Probability Distributions Calculator

• •Use the Probability Distributions Calculator when solving homework or exam problems that require quick numerical verification of your hand calculations — instant feedback helps identify arithmetic errors before they propagate.
• •Use it during the early design phase to rapidly iterate on parameters and narrow down feasible configurations before committing time to detailed finite element simulations or full design packages.
• •Use it when reviewing a colleague's calculation or checking a vendor's data sheet for plausibility — a quick sanity check can prevent costly downstream errors.
• •Use it to generate reference data for a technical report or presentation without manual computation, ensuring consistent, reproducible numbers throughout the document.
• •Use it in the field when a quick estimate is needed and a full engineering software package is not available.

The Probability Distributions Calculator is a precision engineering calculation tool designed for students, engineers, and technical professionals. PMF/PDF, CDF, mean, and variance for Binomial, Poisson, Exponential, Uniform, and Geometric distributions with interactive charts All calculations are performed using established engineering formulas from the relevant scientific literature and standards. Inputs support both metric (SI) and imperial unit systems, with unit conversion handled automatically — simply select your preferred unit from the dropdown next to each field. Results are computed instantly in the browser without sending data to a server, ensuring both speed and privacy. This calculator is intended as a supplementary tool for learning and design exploration; always verify results against authoritative references for safety-critical applications.

This calculator supports five common discrete and continuous probability distributions used in engineering and statistics. (1) Binomial: discrete, models the number of successes in n independent trials with probability p. Mean = np, variance = np(1−p). (2) Poisson: discrete, models the number of events in a fixed interval when events occur at constant rate λ. Mean = variance = λ. Good approximation to binomial when n is large and p is small. (3) Exponential: continuous, models the time between events in a Poisson process with rate λ. Memoryless property (P(X > s+t | X > s) = P(X > t)). Mean = 1/λ, variance = 1/λ². (4) Uniform: continuous, all values in [a, b] equally likely. Mean = (a+b)/2, variance = (b−a)²/12. (5) Lognormal: continuous, arises when the logarithm of the variable is normally distributed. Used for variables that can only be positive and span orders of magnitude (component lifetimes, particle sizes). Each distribution has a specific PMF (discrete) or PDF (continuous), CDF, and moment-generating function. The calculator computes PMF/PDF values, cumulative probabilities, inverse CDF (quantile), mean, and variance for each distribution with user-specified parameters.

• •Binomial for quality pass/fail testing: probability of seeing k defective units in a sample of n.
• •Poisson for arrivals and events: number of customers per hour, number of defects per square meter, particle count per cubic centimeter.
• •Exponential for reliability: time between failures in constant-failure-rate systems, often used in early burn-in period or wearout-free regime.
• •Uniform for simulation inputs: when a variable is known only to lie in a range with no further information, uniform is the maximum-entropy choice.
• •Lognormal for life data: fatigue life, component wear, financial returns, particle size distributions all commonly follow lognormal.