What a permutation and combination calculator tells you
If rearranging the winners changes the outcome, it is a permutation. A lottery draw is a combination; a race podium is a permutation.
Getting the right answer matters less than being able to reproduce it. This guide walks the formula step by step so you can redo the work on paper, in an exam, or in a spreadsheet later.
It is also a fast way to check homework. Solve it yourself first, then run the numbers here — if the two disagree, the difference usually points straight at the step you rushed.
What you need before you start
The Permutation and Combination Calculator asks for 2 inputs. Gather them first — every one of them changes the answer, and guessing at one makes the rest of the precision meaningless.
- Total items (n) — use the same units you measured in.
- Chosen (r) — use the same units you measured in.
The formula, in plain language
P(n,r) = n! ÷ (n−r)! · C(n,r) = n! ÷ (r!(n−r)!).
Work left to right and keep full precision until the very last step. If you want to rebuild this in a spreadsheet, each term above maps to one cell — that makes it easy to change a single assumption and watch the answer move.
Step by step
Open the Permutation and Combination Calculator, then work through it in this order. The calculator updates as you type, so you can leave one field selected and nudge it to see how sensitive the result is.
- Step 1: fill in total items (n).
- Step 2: fill in chosen (r).
- Step 3: read the results panel and note every line, not just the headline number — the supporting figures are usually what you actually need to act on.
- Step 4: change one input and re-read. If a small change swings the answer hard, that input is the one worth measuring carefully.
A worked example
Here are the example values the calculator loads by default, and the answer it produces from them. Reset the calculator at any time to get back to exactly these numbers and check your own working against them.
Inputs
- Total items (n)
- 10
- Chosen (r)
- 3
Result
- Permutations P(n,r)
- 720
- Combinations C(n,r)
- 120
- With repetition (n^r)
- 1,000
Common mistakes to avoid
Most wrong answers from a permutation and combination calculation are not arithmetic errors — they are input errors. These are the three that come up most.
- Rounding early. Carry full precision through the working and round only the final answer.
- Losing track of units or sign. A negative that should be positive quietly flips the whole result.
- Reading the question as a different question — check that the value you are solving for is the value being asked for.
How to make it a habit
A single calculation is a snapshot. The value comes from re-running it on a schedule — monthly for money, every few weeks for health and training, and every time the inputs change for everything else.
Pair it with a timer if the task itself needs a boundary: set a 25-minute Pomodoro to gather your figures, run the numbers, and write down the result before you move on. That is the whole reason a calculator collection lives on a timer site — the two habits reinforce each other.
Privacy and accuracy
Every calculation runs entirely in your browser. Nothing you type — salary, measurements, health numbers — is sent to a server, stored, or shared. There is no account and no tracking of your inputs.
Use this to check and understand your working, not to skip it. The steps below exist so you can reproduce the answer without the tool.