Which formula variant each calculator on this site actually runs, how we check it, and one place where the tool has a real limit.
A statistics calculator is only worth using if it names the exact method behind a result. This page lists which formula each tool on StatsCalc implements, how we verify that against a published source, and what we do if a reader finds a mismatch.
The standard deviation and variance calculators both compute two numbers from one data set: the sample figure, sum of squared deviations divided by n minus 1 (Bessel's correction), and the population figure, divided by n. The standard deviation tool shows both at once; the variance tool lets you pick which one you need from a dropdown. The mean, median, and mode calculator reports both SDs too, alongside a mode that lists every value tied for most frequent rather than forcing a single answer when there is a tie.
The p-value calculator accepts a z, t, or chi-square statistic, and it does not use one formula for all three. A z statistic goes through the Abramowitz and Stegun rational approximation to the normal CDF (their formula 7.1.26, accurate to about 1.5 times ten to the minus seven). A t statistic uses the exact relationship between the t-distribution and the regularized incomplete beta function, evaluated with a continued-fraction expansion in the style of Numerical Recipes, with the degrees of freedom you supply. A chi-square statistic uses the regularized upper incomplete gamma function, and that path is inherently one-tailed since a chi-square test does not have a lower tail in the usual sense. The z-score, normal distribution, and the normal branch of the probability calculator all share that same 7.1.26 approximation for their percentile and area figures.
The binomial and Poisson branches of the probability calculator sum the real probability mass function term by term, using log-gamma arithmetic to keep large factorials from overflowing, rather than substituting a normal approximation. That matters most at small n or a small lambda, exactly the range where a bell-curve shortcut drifts furthest from the true value.
The confidence interval and margin of error calculators use a normal (z) critical value, 1.645, 1.96, or 2.576 depending on the confidence level you pick, for both means and proportions. They do not switch to a t critical value even when your sample is small and the population standard deviation is unknown, which is the textbook condition for using the t-distribution instead. For n above roughly 30 this makes little practical difference; below that, treat the interval as an approximation and, if the distinction matters for your work, use a t-table or statistical software that lets you set the degrees of freedom. The t-test calculator itself only returns the t statistic and degrees of freedom, by design; feed both into the p-value calculator's t option to get the actual p-value.
The percentile calculator uses linear interpolation between closest ranks (rank equals k divided by 100, times n minus 1), the same method behind Excel's PERCENTILE.INC and NumPy's default linear interpolation. The permutation and combination calculator computes nPr and nCr with exact integer arithmetic, no approximation involved. The scientific notation calculator derives the exponent as the floor of the base-ten logarithm of the number's absolute value and divides through to get the coefficient.
Every calculator is hand-checked against a worked example with a known correct answer before it goes live, the kind of example found in the NIST Engineering Statistics Handbook or the end-of-chapter exercises in OpenStax Introductory Statistics, not just checked for internal consistency against itself. Where a spreadsheet function exists for the same calculation, STDEV and STDEVP for standard deviation, CONFIDENCE.NORM for a normal-based interval, we confirm the calculator's output matches it on at least one nontrivial example.
Some sites in this network track a number that moves, a mortgage rate or a CPI figure, and post a dated refresh schedule for it. Nothing here works that way: the formulas are public-domain mathematics that do not go stale, so there is no rate table to refresh. What can change is the code itself, and every formula gets rechecked whenever its calculator is edited, not on a calendar.
If a calculator returns a number that does not match a hand calculation, a textbook answer key, or output from R, Python, Excel, or another stats package, use the contact form and include your inputs. We re-derive the result by hand, and if the calculator is wrong we fix it and note the date the fix went live rather than editing it quietly.
StatsCalc is free to use and is paid for through Google AdSense display ads and a small number of affiliate links. If you click one of those links and buy something, we may earn a commission at no extra cost to you. Neither ad revenue nor affiliate revenue has any influence on what a formula computes.
Curious who is behind the calculators and the guides? See the authors page for what gets checked before a page ships.