Probability Calculator — Free Online Tool

What Is Probability Calculator?

A free online probability calculator for single events, multiple events, combinations, and permutations. Compute probability as fraction, decimal, and percentage. Calculate odds, "all events occur" and "at least one occurs" probabilities. Find combinations C(n,k) and permutations P(n,k) with factorial display.

Probability is the mathematical measure of how likely an event is to occur, expressed as a number between 0 (impossible) and 1 (certain). Probability Calculator handles single events, multiple events, combinations, and permutations — the core calculations needed for understanding odds in games, statistics, and decision making.

In Single Event mode, enter the number of favorable outcomes and total possible outcomes. The probability is displayed as a fraction, decimal, percentage, and odds — for example, rolling a 6 on a d6: 1/6, 0.1667, 16.67%, odds of 1:5. The odds display shows both "for" and "against" formats.

Multiple Events mode calculates the probability of all events occurring (multiplying individual probabilities) and at least one event occurring (1 minus the probability of none occurring). Enter up to 5 independent events with their individual probabilities. This is essential for understanding compound probabilities — like the chance of rolling two 6s in a row.

The Combinations and Permutations modes complement the probability calculations. Use C(n,k) to count combinations (order does not matter) and P(n,k) to count permutations (order matters). The factorial display shows the step-by-step computation. Large numbers are handled with integer arithmetic for precision.

Real-World Use Cases for Probability Calculator

Calculating the Odds of Drawing a Specific Card

What is the probability of drawing an Ace from a standard 52-card deck? Enter favorable outcomes: 4 (four aces), total outcomes: 52. Result: 4/52 = 1/13 ≈ 7.69%. Odds: 1:12. This means for every time you draw an ace, you expect to draw a non-ace 12 times.

Finding the Chance of Winning Two Coin Flips in a Row

What is the probability of getting heads twice in a row? Use Multiple Events mode with 2 events, each with 1/2 probability. The "all occur" probability is 1/2 × 1/2 = 1/4 (25%). The "at least one" probability is 1 - (1/2 × 1/2) = 3/4 (75%).

Counting Possible Poker Hands with Combinations

How many 5-card hands can be dealt from a 52-card deck? Use Combination mode with n=52, k=5. C(52,5) = 2,598,960 possible hands. This is useful for understanding the rarity of specific poker hands — a royal flush is just 4 of these 2.6 million combinations.

Why Use Probability Calculator?

Single event probability with fraction/decimal/percent/odds
Multiple event: all occur and at least one
Combinations C(n,k) and Permutations P(n,k)
Large number support with integer arithmetic

How to Use Probability Calculator — Step by Step

Choose a mode: Single Event, Multiple Events, Combinations, or Permutations.

Enter the favorable and total outcomes or n and k values.

View results as percentage, fraction, decimal, and odds.

Copy results to clipboard as needed.

Who Is Probability Calculator Best For?

students
statistics learners
gamers
data scientists

Pro Tips for Probability Calculator

1The odds "for" format (e.g., 1:5) means 1 success for every 5 failures — a probability of 1/6. The odds "against" format (5:1) is more common in gambling and means 5 failures for every 1 success.
2The "at least one" calculation works for multiple independent events. It is the complement of "none occurring." For example, the chance of at least one 6 in two dice rolls is 1 - (5/6 × 5/6) = 30.56%.
3Combinations and permutations are related: P(n,k) = C(n,k) × k! Permutations count every ordering separately, while combinations treat different orderings as the same selection.
4Probabilities of compound events assume independence unless specified. Real-world events (like weather and traffic) are often correlated, making simple probability multiplication inaccurate.

Probability Calculator — Frequently Asked Questions

What is the difference between combinations and permutations?

Combinations (C) count selections where order does not matter. Permutations (P) count selections where order matters. For example, picking 2 from {A,B,C}: C=3 (AB,AC,BC) vs P=6 (AB,BA,AC,CA,BC,CB).

How is the "at least one" probability calculated?

The probability of at least one event occurring in n trials is 1 - (1-p)^n, where p is the probability of a single event.

How accurate are the calculations?

All calculations use double-precision floating-point arithmetic following IEEE 754 standards. Financial calculations like loans and compound interest are verified against standard spreadsheet formulas.

Can I round results to a specific number of decimal places?

Results are typically displayed with up to 10 significant digits. You can mentally round to your desired precision for most practical use cases.

Is Probability Calculator really free to use?

Yes, Probability Calculator is completely free with no hidden charges, no usage limits, and no premium tiers. You can use it as often as you need without signing up or providing any personal information.

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