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Probability Distribution Calculator

Calculate PMF/PDF, CDF, mean and variance for common discrete and continuous distributions.

About Probability Distribution Calculator

This multi-distribution calculator evaluates PMF (for discrete) or PDF (for continuous), along with the CDF, mean and variance. Select a distribution and provide its parameters to evaluate at any point x.

Formulas

Binomial PMF

P(X=k) = C(n,k) × p^k × (1−p)^(n−k)

n
Trials
k
Successes
p
Success probability

Normal PDF

f(x) = (1/(σ√(2π))) × exp(−(x−μ)²/(2σ²))

μ
Mean
σ
Standard deviation

Worked example

With the default values below, Probability Distribution Calculator returns PMF/PDF at x of 0.26682793. Change any input above and every figure here is recalculated in your browser.

Inputs used

Distributionone of Binomial, Poisson, Geometric, Normal
Binomial
n (trials, for Binomial)accepts 1–1,000,000
10
p (probability, for Binomial/Geometric)accepts 0–1
0.3
λ (rate, for Poisson)accepts 0.001–1,000,000
4
μ (mean, for Normal)
0
σ (std dev, for Normal)minimum 0.001
1
x (value to evaluate)
3

Results

PMF/PDF at x
0.26682793
CDF at x: P(X ≤ x)
0.64961072
Distribution Mean
3.000000
Distribution Variance
2.100000

Step by step

  1. 1Values used
  2. 2Binomial PMF
  3. 3Normal PDF
  4. 4PMF/PDF at x= 0.26682793
  5. 5CDF at x: P(X ≤ x)= 0.64961072
  6. 6Distribution Mean= 3.000000
  7. 7Distribution Variance= 2.100000

Assumptions and limits

  • The result is derived only from the 7 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

What is the difference between PMF and PDF?

PMF (probability mass function) is for discrete distributions — it gives the exact probability of a specific value. PDF (probability density function) is for continuous distributions — it gives density, not probability, at a point.

What is the CDF?

The cumulative distribution function CDF(x) = P(X ≤ x), the probability of observing a value at most x.

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