How do I calculate the probability of a single event?

To calculate the probability of a single event, enter the number of favourable outcomes and the total number of possible outcomes. The calculator uses P(Event) = favourable outcomes ÷ total outcomes and returns the probability as a decimal, percentage and odds.

Can I enter percentages for multiple events?

Yes. In the Multiple Events tab you can enter probabilities either as decimals (for example 0.4) or percentages (for example 40). The calculator automatically normalises values greater than 1 as percentages divided by 100.

What is the difference between combinations and permutations in this calculator?

Use the Combinations (nCr) tab when order does not matter, such as choosing a team from a group. Use the Permutations (nPr) tab when order matters, such as arranging people in a queue or ordering letters in a word. The calculator uses the standard nCr and nPr formulas.

When should I use the binomial probability option?

Choose the Binomial tab when you have repeated independent trials, each with the same probability of success, and you want the probability of getting exactly k successes in n trials. Typical examples include coin flips, quality checks and yes/no survey responses.

How does the dice probability calculator work?

The dice probability calculator uses dynamic programming to count all possible outcomes that produce a target sum for a given number of dice and sides. It then divides the favourable outcomes by the total possible outcomes to give you the exact dice probability and percentage.

Can I download my probability results?

Yes. For each type of probability calculation you can download your results as a TXT file or as an XLS-style spreadsheet. This makes it easy to add your calculations to homework, reports or presentations.

Probability Calculator – Single, Multiple, Binomial & Dice Odds

Multiple Events Probability

Binomial Probability

Calculate the probability of getting exactly k successes in n independent trials.

How to Use a Probability Calculator (With Clear Examples)

Probability is simply a way of measuring how likely something is to happen. Whether you are revising for an exam, checking the odds in a game, or analysing data at work, a good probability calculator saves time and avoids mistakes. On this page you can analyse single events, multiple events, combinations, permutations, binomial experiments and dice rolls — all in one place.

1. The basics: single event probability

The simplest type of probability question looks like this: “What is the chance of this event happening?”. The formula behind the Single Event tab is:

P(Event) = Number of favourable outcomes ÷ Total number of possible outcomes

For example, rolling a 4 on a fair six-sided die has 1 favourable outcome and 6 possible outcomes, so P(rolling a 4) = 1 ÷ 6 ≈ 0.1667 or 16.67%.

Tip: You can always switch between fraction, decimal and percentage. If you prefer to work in percentages, our Percentage Calculator can help with the conversions.

2. Multiple events: AND vs OR

As soon as you have more than one event, the wording matters a lot. The Multiple Events tab supports:

AND – both events must happen (for independent events we multiply the probabilities).
OR – at least one of the events happens (we add probabilities and subtract any overlap).

Example: the probability of flipping two heads in a row is:

P(Head AND Head) = 0.5 × 0.5 = 0.25 (25%)

You can enter each probability either as a decimal (0.4) or as a percentage (40). The calculator normalises values above 1 by treating them as percentages.

3. Combinations vs permutations

Many exam and homework questions involve choosing or arranging items. The tricky part is knowing which formula to use:

Combinations (nCr) – order does not matter (choosing a committee of 3 from 10 people).
Permutations (nPr) – order matters (arranging 3 trophies on a shelf).

The Combinations tab uses:

C(n, r) = n! ÷ (r! × (n − r)!)

and the Permutations tab uses:

P(n, r) = n! ÷ (n − r)!

For deeper work with averages and spread after counting outcomes, you can continue analysis with the Statistics Calculator or Basic Calculator.

4. Binomial probability in one click

Binomial probability appears often in textbooks, tests and data analysis. It applies when:

You have a fixed number of trials (n).
Each trial has only two outcomes (success/failure).
The probability of success stays the same in every trial.

The Binomial tab uses the formula:

P(X = k) = C(n, k) × p^k × (1 − p)^{n − k}

Think of flipping a coin, checking if a product passes quality control, or counting how many customers say “yes” in a survey. Instead of doing the heavy factorial maths by hand, you just enter n, k and p and the calculator returns the exact probability.

5. Exact dice roll probabilities

The Dice Probability tab lets you answer questions like: “What is the chance that two six-sided dice add up to 7?” or “What are the odds that three 8-sided dice sum to 15?”.

Behind the scenes, the tool uses a dynamic programming table to count every possible way the dice can reach the target sum. It then divides those favourable outcomes by the total number of outcomes (sides^dice) to give an exact probability and percentage.

6. Common mistakes to avoid

Gambler’s fallacy: past independent results (like previous coin flips) do not change the probability of the next flip.
Mixing up AND and OR: “A and B” almost always gives a smaller probability than “A or B”.
Forgetting the sample space: always be clear about the total number of possible outcomes, especially with cards, dice or multi-step experiments.

Ready to practice? Start with a simple single event, then try multiple events, combinations and finally a binomial example. If you’re also working with percentages or growth, open the Percentage Calculator in a new tab for quick conversions.

Probability Calculator – Frequently Asked Questions

What can I calculate with this probability calculator?

You can calculate single event probability, combined probability for multiple events (AND/OR), combinations (nCr), permutations (nPr), binomial probabilities and dice roll odds, all with formulas and plain-language explanations.

Do I need to enter probabilities as decimals or percentages?

You can use either. If you type values like 40 or 75, the calculator treats them as 40% and 75%. If you type 0.4 or 0.75, it keeps them as decimals. This flexibility works especially well in the Multiple Events and Binomial tabs.

What is the difference between combinations and permutations here?

Use combinations when the order of items does not matter (for example, picking 5 lottery numbers). Use permutations when order does matter (for example, arranging 3 winners in 1st, 2nd and 3rd place).

Can I use this calculator for exam preparation?

Yes. The calculator is helpful for GCSE, A-Level, university statistics, SAT/ACT prep and any course that covers basic probability, combinatorics or binomial distributions. Many students use it to check their working and understand formulas step by step.

How accurate are the dice probabilities?

The dice tool uses exact counting methods (dynamic programming) to calculate the number of ways to reach a given sum. For reasonable numbers of dice and sides, the probabilities are exact, not approximations.

Can I download or save my results?

Yes. Each tab includes buttons to download TXT or XLS-style files. That makes it easy to paste the results into homework, reports, spreadsheets or documentation.

What other calculators work well with this one?

After calculating probabilities, you may want to explore average and spread using our Statistics Calculator, Standard Deviation Calculator or Average Calculator.

🎲 Probability Calculator

Single Event Probability