Probability Calculator
Calculate Binomial, Geometric, and Normal distribution probabilities — PDF, CDF, mean, and standard deviation — instantly.
This free probability calculator works out PDF and CDF values for the three most common probability distributions: Binomial, Geometric, and Normal. Enter your parameters and get the exact probability, cumulative probability, mean, standard deviation, and the formula breakdown instantly. It covers everything from coin-flip problems to bell-curve z-scores, all calculated in your browser with no sign-up needed.
How to Use the Probability Calculator
Choose a distribution from the dropdown, enter your values, and the calculator shows the exact probability (PDF), cumulative probability (CDF), the complement, and the distribution’s mean and standard deviation. The formula used is shown below the results so you can verify or learn from the calculation.
Binomial Distribution
The binomial distribution models the probability of getting exactly k successes in n independent trials, where each trial has the same probability p of success. A classic example is flipping a coin 10 times and asking the probability of getting exactly 3 heads. Enter n (number of trials), k (number of successes), and p (probability per trial).
Geometric Distribution
The geometric distribution models how many trials it takes to get the first success. For example, if you roll a die repeatedly, how likely is it that the first six appears on the third roll? Enter k (the trial number of the first success) and p (probability of success on each trial).
Normal Distribution
The normal (Gaussian) distribution is the familiar bell curve used throughout statistics. Enter a value x, the mean, and the standard deviation, and the calculator returns the PDF value (the height of the curve at x), the CDF (the probability that a value falls at or below x), and the z-score. This is exactly what students look up in a z-table, calculated instantly.
PDF vs CDF Explained
The PDF (probability density function) gives the probability of one specific outcome, while the CDF (cumulative distribution function) gives the probability of getting that outcome or anything less. Together they answer the two most common probability questions: how likely is exactly this result, and how likely is this result or better.
Frequently Asked Questions
What is a binomial PDF?
The binomial PDF gives the probability of getting exactly k successes in n trials, each with probability p. The formula is P(X=k) = C(n,k) × p^k × (1−p)^(n−k).
How do I calculate CDF from PDF?
The CDF at a value k is the sum of all PDF values from 0 up to k. This calculator computes it automatically alongside the PDF.
What is a z-score?
A z-score measures how many standard deviations a value is from the mean. It is calculated as z = (x − μ) / σ, and the calculator shows it for the Normal distribution.
Can I use this on a phone?
Yes. The calculator runs in your browser on any device with no download or account needed.