What is a Probability Distribution?

A probability distribution is a mathematical and statistical function that describes the likelihood of different possible values of a variable. Probability distributions are often depicted using graphs or probability tables.
All Calculator helps you calculate distributions accurately using basic probability formulas without the need for tedious manual calculations.

How to Use the All Calculator Probability Distribution Calculator?

Follow these simple steps to use the probability solver:

Choose a distribution type from the drop-down list:

Select a calculation type:

Enter the required values:

Lambda-rate parameter
Number of events (k)
X values
Minimum value (a)
Maximum value (b)
Alpha-shape parameter
Beta-scale/shape parameter
Scale parameter
Shape parameter
Mu-location parameter
Sigma-scale parameter
Probability (0–1)

Click “Calculate”, and the basic probability calculator instantly provides your results.

Examples of Probability Calculations – All Calculator

Poisson Distribution Example

Lambda: 3.5
k: 2

Solution:
P(X=k)= (λ^k · e^-λ) / k! = 0.184959
Result: Probability = 0.184959

Exponential Distribution Example

Lambda: 0.2
X Value: 5

Solution:
PDF: f(x)= λe^-λx = 0.073576
CDF: F(x)= 1 − e^-λx = 0.632121
Result:
PDF = 0.073576
CDF = 0.632121

Uniform Distribution Percentile Example

Minimum value (a): 10
Maximum value (b): 30
Probability: 0.25

Result:
PDF = 0
CDF = 0

Gamma Distribution Example

X Value = 5
Alpha (α) = 3
Beta (β) = 2

Solution:
f(x)= (x^(α-1)e^(-x/β)) / (Γ(α)β^α) = 0.128258
Result: PDF = 0.128258

Beta Distribution Example

Alpha (α) = 2
Beta (β) = 5
X Value = 0.6

Solution:
f(x)= (x^(α-1)(1-x)^(β-1)) / B(α,β) = 0.4608
Result: PDF = 0.4608

Weibull Distribution Percentile Example

Shape = 1.5
Scale = 20
Probability = 0.9

Result: PDF = 0

Log-Normal Distribution Example

Mu (μ) = 0
Sigma (σ) = 1
X Value = 2.5

Solution:
f(x)= [1 / (xσ√2π)] e^(-((ln x − μ)^2 / 2σ^2)) = 0.104871
Result: PDF = 0.104871

Why Use the All Calculator Probability Distribution Calculator?

Get Quick Results: Save time when calculating Poisson, Exponential, Uniform, Gamma, Beta, Weibull, or Log-Normal distributions.

Reduce Human Error: Manual calculations may lead to mistakes. This combined probability calculator uses proven formulas to deliver accurate results every time.

User-Friendly: Perfect for students, teachers, and professionals, this free probability solver calculates probabilities, percentiles, and distribution statistics.

Tips for Best Results:

Enter probability as a decimal (0–1).
Use correct field names for each distribution.
Double-check your inputs before calculating.

FAQs – All Calculator

Q1: What is the difference between PDF/PMF and CDF?

PMF/PDF gives the probability at a single point; CDF gives cumulative probability up to that point. For continuous distributions, probabilities come from areas (CDF differences).

Q2: When should I use “probability (0-1)”?

Use this in Find Percentile mode. Enter values like 0.1, 0.5, 0.95 to get 10th, 50th, or 95th percentiles.

Q3: Can I use this as a basic probability calculator?

Yes, All Calculator includes basic probability formulas and helps calculate probabilities quickly and accurately.

Q4: Does it support combined probability calculations?

Absolutely! You can calculate probabilities for multiple events using this combined probability calculator.

Q5: Which distributions are supported?

Poisson, Exponential, Uniform, Gamma, Beta, Weibull, and Log-Normal.

Q6: Is this tool suitable for beginners?

Yes, the probability solver is intuitive, user-friendly, and perfect for students and professionals.