Math & Statistics Calculators

This category covers most of what you'd reach for in an applied stats workflow plus the math tooling that supports it. Twenty-six calculators across four loose buckets: descriptive and inferential statistics, probability distributions, regression and prediction, and a smaller cluster of linear algebra, calculus, and numerical methods.

What's actually here. Hypothesis testing across the usual suspects (z, t, ANOVA, chi-square, Pearson correlation), confidence intervals for both means and proportions, the standard discrete and continuous distributions, simple and multiple linear regression, a logistic regression predictor for binary outcomes, matrix operations and a separate eigenvalue/rank helper, derivative and integral evaluation, root-finding via Newton-Raphson and bisection, plus utility tools for error propagation, interpolation, sample size planning, time-series smoothing, and Bayesian updating with Beta-Binomial priors.

What's not here. Anything in the survival-analysis, mixed-models, or generalized-additive-models territory. No bootstrap resampling or permutation testing as separate tools yet. No Mann-Whitney or Kruskal-Wallis non-parametric tests either (also pending). And nothing structural-equation or factor-analysis flavored. If you need any of that, you'll want R or Python, and we'd point you to scipy.stats and statsmodels rather than try to fake it in a browser.

Most of the formulas across the suite cross-check against scipy.stats and the NIST e-Handbook of Statistical Methods. We keep references on each calculator's own page rather than rewriting them here.

Almost every problem in this category starts with the same two questions: what does your data actually look like, and what do you want to know about it.

If you have a single dataset and you need summary stats, the descriptive statistics calculator covers mean, median, standard deviation, skewness, and kurtosis, which is usually enough to get oriented. From there, if you also want to know whether your data is plausibly normal before running anything parametric, the normal distribution calculator lets you visualize and compare percentiles directly.

For two groups and a question about means, the t-test calculator handles one-sample, two-sample (independent), and paired designs, with Welch's correction available for unequal variances. Three or more groups, you want one-way ANOVA, which lives in the one-way ANOVA calculator and reports the F-statistic with post-hoc context. If your data is categorical (counts in cells, not measurements), the chi-square test calculator does both goodness-of-fit and independence flavors.

Looking at relationships between two continuous variables, you have two routes. Pure association, no model: the correlation significance calculator gives you Pearson r and the t-statistic for testing H0: ρ = 0. Predictive model with prediction intervals and R²: the regression calculator for linear or polynomial fits. If your outcome is binary (yes/no, click/no-click), the logistic regression predictor is a small educational demo, not a replacement for sklearn, but useful for sanity-checking coefficient interpretation.

Working backwards from a planned study, the sample size for proportions calculator tells you how many observations you need for a given confidence interval width or comparison test, and the hypothesis test power calculator gives you power for z and t tests on means.

Standalone z-scores and p-values, no setup: the z-score / p-value calculator. Confidence interval on a mean (you know σ, or you have a t-distribution case): the confidence interval calculator. On a proportion, with both Wald and Wilson methods because Wald is genuinely bad below n = 30: confidence interval for proportions.

Counting problems live in the combinations and permutations calculator. If you're updating a prior belief with new evidence and want to see the posterior shift, the Bayesian update visualizer walks through the Beta-Binomial conjugate case. And for time-series data where you want to strip out short-term noise before plotting, the smoothing and moving average calculator applies SMA, WMA, or EMA filters with adjustable windows.

Most of the tests in this category are parametric, which means they assume your data follows a specific distribution (usually normal) and that variances behave a certain way. When those assumptions hold, parametric tests are more powerful, you reject false nulls more often at the same sample size. When they don't hold, you get inflated false-positive rates, and the test stops meaning what you think it means.

Normality matters most for the t-test, one-way ANOVA, and the residuals in linear regression. Below n = 30, normality assumptions actually bind. Above that, the central limit theorem usually rescues the means even from moderately skewed parents, but the prediction intervals on the regression calculator still depend on residual normality. Equal variances matter for ANOVA and the standard two-sample t. For the t-test specifically, just use Welch's correction by default. There's no real downside, and it's stable when variances differ without costing power when variances happen to be equal.

Where assumptions don't bind much: the chi-square test of independence is non-parametric in the sense that it doesn't assume a specific distribution for your data, only that expected cell counts are reasonable (rule of thumb: all expected counts ≥ 5, though Cochran's original recommendation was looser). Exact binomial probabilities from the binomial distribution calculator don't approximate anything, so they're exact regardless of n.

When assumptions fail and you can't transform your way out (log, square root, Box-Cox), the right answer is usually a non-parametric alternative. Mann-Whitney U for two-group comparisons. Kruskal-Wallis for k-group. Spearman rank correlation when Pearson's normality assumptions fail. We don't have those as standalone tools yet. In R, the standard implementations are wilcox.test(), kruskal.test(), and cor(method = "spearman").

Distributions split cleanly into discrete (countable outcomes) and continuous (measurements on a real line), and which one you reach for depends on what's generating your data.

On the discrete side, the binomial distribution calculator handles the classic n trials, p probability of success setup: coin flips, defective parts in a batch, conversion-rate samples. The Poisson distribution calculator is for counts over a fixed interval where the rate is roughly constant, like arrivals per hour, defects per square meter, or alerts per minute. Geometric (number of trials until first success) and hypergeometric (sampling without replacement) cases land in the general probability calculator, which is a multi-distribution tool rather than a separate dedicated page.

Continuous distributions are where the inferential machinery actually lives. The normal distribution calculator is the workhorse: any sample mean of any reasonable size lands here eventually thanks to the CLT, which is why z-tests, confidence intervals on means, and the entire regression apparatus depend on it. Student's t (small samples, σ unknown), chi-square (sums of squared standard normals, used in independence tests and variance inference), and F (ratios of chi-squares, used in ANOVA) are all chained off the normal. The random variable transformation helper handles z-scoring, scaling, and shifting between any of them.

The exponential distribution shows up for waiting times when events arrive Poisson, and is part of the same probability calculator above.

A useful relationship to keep in mind: the Poisson is the limiting case of the binomial as n grows large and p shrinks (np = λ stays fixed), which is why Poisson approximations appear constantly in quality control and rare-event analysis where the binomial is cleaner in principle but unwieldy in practice. Same idea connects the chi-square (df = n) to the gamma (shape = n/2, scale = 2) and the t-distribution to the standard normal as df grows. Once you internalize a few of these limit relationships, you spend a lot less time deciding which calculator to open. The named distributions are mostly different angles on the same underlying CLT.

The non-stats portion of the category is smaller but covers the cases that come up alongside applied work.

For linear algebra, the matrix operations calculator covers determinants, inverses, multiplication, and solving linear systems Ax = b. The linear algebra helper is the companion tool for structural properties: rank, trace, eigenvalues, eigenvectors. You'd use the first when you have a system to solve, the second when you're checking whether a matrix is well-conditioned or trying to understand its decomposition. Condition numbers above ~10⁶ mean your inverse is numerically unreliable and you should probably switch to a pseudo-inverse or QR factorization in real code.

For calculus and numerical methods, the calculus helper does symbolic derivatives and integrals with steps shown, suitable for coursework and quick sanity checks. The numerical root finder implements Newton-Raphson (fast when it works, divergent when it doesn't) and bisection. Slow, but unconditionally convergent on any sign-change interval. The interpolation and extrapolation tool fits linear or polynomial curves through observed points and is the right tool when you want a quick estimate between data you already have. The error propagation calculator handles uncertainty arithmetic for derived quantities, which physics and chem labs care about more than a stats class would.