What is my t score?

Paste your numbers, or type the mean, standard deviation and sample size, or a t score you have. The t score calculator gives t, its p-values and the critical value.

t score: 3.63736

Your t score is 3.63736 with 7 degrees of freedom; the two-tailed p-value is 0.00831621.

Degrees of freedom: 7
p-value, two-tailed: 0.00831621
p-value, right-tailed: 0.00415811
p-value, left-tailed: 0.995842
Critical value (two-tailed): 2.36462
Decision at α (two-tailed): Significant: reject the null hypothesis at α = 0.05
Sample mean: 5.475
Sample standard deviation: 0.369362385
Standard error (s ÷ √n): 0.1305893236
Sample size: 8

t score: 3.63736. Your t score is 3.63736 with 7 degrees of freedom; the two-tailed p-value is 0.00831621.

Where does your t score fall?

How to calculate

Computes the t score t = (x̄ − μ₀) ÷ (s ÷ √n) from a list of numbers or from the mean, standard deviation and sample size, or takes a t score you have, and gives its p-values and critical value.

Example with the default inputs (I have My numbers, Your numbers [5.1, 4.9, 5.6, 5.8, 6, 5.4, 5.3, 5.7], Hypothesized mean (μ₀) 5, Significance level (α) 0.05): Your t score is 3.63736 with 7 degrees of freedom; the two-tailed p-value is 0.00831621.

Method: t = (x̄ − μ₀) ÷ (s ÷ √n), df = n − 1; p-values from Student’s t distribution with df degrees of freedom.

The observations are independent and roughly normal, or the sample is large.
s is the sample standard deviation, dividing by n − 1.
The critical value is two-tailed: P(T > t) = α ÷ 2.

Machine-readable copies: Markdown, JSON.

Worked examples

Each example is checked against the calculator on every build.

I have My numbers, Your numbers 5.1, 4.9, 5.6, 5.8, 6, 5.4, 5.3, 5.7, Hypothesized mean (μ₀) 5, Significance level (α) 0.05 gives Sample mean (x̄) 5.475, Sample standard deviation (s) 0.369362, t score 3.637357, Degrees of freedom 7, p-value, two-tailed 0.008316, p-value, right-tailed 0.004158, Critical value (two-tailed) 2.364624.Source: NIST/SEMATECH e-Handbook of Statistical Methods, §7.2.2 Are the data consistent with the assumed process mean?: t = (Ȳ − μ₀) ÷ (s ÷ √N), N − 1 degrees of freedom (https://www.itl.nist.gov/div898/handbook/prc/section2/prc22.htm, retrieved 2026-10-02)
I have Mean, SD and n, Sample mean (x̄) 105, Sample standard deviation (s) 12, Sample size (n) 25, Hypothesized mean (μ₀) 100, Significance level (α) 0.05 gives t score 2.083333, Degrees of freedom 24, Standard error (s ÷ √n) 2.4, p-value, two-tailed 0.048044, Critical value (two-tailed) 2.063899, Decision at α (two-tailed) Significant: reject the null hypothesis at α = 0.05.Source: NIST/SEMATECH e-Handbook of Statistical Methods, §7.2.2 Are the data consistent with the assumed process mean?: t = (Ȳ − μ₀) ÷ (s ÷ √N), N − 1 degrees of freedom (https://www.itl.nist.gov/div898/handbook/prc/section2/prc22.htm, retrieved 2026-10-02)
I have A t score, t score 2, Degrees of freedom 10, Significance level (α) 0.05 gives p-value, two-tailed 0.073388, p-value, right-tailed 0.036694, p-value, left-tailed 0.963306.Source: NIST/SEMATECH e-Handbook of Statistical Methods, §7.2.2 Are the data consistent with the assumed process mean?: t = (Ȳ − μ₀) ÷ (s ÷ √N), N − 1 degrees of freedom (https://www.itl.nist.gov/div898/handbook/prc/section2/prc22.htm, retrieved 2026-10-02)

How it works

Pick what you have:

My numbers: 2 to 10,000 numbers. The sample mean x̄ = Σx ÷ n and the sample standard deviation s = √(Σ(x − x̄)² ÷ (n − 1)) come from them. There is no answer when every number is the same (s = 0).
Mean, SD and n: the sample mean x̄, the sample standard deviation s (more than 0) and the sample size n (at least 2).
A t score: t (from −10⁶ to 10⁶) and its degrees of freedom (from 0.1 up; fractions allowed).

For the first two, with the hypothesized mean μ₀:

t score t = (x̄ − μ₀) ÷ (s ÷ √n). The page works out t² = (x̄ − μ₀)² × n ÷ s² exactly from the typed decimals, then takes one square root, with the sign of x̄ − μ₀. There is no answer when |t| would be over 10¹⁵.
Degrees of freedom df = n − 1.
Standard error = s ÷ √n. With your numbers, the sample mean, standard deviation and size are shown too.

For all three, with Student’s t distribution with df degrees of freedom:

p-value, right-tailed = P(T ≥ t); left-tailed = P(T ≤ t); two-tailed = 2 × the smaller of the two, at most 1.
Critical value (two-tailed): the t with P(T > t) = α ÷ 2, for the significance level α (default 0.05, from 0.000001 to 0.5).
Decision: significant (reject the null hypothesis) when the two-tailed p-value is at most α; otherwise not significant.

The t score, p-values and critical value are shown to 6 significant figures; the mean, standard deviation and standard error to 10.

Worked examples by hand

8 numbers against μ₀ = 5. 5.1, 4.9, 5.6, 5.8, 6.0, 5.4, 5.3, 5.7 add up to 43.8, so x̄ = 43.8 ÷ 8 = 5.475. The squared distances from 5.475 add up to 0.955, so s² = 0.955 ÷ 7 = 0.136429 and s = 0.369362. The standard error is 0.369362 ÷ √8 = 0.130589, so t = 0.475 ÷ 0.130589 = 3.63736 with 7 degrees of freedom. The two-tailed p-value is 0.00831621; the critical value at α = 0.05 is 2.36462, so the result is significant.

x̄ = 105, s = 12, n = 25, μ₀ = 100. SE = 12 ÷ √25 = 2.4; t = 5 ÷ 2.4 = 2.08333, df = 24. Two-tailed p = 0.0480441, under 0.05; the critical value is 2.0639: significant.

t = 2 with 10 degrees of freedom. P(T > 2) = 0.036694, P(T < 2) = 0.963306, and the two-tailed p-value is 0.073388.

Other questions people ask

How do I calculate a t score?

Subtract the hypothesized mean from the sample mean, then divide by the standard error s ÷ √n: t = (x̄ − μ₀) ÷ (s ÷ √n). With x̄ = 105, μ₀ = 100, s = 12 and n = 25, the standard error is 12 ÷ 5 = 2.4, so t = 5 ÷ 2.4 = 2.083.

What are the degrees of freedom?

For one sample, n − 1. Eight measurements have 7 degrees of freedom. Fewer degrees of freedom give a t distribution with fatter tails, so a larger t is needed to be significant.

How do I get a p-value from a t score?

Choose "A t score", then type t and the degrees of freedom. The two-tailed p-value is the chance of a t at least as far from 0 in either direction: for t = 2 with 10 degrees of freedom it is 0.0734.

What is the difference between a t score and a z score?

A z score divides by the population standard deviation, which you rarely know. A t score uses the sample standard deviation instead, so it follows Student’s t distribution, which approaches the normal distribution as n grows.

What does the critical value mean?

It is the t beyond which a two-tailed result is significant at α. At α = 0.05 with 24 degrees of freedom it is 2.064, so t = 2.083 is just significant.

Is this the bone density T-score?

No. A bone density T-score compares your bone density with a healthy young adult’s, in standard deviations. This page computes the t statistic of Student’s t-test.