Statistics Calculators
Mean, standard deviation, probability & more.
What Are Statistics Calculators?
Statistics calculators transform raw numerical data into meaningful measures that describe, summarise, and draw conclusions about the world. Whether you are a student completing a data analysis assignment, a researcher testing a hypothesis, a data analyst summarising survey results, or a quality engineer measuring process variation, statistical calculators handle the heavy computation so you can focus on interpreting the results.
Descriptive statistics summarise the key properties of a data set: measures of central tendency (mean, median, mode) and measures of spread (range, variance, standard deviation, interquartile range). The mean is the arithmetic average; the median is the middle value when data is sorted; the mode is the most frequent value. Standard deviation measures how spread out the values are around the mean — a low standard deviation means the data is clustered tightly, while a high standard deviation indicates wide variation.
Probability and distributions tools calculate the likelihood of events under specific statistical models. The normal distribution — the famous bell curve — describes how many natural phenomena distribute themselves around a mean. Our Z-score calculator converts a raw value to a standardised score showing how many standard deviations it sits above or below the mean, enabling comparisons across different scales. Binomial and Poisson distributions cover discrete event probabilities.
Hypothesis testing is the backbone of scientific research and quality management. A t-test determines whether the means of two groups are significantly different. A chi-square test assesses whether observed frequencies differ significantly from expected frequencies. ANOVA extends this to three or more groups. Our calculators compute the test statistic, degrees of freedom, and p-value for each test.
Regression and correlation tools measure the relationship between variables. Pearson correlation (r) ranges from −1 (perfect negative relationship) to +1 (perfect positive relationship), with 0 indicating no linear relationship. A linear regression calculator finds the best-fit line through a scatter of data points, enabling predictions for new values of the independent variable.
All Statistics Calculators (25)
Standard Deviation Calculator
Calculate mean, variance, and standard deviation for any data set.
Mean Calculator
Calculate arithmetic mean, geometric mean, and harmonic mean for any data set.
Median Calculator
Find the median (middle value) of any data set, sorted and unsorted.
Mode Calculator
Find the mode (most frequent value) of any data set, including multimodal sets.
Variance Calculator
Calculate population and sample variance for any data set.
Probability Calculator
Calculate basic probability, combined events, and conditional probability.
Z-score Calculator
Calculate z-score (standard score) and find corresponding probabilities.
Percentile Calculator
Calculate percentile rank and find the value at any percentile in a data set.
Sample Size Calculator
Calculate the required sample size for surveys and statistical studies.
Correlation Calculator
Calculate Pearson correlation coefficient between two variables.
Regression Calculator
Calculate linear regression equation, slope, and intercept for any data set.
Confidence Interval Calculator
Calculate confidence intervals for means and proportions.
Permutation Calculator
Calculate the number of permutations P(n,r) — ordered arrangements.
Combination Calculator
Calculate the number of combinations C(n,r) — unordered selections.
Binomial Distribution Calculator
Calculate binomial probability P(X=k), cumulative probabilities, mean, and variance.
T-Test Calculator
Perform one-sample, two-sample, and paired t-tests with p-value and confidence interval.
Chi Square Calculator
Calculate chi-square test statistic, p-value, and degrees of freedom for goodness of fit and independence tests.
Normal Distribution Calculator
Calculate probabilities and percentiles for the normal (Gaussian) distribution.
Poisson Distribution Calculator
Calculate Poisson distribution probabilities for events occurring at a known rate.
Geometric Distribution Calculator
Calculate geometric distribution probabilities for the number of trials until first success.
ANOVA Calculator
Perform one-way ANOVA test to compare means across multiple groups.
Covariance Calculator
Calculate sample and population covariance and correlation coefficient between two datasets.
Relative Risk Calculator
Calculate relative risk (risk ratio) from a 2×2 contingency table.
Odds Ratio Calculator
Calculate odds ratio and confidence interval from a 2×2 contingency table.
Margin of Error Calculator
Calculate the margin of error for survey results given sample size and confidence level.
Statistics Calculator Guides
Descriptive Statistics
The core descriptive statistics for a data set are: Mean = Σx ÷ n; Variance = Σ(x − mean)² ÷ n (population) or Σ(x − mean)² ÷ (n − 1) (sample); Standard Deviation = √Variance. The sample variance divides by n − 1 (Bessel's correction) to produce an unbiased estimate of the population variance when you are working from a sample rather than the whole population.
Quartile and percentile calculations split a sorted data set into equal portions. The interquartile range (IQR = Q3 − Q1) is the span of the middle 50% of values and is robust to outliers in a way that range and standard deviation are not. Our descriptive statistics calculator computes all these measures from a pasted or typed list of values.
Probability & Distributions
A Z-score converts any data point x to a standardised value: Z = (x − μ) ÷ σ, where μ is the population mean and σ is the standard deviation. From the Z-score you can read the cumulative probability — the proportion of the distribution that falls below that value — from the standard normal table, or use our calculator to get it instantly. Z-scores are used in hypothesis testing, quality control (Six Sigma), and comparing scores across different scales.
The binomial distribution calculates the probability of exactly k successes in n independent trials each with probability p: P(X = k) = C(n,k) × p^k × (1−p)^(n−k). It is used in quality control (defect rates), survey analysis (yes/no responses), and clinical trials. Our binomial calculator gives point probabilities and cumulative probabilities for any (n, k, p) combination.
Hypothesis Testing & Regression
The p-value is the probability of observing a test statistic at least as extreme as the one computed, assuming the null hypothesis is true. If p < significance level (typically 0.05), the result is statistically significant and the null hypothesis is rejected. Our t-test, chi-square, ANOVA, and correlation calculators all output the exact p-value alongside the test statistic so you can make the decision objectively.
Linear regression finds the line y = a + bx that minimises the sum of squared residuals between observed and predicted values. The slope b indicates how much y changes for a one-unit increase in x, and the intercept a gives the predicted value of y when x is zero. The R² (coefficient of determination) measures the proportion of variance in y explained by x — higher is better, with 1.0 meaning a perfect fit.
Top Statistics Calculators
Standard Deviation Calculator
Calculate mean, variance, and standard deviation for any data set with both population and sample versions.
Confidence Interval Calculator
Compute confidence intervals for means and proportions at any significance level from sample data.
Z-Score Calculator
Convert raw values to Z-scores and look up cumulative probabilities from the standard normal distribution.
Correlation Calculator
Measure the strength and direction of the linear relationship between two variables using Pearson's r.
Chi-Square Calculator
Test whether two categorical variables are independent using the chi-square test of independence.
Key Formulas & References
Sample Standard Deviation
s = √[Σ(xᵢ − x̄)² ÷ (n − 1)]
x̄ = sample mean, n = number of observations
Z-Score
Z = (x − μ) ÷ σ
μ = population mean, σ = population standard deviation
Pearson Correlation
r = Σ[(xᵢ−x̄)(yᵢ−ȳ)] ÷ [n·sₓ·sᵧ]
Ranges from −1 (perfect negative) to +1 (perfect positive)
Binomial Probability
P(X=k) = C(n,k) × pᵏ × (1−p)^(n−k)
n = trials, k = successes, p = probability per trial
Frequently Asked Questions About Statistics Calculators
Population standard deviation (σ) divides by n and is used when you have data for the entire population. Sample standard deviation (s) divides by n − 1 (Bessel's correction) and is used when your data is a sample from a larger population. The sample version is an unbiased estimator of the population standard deviation.
A Z-score measures how many standard deviations a data point lies above or below the mean: Z = (x − μ) ÷ σ. A Z-score of 0 means the value equals the mean; +1 means one standard deviation above; −2 means two standard deviations below. Z-scores are used to standardise values from different distributions so they can be compared.
A p-value is the probability of getting a test result at least as extreme as the one observed, assuming the null hypothesis is true. A small p-value (typically < 0.05) is evidence against the null hypothesis — meaning the observed result is unlikely to have occurred by chance alone. It does not measure the size or practical importance of an effect, only the strength of evidence against the null.
Correlation measures the strength and direction of the linear relationship between two variables (−1 to +1). Regression goes further: it fits a line (or curve) to the data and produces a formula you can use to predict one variable from the other. Correlation answers "are these related?" while regression answers "what is the predicted value of Y given X?"
Use a t-test when comparing the means of exactly two groups (e.g., treatment vs control). Use ANOVA (Analysis of Variance) when comparing three or more groups simultaneously. Running multiple t-tests inflates the risk of false positives — ANOVA avoids this by testing all groups in a single procedure.
A 95% confidence interval means that if you repeated the study 100 times, approximately 95 of the resulting intervals would contain the true population parameter. It does NOT mean there is a 95% probability that the true value lies in the interval you calculated — once calculated, the interval either contains the true value or it does not.
The chi-square test of independence tests whether two categorical variables are associated. You compare observed frequencies in a contingency table to the frequencies you would expect if the variables were independent. A significant result (p < 0.05) suggests the variables are not independent — there is a statistically meaningful association between them.
BrainyCalculators Editorial Team
Our Statistics calculators are researched, built, and reviewed by the BrainyCalculators editorial team using industry-standard formulas and validated against authoritative references. Results are updated whenever underlying standards, rates, or guidelines change. All calculators are free, require no account, and run entirely in your browser.