Statistics Calculators
Averages, standard deviation, probability and combinatorics tools.
Tools for describing a set of numbers and reasoning about uncertainty: averages and spread, standardised scores, confidence intervals, sample sizes and basic probability and counting. Paste in your data or enter summary figures; each page states the formula it uses.
Which Statistics calculator do you need?
- Mean, median and mode of a data setMean, Median & Mode CalculatorAll three averages at once, so you can see how skewed the data is.
- How spread out the values areStandard Deviation CalculatorStandard deviation, with the variance behind it.
- How unusual a single value isZ-Score CalculatorStandard deviations above or below the mean.
- A range likely to contain the true meanConfidence Interval CalculatorConfidence interval from a sample mean, spread and size.
- How many responses a survey needsSample Size CalculatorSample size for a chosen confidence level and margin of error.
- Counting arrangements or selectionsCombination CalculatorNumber of combinations (order doesn't matter) and permutations (order matters) of r items from n.
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All Statistics Calculators
Which average to report
The mean uses every value, so a few extreme values pull it. The median is the middle value and ignores how extreme the ends are. When the two differ a lot, the data is skewed and the median usually describes a "typical" value better. Geometric and harmonic means answer narrower questions — average growth rates and average rates respectively.
Limitations
- Confidence-interval and sample-size results assume a random sample; they cannot correct for a biased one.
Statistics Calculator Guides
How a Confidence Interval and Margin of Error Are Calculated
A confidence interval's margin of error is a Z-value times the sample's standard deviation divided by the square root of the sample size — and because sample size sits under a square root, doubling the sample only shrinks the margin by about 30%, not by half.
Read guideHow the Geometric Mean Is Calculated
The geometric mean multiplies all the numbers together and takes the nth root of the product — the correct way to average growth rates, ratios, and returns that compound over time.
Read guideHow the Harmonic Mean Is Calculated
The harmonic mean divides the count of numbers by the sum of their reciprocals — the correct way to average rates, like speeds traveled over equal distances, where a simple average would overstate the true result.
Read guideHow the Required Sample Size for a Survey Is Calculated
Cochran's formula sets the sample size a survey needs from three choices — confidence level, target margin of error, and an assumed proportion — and assuming a 50/50 split when the true proportion is unknown always demands the largest, safest sample.
Read guideHow to Calculate Mean, Median, and Mode
Mean is the sum divided by the count, median is the middle value once the list is sorted (or the average of the two middle values for an even-sized list), and mode is whichever value appears most often.
Read guideMean vs Median vs Mode: Which Average Should You Use?
Mean is the best "typical value" when data has no extreme outliers, median holds up better when a few extreme values would drag the mean off course, and mode is the only one of the three that makes sense for "which value shows up most" questions.
Read guide