Permutation and Combination Calculator

Calculated using standard mathematical and industry formulas.

Free online Permutation Combination Calculator calculator and unit conversion tool for everyday, engineering, and home projects.

How to use this calculator?

1. Enter n (total items in the pool) and r (items to select).
2. Read C(n,r) for combinations (order does not matter) and P(n,r) for permutations (order matters).
3. Repetition variants and the factorial n! are also shown for reference.

Formula & calculation method

Permutation and combination formulas

C(n,r) = n! / (r! × (n−r)!) · P(n,r) = n! / (n−r)! · C with rep = (n+r−1)! / (r! × (n−1)!) · P with rep = nʳ

n! = n × (n−1) × … × 1. Limited to n ≤ 170 to avoid floating-point overflow.

Step-by-step calculation example

n=10, r=3: C(10,3) = 10! / (3! × 7!) = 120. P(10,3) = 10! / 7! = 720.

Key insights to remember

• Combinations C(n,r): choosing 3 pizza toppings from 10 = C(10,3) = 120.
• Permutations P(n,r): arranging 3 runners on a podium from 10 = P(10,3) = 720.
• P(n,r) = r! × C(n,r) — permutations are combinations multiplied by the number of arrangements.
• With repetition: combinations = C(n+r−1, r), permutations = nʳ.

How to interpret your results?

C(n,r) — Combination

The number of ways to choose r items from n without regard to order. Used in probability, lottery, and statistics.

P(n,r) — Permutation

The number of ways to arrange r items from n where order matters. Used in scheduling, race placements, and password generation.

Frequently asked questions

How do I use the Permutation Combination Calculator calculator?

Enter your numerical input and select desired units to get instant accurate results.

How accurate are the conversions?

Conversions use official ISO conversion factors for maximum precision.

Does it convert metric and imperial units?

Yes, seamless conversions between metric (meters, kg) and imperial (feet, lbs) are supported.

Is my data stored?

No, all calculations execute 100% locally in your browser with zero data logging.

Can I use this for DIY or engineering projects?

Yes, it provides reliable estimates for construction, crafting, science, and everyday math.

What if I enter invalid inputs?

The calculator will display a friendly error prompt if non-numeric values are entered.

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