Statistics Calculators
Standard deviation, z-scores, confidence intervals, p-values: the stats toolkit for students, researchers, and the statistically curious.
Core Statistics 7
- Standard Deviation CalculatorSample or population standard deviation from any list of numbers.
- Variance CalculatorSample or population variance, plus mean and standard deviation.
- Z-Score CalculatorHow many standard deviations from the mean, with percentile.
- Normal Distribution CalculatorBell curve probability: below, above, or between any values.
- Confidence Interval CalculatorConfidence interval and margin of error for a sample mean.
- Sample Size CalculatorHow many responses you need, and why the population barely matters.
- P-Value CalculatorP-value from a z-score: two-tailed, left-tailed, or right-tailed.
Probability & Odds 10
- Probability CalculatorSingle events, and/or combinations, and at-least-once odds with steps.
- Combination CalculatornCr and nPr with step-by-step work, plus which one you actually need.
- Odds CalculatorConvert American, decimal, and fractional odds, and see the vig hiding in the price.
- MTG Opening Hand CalculatorExact odds of drawing your card: opener, by turn, and mulligans.
- NFL Win Probability CalculatorPoint spread in, outright win probability out, with the vig stripped away.
- NBA Win Probability CalculatorTurn an NBA spread or moneyline into an honest chance of winning outright.
- WNBA Win Probability CalculatorSpread or moneyline in, win probability out, with the sigma assumption said out loud.
- NHL Win Probability CalculatorMoneylines to fair win odds, or Poisson goals math with overtime handled honestly.
- Hypergeometric CalculatorExact odds for drawing without replacement, every tail shown.
- Binomial Distribution CalculatorExact odds over a fixed number of independent tries.
More tools 5
- Expected Value CalculatorEV per trade after costs, plus the win rate you actually need to break even.
- Kelly Criterion CalculatorOptimal bet size from your edge, plus half Kelly and the cost of overbetting.
- MTG Land CalculatorHow many lands your curve actually needs, and what that count delivers.
- MTG Manabase CalculatorHow many sources your spell actually needs, computed not quoted.
- Risk of Ruin CalculatorThe chance your bet size ends the account before your edge ever shows.
Which statistics calculator do you need?
Statistics splits into two jobs: describing the data you have, and deciding what it implies about data you do not have.
- Describing a data set. The standard deviation calculator and variance calculator measure spread. Standard deviation is the one to quote, because it is in the same units as your data.
- Placing one value in context. A z-score says how many standard deviations from the mean a single observation sits, which is what makes two differently scaled measurements comparable.
- Working with the bell curve. The normal distribution calculator converts between values and probabilities: the chance of landing below, above, or between two points.
- Testing a claim. The p-value calculator turns a z-score into a one or two-tailed p-value. The confidence interval calculator gives the range your sample is consistent with, which is usually the more honest way to report the same finding.
- Counting possibilities. The combination calculator handles nCr and nPr, and tells you which of the two you actually want. The probability calculator covers single events, and or combinations, and at-least-once odds.
Sample or population: the mistake that changes your answer
Every spread calculation asks whether your numbers are the whole population or a sample drawn from it. The distinction is not pedantry. A sample divides by n minus 1 instead of n, which makes the result slightly larger, because a sample almost always understates the true spread of the thing it came from. On small data sets the gap is big enough to matter.
The rule of thumb: if you measured every member of the group you are describing, it is a population. If you measured some in order to say something about all, it is a sample. When you are unsure, use the sample formula, since it is the more cautious of the two.
What a p-value does not tell you
A p-value is the probability of seeing data at least this extreme if nothing were going on. It is not the probability that your hypothesis is true, and it is not a measure of how large or important an effect is. A tiny p-value on a trivial difference is common in large samples, and a large p-value does not prove there is no effect. This is why we show confidence intervals alongside: a range communicates both the direction and the precision of a finding, and it is much harder to over-read.
Frequently asked questions
Should I use sample or population standard deviation?
If your numbers are the complete group you are describing, use population. If they are a subset measured in order to say something about a larger group, use sample, which divides by n minus 1 and returns a slightly larger figure. When in doubt use sample: it is the more conservative choice and it is what most statistical software defaults to.
What does a p-value of 0.05 actually mean?
It means that if there were genuinely no effect, you would see data at least this extreme about 5 percent of the time. It does not mean there is a 95 percent chance your hypothesis is correct, and it says nothing about whether the effect is big enough to care about. The 0.05 threshold is a convention, not a law of nature.
Why is my confidence interval so wide?
Usually sample size. Precision improves with the square root of n, so quadrupling your sample halves the width of the interval. High variability in the data widens it too. A wide interval is not a failure, it is an honest statement that your data is consistent with a broad range of possibilities.
Do these calculators show the working?
Yes. The statistics and math tools render the steps using the numbers you entered, generated by the same code that produced the answer, so the explanation and the result can never disagree. That is a deliberate rule on this site rather than a feature of a few pages.