Calculator Inputs
Use the responsive grid below. It shows three columns on large screens, two on smaller screens, and one on mobile.
Formula Used
This calculator transforms a Pearson correlation into a t-statistic for significance testing.
- r is the Pearson correlation coefficient.
- n is the sample size.
- df equals n - 2.
- The p-value comes from the Student t distribution.
- R squared equals r² and shows shared variance.
When n is greater than 3, the calculator also estimates a confidence interval for r using Fisher’s z transformation.
How to Use This Calculator
- Enter the observed correlation coefficient.
- Enter the total sample size.
- Choose your alpha level.
- Select a two-tailed or one-tailed test.
- Pick the decimal precision.
- Press the calculate button.
- Review the t-value, p-value, and interval.
- Download the result as CSV or PDF if needed.
Plotly Graph
This graph shows how the t-value changes as r changes for sample size n = 30.
Example Data Table
These sample values show how different correlations map into t-statistics and p-values.
| Example r | Sample size | Degrees of freedom | T-value | Two-tailed p-value |
|---|---|---|---|---|
| 0.18 | 18 | 16 | 0.7320 | 0.4748 |
| 0.42 | 30 | 28 | 2.4489 | 0.0208 |
| -0.58 | 45 | 43 | -4.6688 | 2.9708e-5 |
| 0.73 | 60 | 58 | 8.1345 | 3.6457e-11 |
| -0.88 | 25 | 23 | -8.8854 | 6.7661e-9 |
Frequently Asked Questions
1. What does this calculator compute?
It converts a Pearson correlation coefficient into a t-value. It also reports degrees of freedom, p-value, shared variance, interpretation, and a confidence interval when the sample size allows it.
2. Why do I need the sample size?
Sample size affects the degrees of freedom. Larger samples usually produce larger absolute t-values for the same correlation, which can make statistical significance easier to detect.
3. Can the correlation be negative?
Yes. A negative correlation gives a negative t-value. The sign shows direction, while the absolute size helps determine significance through the selected hypothesis test.
4. Why can’t I enter exactly 1 or -1?
At exactly 1 or -1, the denominator becomes zero. That makes the t-value undefined in ordinary calculation, so the form restricts those perfect endpoints.
5. Does a significant result prove causation?
No. Statistical significance only suggests the observed linear relationship is unlikely under the null model. It does not prove one variable causes the other.
6. When should I use a one-tailed test?
Use a one-tailed test only when your hypothesis was directional before seeing the data. Otherwise, a two-tailed test is usually the safer default choice.
7. Why is the confidence interval unavailable for very small n?
The Fisher z interval needs n greater than 3. With n equal to 3, its standard error formula breaks down, so the interval is not shown.
8. Can I use rounded correlation values?
Yes, but heavy rounding can slightly change the t-value and p-value. Use more decimal places when you need precise reporting or reproducible results.