Statistics and Probability Calculators
These calculators cover introductory statistics and probability. Paste a list of numbers to get the mean, median, mode, quartiles and standard deviation; convert a value to a z-score and a percentile; build a confidence interval for a mean or a proportion; work out the sample size a survey needs; and count permutations, combinations and the probability of combined events.
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All Statistics Calculators (7)
Standard Deviation Calculator
Sample and population standard deviation and variance with stepsMean, Median and Mode Calculator
Mean, median, mode, range and quartiles of a data setZ-Score Calculator
Z-scores, percentiles and normal-distribution probabilitiesConfidence Interval Calculator
Confidence intervals for a mean or a proportionSample Size Calculator
Sample size for a survey or experiment from margin of error and confidencePermutation and Combination Calculator
nPr and nCr, with and without repetitionProbability Calculator
Probability of events, unions, intersections and repeated trials
Which tool do I need?
Summarise a list of test scores
Paste the scores to get the mean, median, mode, range and quartiles, then the standard deviation for the spread.
Mean, Median and Mode CalculatorStandard Deviation Calculator
Work out how many people to survey
Choose the confidence level and margin of error, add the population size if it is small, and read the sample size.
Find the percentile for a test score
Enter the score, mean and standard deviation to get the z-score and the share of the distribution below it.
Count the possible lottery or team combinations
Enter n and r to get combinations and permutations, with or without repetition.
Permutation and Combination CalculatorProbability Calculator
About Statistics Calculators
They are useful to students checking coursework, analysts writing a quick summary and anyone planning a survey or an A/B test. Each tool states which formula it uses, such as the sample versus population standard deviation or the t-distribution for small samples, because the right choice depends on how the data was collected.
Statistics answers depend on assumptions. Confidence intervals and z-scores assume a roughly normal sampling distribution, sample size formulas assume random sampling, and probability rules for "and" assume independent events unless you say otherwise. The calculators point these out where they matter instead of hiding them.
Guides
- Mean, Median, Standard Deviation and Z-Scores ExplainedWhich average to report, why sample standard deviation divides by n - 1, why calculators disagree on quartiles, and how a z-score becomes a percentile.
- Confidence Intervals and Sample Size, Worked ThroughWhere the margin of error comes from, when to use t instead of z, why the Wilson interval beats Wald for proportions, and how 385 became the default survey size.
- Probability Rules, Permutations and CombinationsCounting outcomes with nPr and nCr, the addition and multiplication rules, conditional probability, the at-least-one trick and when the binomial model applies.
Frequently asked questions
Should I use the sample or the population standard deviation?
Use the sample version, which divides by n − 1, when your numbers are a sample from a larger group. Use the population version only when you have every member of the group.
How should I read a 95% confidence level in these tools?
If you repeated the sampling many times, about 95% of the intervals built this way would contain the true value. It is not a 95% chance that this particular interval contains it.
Why does the sample size barely change for very large populations?
Because precision depends mainly on the number of people sampled, not the population. The finite population correction only matters when the sample is a sizeable share of the whole group.
When should I count permutations instead of combinations?
Order matters in a permutation and does not in a combination. Picking a president and treasurer is a permutation; picking a two-person committee is a combination.