Statistics tools suite
Calculate probabilities, look up statistical distribution tables and solve hypothesis tests, confidence intervals, sample sizes and A/B tests. Free, no sign-up, directly in your browser.
Main areas
ProbLab brings together the main families of statistical resources for lookup, calculation and interpretation of results.
For P(X≤x), tails, percentiles or values of the normal, binomial, Poisson, t and other distributions.
See distributions →Look up Z, Student's t, chi-square, F, binomial, Poisson, gamma or beta tables.
See tables →Before collecting data: surveys, means, proportions, power, survival or A/B tests.
Calculate sample size →Tests for means, proportions, variances, ANOVA, chi-square and normality.
Choose a test →Get plausible ranges for means, proportions, differences of means, differences of proportions or variances.
See intervals →Significance, Bayesian Beta-Binomial, power, MDE, sample size and simulation.
Analyze A/B test →Interactive CLT, confidence intervals, Markov chains, Poisson process and random walk.
Explore simulations →Calculate exact, cumulative, tail probabilities and percentiles for 16 continuous and discrete probability distributions. Each calculator offers an interactive chart, a table of values and the applied formula. Includes classic distributions such as the normal, binomial and Poisson, and advanced distributions such as the gamma, beta, lognormal and Weibull, with options to compute the probability density function (PDF), cumulative distribution function (CDF), quantiles and probability intervals.
Classic statistical tables with density function, cumulative distribution and critical values. Look up the standard normal table Φ(z), Student's t by degrees of freedom, chi-square, Snedecor's F, binomial and Poisson directly on screen, or print them for class or exam use without a calculator. Useful for verifying results and finding critical values quickly.
Calculate how many observations your study or survey needs to guarantee statistically reliable results. Enter the confidence level, the margin of error and, if the test requires it, the desired statistical power. Covers the most common cases: one proportion or one mean, comparison of two groups, finite populations with correction factor, and paired-sample designs.
Get the range of plausible values for a population parameter — mean, paired mean, proportion, difference of means, difference of proportions, ratio of proportions, odds ratio or variance — from your sample data. Choose the confidence level (90%, 95%, 99% or another), enter your data and the calculator returns the interval bounds, the margin of error and a graphical representation of the sampling distribution and the confidence region.
Run hypothesis tests for means, proportions, variances and contingency tables. The calculator shows the test statistic, the p-value, the critical region and an interpretation of the result at the chosen significance level. Includes one-way ANOVA to compare multiple groups, chi-square independence and goodness of fit, Fisher's exact test, and normality tests such as Kolmogorov-Smirnov and Shapiro-Wilk.
Design, analyze and simulate A/B experiments with four complementary approaches. The frequentist Z-test computes the p-value and statistical significance of the difference between variants. The Bayesian Beta-Binomial analysis estimates the probability that B beats A. The MDE and power calculator helps you plan the sample size before launching the experiment. The Monte Carlo simulation shows the distribution of possible outcomes. Ideal for product, digital marketing and CRO teams.
Interactive experiments that generate random data in real time to build statistical intuition. Adjust parameters and watch how the behavior of distributions, estimators and stochastic processes changes. Each simulation includes dynamic visualizations, a comparison between empirical and theoretical results, and step-by-step interpretations of the results.
The key question is which stage of the analysis you are at. If you have not collected data yet, start with the sample size calculators: they tell you how many observations your survey or experiment needs to reach the precision and statistical power you are after. Working out the sample size before measuring avoids two very common problems: falling short and ending up with inconclusive results, or overshooting and paying an unnecessary data-collection cost.
If you already have the data and want to estimate a population parameter — a mean, a proportion, a variance — the right tool is a confidence interval: you get a range of plausible values together with its margin of error. If instead you want to make a decision about a specific claim ("the mean is 50", "the new process reduces defects"), you need a hypothesis test, which answers with a test statistic, a p-value and an interpretation at your chosen significance level.
When what you need is a specific probability or a critical value — P(X≤x), a percentile, the z or t value that leaves 5% in the tail — go straight to the distribution calculators or, if you prefer the classic exam format, to the browsable and printable statistical tables.
Two use cases round out the suite. Product and digital marketing teams have a dedicated A/B testing section with frequentist significance, Bayesian analysis, power and experiment simulation. And anyone learning statistics can build intuition with the interactive simulations, which show phenomena such as the central limit theorem, the bootstrap or type I and type II errors live on screen.
If you are still unsure where to start, the "Main areas" cards at the top of this page group every tool by goal, so you can navigate from what you want to achieve rather than from the name of a technique.
ProbLab is a free suite of more than 90 online statistics tools for solving probability and inference calculations directly in your browser, with no software to install and no account to create. You'll find calculators for 16 probability distributions — normal, binomial, Poisson, Student's t, chi-square, Snedecor's F, exponential, gamma, beta, lognormal, Weibull and more — classic statistical tables, sample sizes, confidence intervals, hypothesis tests and complete A/B testing tools.
The platform is built for statistics and probability students, university instructors, researchers, data analysts and product teams who need rigorous, verifiable results. Each calculator includes an interactive form, the formula used, a graphical representation of the distribution and an interpretation of the result that helps you understand the statistical meaning, not just copy a number.
Unlike a static paper table or a standalone calculator, ProbLab lets you adjust parameters instantly and see how the distribution or result changes. You can go from calculating the cumulative probability of a normal distribution to looking up the critical values of Student's t, estimating how many observations your study needs, or running a hypothesis test on means or proportions — all without leaving the browser, with an explanation of the procedure at every step.
The calculation procedures, formulas and numerical approximations used by each calculator are documented on the methodology page, and on About ProbLab you can learn about the project and how to suggest corrections or new tools.
ProbLab brings together more than 90 statistical tools and simulations: 16 probability distributions, 8 statistical tables, 25 sample size calculators (10 for confidence intervals and 15 for hypothesis tests), 11 confidence interval calculators, 18 hypothesis tests, 5 A/B testing tools and 7 interactive simulations (CLT, confidence intervals, Markov chains, Poisson process, random walk, type I and type II errors, and bootstrap).
Yes. There are calculators for the normal, binomial and Poisson distributions, plus Student's t, chi-square, Snedecor's F, exponential, uniform, gamma, beta, lognormal, Weibull, negative binomial, geometric, hypergeometric and Bernoulli. Each one computes the PDF, CDF, percentiles and critical values.
The p-value is the probability of obtaining a result as extreme as the one observed if the null hypothesis were true. If the p-value is lower than the chosen significance level (usually 0.05), the null hypothesis is rejected. ProbLab's hypothesis test calculators show the p-value with a contextual interpretation to help you make the right decision.
Choose the calculator that matches your design: "One proportion" for yes/no surveys, "One mean" if you're measuring a continuous variable, or "Two proportions" to compare two groups. Enter the confidence level (typically 95%), the maximum acceptable margin of error and the expected variability. The calculator returns the minimum number of observations needed.
Yes. It includes tests for one mean, two independent or paired means, proportions, variances, one-way ANOVA, chi-square independence and goodness of fit, Fisher's exact test, Kolmogorov-Smirnov and Shapiro-Wilk. Each test shows the test statistic, the p-value and an interpretation of the result.
Yes. ProbLab offers confidence interval calculators for the mean with known sigma (using the standard normal) or unknown sigma (using Student's t), intervals for proportions, differences of means and variance. Each calculator includes a graphical representation of the distribution and the confidence region.
Yes. All ProbLab tools are free, with no installation and no sign-up. They run directly in the browser, on desktop or mobile, without downloading any app.
Probability distributions model how the values of a random variable are spread out. The normal distribution describes many natural phenomena and underlies classical statistical inference. The binomial and Poisson distributions model discrete events. Student's t distribution is used when the sample size is small and the population standard deviation is unknown. Choosing the right distribution is the first step to computing reliable probabilities or running reliable hypothesis tests.