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Probability Calculator

Calculate probabilities for single events, compound events (AND/OR), conditional probability, and complementary probability. Free online probability calculator with fractions, percentages, and odds.

Last revised 25 August 2026

By Team GlobalCalqulate · About our editorial standards

Calculation Type

Type

Single Event Inputs

Favorable Outcomes

Number of outcomes considered success.

Total Possible Outcomes

All equally likely outcomes.

Compound Probability Inputs

P(A) Probability of Event A (0 to 1)

Probability of first event, e.g., 0.5 for 50%.

P(B) Probability of Event B (0 to 1)

Probability of second event, e.g., 0.5 for 50%.

Operation

Methodology

Formula:: Single-event probability
Content last updated:: August 2026
Scheduled re-verification:: August 2027

Calculation type: Exact calculation.

Formula & methodology

Formula used

Single-event probability

P = favourable outcomes ÷ total outcomes

The classical definition, valid when every outcome is equally likely.

Odds

odds = 1 : ((total − favourable) ÷ favourable)

The ratio of ways the event happens to ways it does not.

Both events (AND)

P(A and B) = P(A) × P(B)

The multiplication rule. Valid only when A and B are independent — when the outcome of one does not change the other.

Either event (OR)

P(A or B) = P(A) + P(B)

The addition rule for mutually exclusive events, which cannot both happen. If they can overlap, subtract P(A and B).

Conditional probability

P(A|B) = P(A ∩ B) ÷ P(B)

The chance of A given that B has already happened.

Variable definitions

Symbol	Meaning	Unit
P(A)	Probability of A. a value between 0 (impossible) and 1 (certain)	decimal
P(B)	Probability of B. a value between 0 and 1	decimal

Step-by-step calculation

1. Pick the calculation type
Single event, compound (AND/OR), or conditional.
2. Enter the outcomes or probabilities
Compound and conditional modes take probabilities as decimals from 0 to 1.

Limitations

The single-event formula assumes every outcome is equally likely. It does not apply to a weighted or biased process.
The AND rule here assumes independence; the OR rule assumes mutual exclusivity. The calculator rejects an OR whose probabilities sum above 1, since such events cannot be mutually exclusive.
Conditional probability is computed from the two probabilities entered and is capped at 1; it does not collect the joint probability separately.

This page is educational. It applies the formula described above to the figures you enter and shows the arithmetic behind the result. The output is only as good as the inputs and the assumptions listed here, and it is general information rather than advice about your particular situation.

Help & FAQs

Frequently Asked Questions

Clear answers to common questions to help you use this calculator confidently.

How do I calculate simple probability?

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Divide favorable outcomes by total possible outcomes: P = Favorable / Total. For rolling a 6 on a die: P = 1/6 ≈ 16.67%. All outcomes must be equally likely.

What's the difference between AND and OR probability?

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AND (multiplication rule): P(A and B) = P(A) × P(B), used for independent events. OR (addition rule): P(A or B) = P(A) + P(B), used for mutually exclusive events where both can't occur simultaneously.

What is conditional probability?

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Conditional probability P(A|B) = P(A and B) / P(B). It answers the question: 'Given that B has occurred, what is the probability of A?' For independent events, P(A|B) = P(A).

What is the complement rule in probability?

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The complement rule states P(not A) = 1 − P(A). If the probability of rain is 0.3 (30%), the probability it won't rain is 0.7 (70%). This simplifies calculations when it's easier to find the probability of something NOT happening.

Why must probability always be between 0 and 1?

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0 means an event is impossible and 1 means it's certain — every real event falls somewhere between. If your inputs produce a probability below 0 or above 1, it signals invalid inputs (e.g., more favorable outcomes than total outcomes), not a genuine result.

Need more help? Contact support or email globalcalqulate@gmail.com

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How to Use This Calculator

Select Calculation Type

Choose single event, compound (AND/OR), conditional, or complement probability.

Enter Your Values

Input favorable/total outcomes for single events, or decimal probabilities (0 to 1) for compound/conditional.

Review Results

Results appear instantly showing probability as decimal, percentage, and odds. Interpretations help you understand likelihood.

Understanding Your Results

Probability Basics
Probability ranges from 0 (impossible) to 1 (certain). Formula: P(A) = Favorable / Total. A fair coin flip has P(heads) = 1/2 = 0.5 = 50%. The probability of rolling a 6 on a die is 1/6 ≈ 0.1667 = 16.67%.
AND Rule
For independent events, the probability of both occurring is the product: P(A and B) = P(A) × P(B). Example: flipping heads (0.5) AND rolling a 6 (0.1667) = 0.5 × 0.1667 = 0.0833 = 8.33%.
OR Rule
For mutually exclusive events (cannot happen together), add probabilities: P(A or B) = P(A) + P(B). The probability of rolling 1 OR 6 = 1/6 + 1/6 = 2/6 = 0.3333 = 33.33%.

Understanding Probability Theory

What Is Probability?

Probability measures the likelihood of an event occurring. It ranges from 0 (impossible) to 1 (certain) and can be expressed as a fraction, decimal, or percentage. Probability was formalized in the 17th century by Blaise Pascal and Pierre de Fermat while analyzing gambling problems. Today, probability underlies fields from weather forecasting to medical diagnosis, finance, and artificial intelligence.

Single Event Probability

The simplest case: P(Event) = Favorable Outcomes / Total Possible Outcomes. For a fair six-sided die, the probability of rolling any specific number is 1/6. For a standard deck of cards, the probability of drawing an Ace is 4/52 = 1/13. The key assumption is that all outcomes are equally likely — this is the classical definition of probability.

Compound and Conditional Probability

Compound probability covers multiple events. For independent events (one doesn't affect the other), use multiplication: P(A and B) = P(A) × P(B). For mutually exclusive events, use addition: P(A or B) = P(A) + P(B). Conditional probability P(A|B) asks: given that B occurred, what's the probability of A? Bayes' Theorem formalizes conditional probability and is fundamental to machine learning, spam filtering, and diagnostic testing.

Formula & methodology

Formula used

Single-event probability

P = favourable outcomes ÷ total outcomes

The classical definition, valid when every outcome is equally likely.

Odds

odds = 1 : ((total − favourable) ÷ favourable)

The ratio of ways the event happens to ways it does not.

Both events (AND)

P(A and B) = P(A) × P(B)

The multiplication rule. Valid only when A and B are independent — when the outcome of one does not change the other.

Either event (OR)

P(A or B) = P(A) + P(B)

The addition rule for mutually exclusive events, which cannot both happen. If they can overlap, subtract P(A and B).

Conditional probability

P(A|B) = P(A ∩ B) ÷ P(B)

The chance of A given that B has already happened.

Variable definitions

Symbol	Meaning	Unit
P(A)	Probability of A. a value between 0 (impossible) and 1 (certain)	decimal
P(B)	Probability of B. a value between 0 and 1	decimal

Step-by-step calculation

1. Pick the calculation type
Single event, compound (AND/OR), or conditional.
2. Enter the outcomes or probabilities
Compound and conditional modes take probabilities as decimals from 0 to 1.

Limitations

The single-event formula assumes every outcome is equally likely. It does not apply to a weighted or biased process.
The AND rule here assumes independence; the OR rule assumes mutual exclusivity. The calculator rejects an OR whose probabilities sum above 1, since such events cannot be mutually exclusive.
Conditional probability is computed from the two probabilities entered and is capped at 1; it does not collect the joint probability separately.

Calculator inputs

Calculation Type

Single Event Inputs

Compound Probability Inputs

Your results

Methodology

Formula & methodology

Formula used

Single-event probability

Odds

Both events (AND)

Either event (OR)

Conditional probability

Variable definitions

Step-by-step calculation

Limitations

How do I calculate simple probability?

What's the difference between AND and OR probability?

What is conditional probability?

What is the complement rule in probability?

Why must probability always be between 0 and 1?

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Calculator inputs

Calculation Type

Single Event Inputs

Compound Probability Inputs

Your results

Methodology

How to Use This Calculator

Example: Rolling a Six on a Die

Understanding Your Results

Key Tips

Understanding Probability Theory

What Is Probability?

Single Event Probability

Compound and Conditional Probability

Formula & methodology

Formula used

Single-event probability

Odds

Both events (AND)

Either event (OR)

Conditional probability

Variable definitions

Step-by-step calculation

Limitations

How to Use This Calculator

Example: Rolling a Six on a Die

Understanding Your Results

Key Tips

Understanding Probability Theory

What Is Probability?

Single Event Probability

Compound and Conditional Probability