. Internally, this is evaluated numerically using the regularized incomplete beta function for good accuracy across typical research values.
Example interpretations
Example A: Significant result
Suppose t = 2.40, df = 20, two-tailed. You will get a p-value around 0.026. Because 0.026 < 0.05, the result is statistically significant at the 5% level.
Example B: Not significant
Suppose t = 1.10, df = 20, two-tailed. The p-value is around 0.285. Because 0.285 > 0.05, this is not statistically significant.
Example C: Directional hypothesis
If t = 1.90, df = 30 and your pre-registered hypothesis was strictly "greater than," a right-tailed test may produce p around 0.033, which can be significant at alpha 0.05.
Common mistakes to avoid
- Using a one-tailed test after seeing data direction (this inflates false positives).
- Entering the wrong degrees of freedom from the wrong test type.
- Treating p-value as effect size (it is not).
- Assuming p > 0.05 means "no effect" rather than "insufficient evidence."
- Ignoring assumptions such as independence and approximate normality of residuals.
Practical tips for reporting
In scientific writing, report the statistic, degrees of freedom, and p-value together, for example:
t(18) = 2.35, p = 0.030 (two-tailed)
Ideally also include:
- Confidence interval
- Effect size (such as Cohen's d)
- Sample sizes and study context
FAQ
Can degrees of freedom be non-integer?
Yes. Some methods (such as Welch's t test) produce fractional df. This calculator supports that.
What if my p-value is extremely small?
The calculator will show scientific notation for very small values. In reporting, you can write p < 0.001 when appropriate.
Is p-value enough to make conclusions?
No. Use p-value with effect size, confidence intervals, design quality, and domain knowledge.