T-Score Calculator

This t-score calculator works out the one-sample t statistic, the figure statisticians and researchers use to test whether a sample mean differs meaningfully from a known or hypothesised population mean when the population's true standard deviation is not known. You enter four figures: the sample mean, the population mean you are testing against, the sample standard deviation, and the sample size (n). From these, the calculator returns the t value, the degrees of freedom, always n minus 1 for a one-sample test, and the standard error, calculated as the sample standard deviation divided by the square root of n. The t value shows how many standard errors your sample mean sits from the hypothesised mean, so the further it is from zero, the stronger the evidence that the true mean differs from what you assumed. To reach a conclusion, compare that t value against a critical value from the t distribution, or convert it to a p-value, using the degrees of freedom shown, since the t distribution has heavier tails than the normal distribution and suits small samples where variability is estimated rather than known. Results update instantly as you change any input, making this a quick way to check a hand calculation, mark student work, or run a fast hypothesis test. It assumes valid numbers and a genuine one-sample comparison; two-sample or paired data need a different test.

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Sample mean

Population mean

Sample SD

Sample size n

t = 2

Degrees of freedom24

Standard error1

The formula

The one-sample t statistic is t = (sample mean minus population mean) divided by the standard error, where the standard error is the sample standard deviation divided by the square root of n. The degrees of freedom are n minus 1.

Worked example

A sample of 25 with mean 52, against a population mean of 50, with sample SD 5: the standard error is 5 over the square root of 25 = 1, so t = (52 minus 50) / 1 = 2, with 24 degrees of freedom. Enter 52, 50, 5, 25 to confirm.

Frequently asked questions

What is a t-score?

The number of standard errors a sample mean is from a hypothesised mean, used in t tests for small samples.

What are the degrees of freedom?

For a one-sample t test, n minus 1, where n is the sample size.

When do I use t instead of z?

Use the t statistic when the population standard deviation is unknown and estimated from a small sample.

Who this calculator is for

This calculator is for statistics students, researchers and analysts.

What this calculator assumes

You enter valid numbers.
The standard formula is applied.
Results are rounded for display.

Formula and sources

Related calculators

Standard Deviation Calculator: spread of data.
Z-Score Calculator: standard score.
Mean Median Mode Calculator: averages.

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