Probability Calculator
Calculate the probability of single and combined events using fundamental probability rules. Covers union, intersection, and complement for independent and dependent events.
This free online probability calculator provides instant results with no signup required. All calculations run directly in your browser — your data is never sent to a server. Enter your values below and see results update in real time as you type. Perfect for everyday calculations, homework, or professional use.
Probability of event A occurring, between 0 and 1.
Probability of event B occurring, between 0 and 1.
Probability that both A and B occur. For independent events this equals P(A)*P(B).
How to Use This Calculator
Enter your input values
Fill in all required input fields for the Probability Calculator. Most fields include unit selectors so you can work in your preferred unit system — metric or imperial, whichever matches your problem.
Review your inputs
Double-check that all values are correct and that you have selected the right units for each field. Incorrect units are the most common source of calculation errors and can produce results that are off by factors of 2, 10, or more.
Read the results
The Probability Calculator instantly computes the output and displays results with units clearly labeled. All calculations happen in your browser — no loading time and no data sent to a server.
Explore parameter sensitivity
Try adjusting individual input values to see how the output changes. This is a quick and effective way to develop intuition about how different parameters influence the result and to identify which inputs have the largest effect.
Formula Reference
Probability Calculator Formula
See calculator inputs for the governing equation
Variables: All variables and their units are labeled in the calculator interface above. Input fields accept values in multiple unit systems — select your preferred unit from the dropdown next to each field.
When to Use This Calculator
- •Use the Probability Calculator when you need accurate results quickly without the risk of manual computation errors or unit conversion mistakes.
- •Use it to verify calculations made by hand or in spreadsheets — an independent check can catch errors before they lead to costly decisions.
- •Use it to explore how changing input parameters affects the output — a quick way to develop intuition and identify the most influential variables.
- •Use it when collaborating with others to ensure everyone is working from the same numbers and applying the same assumptions.
About This Calculator
The Probability Calculator is a free, browser-based calculation tool for engineers, students, and technical professionals. Calculate the probability of single and combined events using fundamental probability rules. Covers union, intersection, and complement for independent and dependent events. It implements standard formulas and supports both metric (SI) and imperial unit systems with automatic unit conversion. All calculations are performed instantly in your browser with no data sent to a server. Use this calculator as a quick reference and sanity-check tool during design, analysis, and learning. Always verify results against primary engineering references and applicable standards for any safety-critical application.
About Probability Calculator
The probability calculator helps you compute the likelihood of single and combined events using the fundamental rules of probability theory. Probability is the mathematical language of uncertainty and is used across science, engineering, medicine, and everyday decision-making. Whether you are calculating the chance of drawing a specific card from a deck, estimating the likelihood of two independent system failures occurring simultaneously, or evaluating risk in a clinical trial, the basic rules of probability provide the framework. This calculator applies the addition rule (union), the complement rule, and accepts a user-supplied joint probability so you can handle both independent and dependent events with ease.
The Math Behind It
Formula Reference
Addition Rule
P(A or B) = P(A) + P(B) - P(A and B)
Variables: P(A) = probability of event A; P(B) = probability of event B; P(A and B) = joint probability
Complement Rule
P(not A) = 1 - P(A)
Variables: P(A) = probability of event A
Worked Examples
Example 1: Drawing cards from a deck
What is the probability of drawing a heart or a face card from a standard 52-card deck?
There is approximately a 42.3% chance of drawing a heart or a face card.
Example 2: Two independent system failures
A server has a 2% chance of failure and a network switch has a 3% chance. What is the probability that at least one fails?
There is about a 4.94% chance that at least one component fails.
Common Mistakes & Tips
- !Adding probabilities without subtracting the intersection, which double-counts the overlap.
- !Assuming events are independent when they are actually dependent, leading to incorrect joint probability calculations.
- !Entering probabilities greater than 1 or less than 0, which are not valid.
- !Confusing P(A or B) with P(A and B) when interpreting results.
Related Concepts
Used in These Calculators
Calculators that build on or apply the concepts from this page:
Frequently Asked Questions
What is the difference between independent and mutually exclusive events?
Independent events can occur simultaneously but do not influence each other (P(A and B) = P(A)*P(B)). Mutually exclusive events cannot occur at the same time (P(A and B) = 0). Two events cannot be both independent and mutually exclusive unless one has probability zero.
How do I calculate probability for more than two events?
Use the inclusion-exclusion principle: add individual probabilities, subtract all pairwise intersections, add back all triple intersections, and so on. For independent events, the probability that at least one occurs is 1 minus the product of all complements.
Can probabilities be negative?
No. By the axioms of probability, all probabilities must be between 0 and 1 inclusive. A negative result indicates an error in your input values.