Binomial Distribution
Calculate binomial probabilities P(X = k) and cumulative probabilities
P(X = 3)
0.1172
11.72%
With n=10, p=0.5: ~11.7% chance of exactly 3 successes
5.00
2.50
1.58
11.72%
Distribution (k vs probability)
About Binomial Distribution
The binomial distribution models the number of successes in a fixed number of independent trials, each with the same probability of success. It is one of the most widely used discrete probability distributions in statistics.
P(X = k) = C(n,k) × pk × (1-p)n-k
Where:
• n = number of trials
• k = number of successes
• p = probability of success on each trial
• C(n,k) = binomial coefficient = n! / (k! × (n-k)!)
Key properties:
• Mean (μ) = n × p
• Variance (σ²) = n × p × (1-p)
• Standard Deviation (σ) = √(n × p × (1-p))
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About This Calculator & Guide
About the Binomial Distribution Calculator
The Binomial Distribution Calculator is a specialized online utility designed to help you calculate binomial probabilities p(x = k), cumulative probabilities, mean, variance, and standard deviation for binomial distributions. It performs calculations in real-time to provide immediate, reliable estimates for study, work, or daily tasks.
How to Use
Simply enter your parameters in the input fields of the calculator widget above. The tool evaluates the inputs instantly and displays the results in real-time. You can modify any value to check alternate scenarios and compare figures dynamically.
Data Privacy & Safety
All calculations are executed locally within your web browser. No inputs are sent to our servers or stored externally, ensuring your personal and financial details remain completely private and secure.
FAQ
Frequently Asked Questions
What does the Binomial Distribution Calculator do?+
Calculate binomial probabilities P(X = k), cumulative probabilities, mean, variance, and standard deviation for binomial distributions. It is designed for quick everyday use and gives clear results without requiring a sign in.
Is the Binomial Distribution Calculator free to use?+
Yes. The Binomial Distribution Calculator is free to use online and works directly in your browser.
Can I use the Binomial Distribution Calculator on mobile?+
Yes. The calculator layout is responsive, so you can use it on phones, tablets, laptops, and desktop screens.