KLOORAHow to Calculate Permutations and Combinations (nPr and nCr)
Published 7 November 2026 by Kloora Tools
Quick answer: use the free Permutation and Combination Calculator to calculate nPr, nCr and factorials for any n and r. It runs in your browser, so nothing you enter is uploaded or stored, and there is no signup.
What is the Permutation and Combination Calculator?
Calculate nPr, nCr and factorials for any n and r. People often search for it as "permutation calculator", "combination calculator" or "ncr calculator". This free version works on any phone or computer and needs no download.
How to use the Permutation and Combination Calculator
- Open the Permutation and Combination Calculator.
- Enter your values in the fields.
- The results update instantly as you type.
- Note or copy the numbers you need.
How it works
nPr = n! / (n - r)! counts ordered arrangements and nCr = n! / (r! x (n - r)!) counts selections where order does not matter. The tool uses exact big-number arithmetic so large factorials stay accurate up to n = 500.
Worked example
- Input: n (total items): 10; r (items chosen): 3
- Result: n factorial (n!): 3,628,800; Permutations nPr: 720; Combinations nCr: 120
Common uses
- Count lottery or password possibilities
- Solve probability and statistics problems
- Plan seating or team selections
Second worked example
Here is the same tool with larger numbers, so you can see how the result scales.
- Input: n (total items): 15; r (items chosen): 4.5
- Result: n factorial (n!): 1,307,674,368,000; Permutations nPr: 32,760; Combinations nCr: 1,365
Tips for the best result
- Check the units and the order of the numbers before you press anything.
- Estimate the answer roughly in your head first, so you can spot an input mistake.
- Keep more decimal places during the work and round only the final answer.
- Try a simple case you already know to confirm the tool does what you expect.
Common mistakes to avoid
- Swapping two inputs, such as base and exponent or x and y.
- Using degrees where radians are expected, or the other way round.
- Rounding too early and carrying the error forward.
- Entering a percentage as a decimal, or a decimal as a percentage.
Permutation and Combination Calculator compared with doing it by hand
| Permutation and Combination Calculator | By hand or in a spreadsheet | |
|---|---|---|
| Speed | Instant, results update as you type | Slow, you rebuild the steps each time |
| Accuracy | Same standard method every time | Easy to slip on a formula or a unit |
| Privacy | Runs in your browser, nothing uploaded | Depends on the software you use |
| Cost | Free, no signup | Free or paid software needed |
Try it now
Open the Permutation and Combination Calculator and try your own numbers or text. If it helps, share it with someone who needs it.
Frequently asked questions
What is the difference between a permutation and a combination?
In a permutation order matters (ABC differs from CBA). In a combination order does not matter.
How are nPr and nCr calculated?
nPr = n! / (n - r)! and nCr = n! / (r! x (n - r)!).
What does the Permutation and Combination Calculator do?
Calculate nPr, nCr and factorials for any n and r.
How do I use the Permutation and Combination Calculator?
1. Enter your values in the fields. 2. The results update instantly as you type. 3. Note or copy the numbers you need.
Is my data safe when I use the Permutation and Combination Calculator?
Yes. Everything runs in your browser on your own device. Nothing you type or choose is uploaded, stored or shared, and no AI service is used.
Does the Permutation and Combination Calculator work on a phone?
Yes. It works on phones, tablets and computers in any modern browser, with nothing to install.
Do I need an account or a payment to use the Permutation and Combination Calculator?
No. It is free, has no daily limit, no watermark and needs no signup.
What information does the Permutation and Combination Calculator need?
You enter: n (total items), r (items chosen). The results update instantly as you change any value.
How does the Permutation and Combination Calculator work?
nPr = n! / (n - r)! counts ordered arrangements and nCr = n! / (r! x (n - r)!) counts selections where order does not matter.
Can I use this for "combination calculator"?
Yes. The Permutation and Combination Calculator is built for exactly that, and it also answers searches such as "permutation calculator" and "ncr calculator".
How accurate is the Permutation and Combination Calculator?
It uses the standard method and shows results to a sensible precision. For legal, medical, financial or safety decisions, confirm important numbers with a qualified professional.
Where can I find more free tools like the Permutation and Combination Calculator?
Kloora Tools has over 150 free tools for CVs, PDFs, images, Urdu, calculators and everyday tasks. Browse them all from the home page.
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