About Combinations and Permutations Calculator
This calculator has nCr and nPr keys. nCr(10,3) is 120, the number of ways to choose 3 items from 10 when order does not matter. nPr(5,2) is 20, the number of ordered pairs from 5 items. It is free, needs no sign-up and runs in your browser, so nothing you enter is uploaded.
Use a combination when only the group matters, such as a committee, and a permutation when order matters, such as a race podium. Permutations are always at least as many as combinations: nPr(n,r) = nCr(n,r) × r!.
Write the numbers after the key with a comma, nCr(10,3), or in the infix form 10 nCr 3. Both n and r must be whole numbers with r not larger than n.
How to use Combinations and Permutations Calculator
- Choose the angle unit first: DEG for degrees, RAD for radians or GRAD for gradians.
- Type the expression with the keyboard, or tap the keys. On a phone the scientific keys sit behind the "Show scientific keys" button.
- Read the live answer under the expression. Press Enter or = to keep it in the history and store it as Ans.
- Press 2nd for inverse functions, then a function key such as sin to get sin⁻¹.
- Use nCr(10,3), nPr(5,2) and root(27,3) with a comma between the numbers, or write 10 nCr 3.
- Tap a history entry to load its expression again, or Use to paste its result into the line you are writing.
Features
- Degrees, radians and gradians, with exact results at the common angles: sin(30°) is 0.5 and sin(180°) is 0, not 1.2e-16.
- Sin, cos, tan, their inverses, sinh, cosh, tanh and their inverses.
- Natural log, base-10 log and log with any base, written log(8,2).
- Squares, cubes, any power, square root, cube root and nth root, factorial, reciprocal and absolute value.
- Combinations nCr and permutations nPr, as functions or in the infix form 10 nCr 3.
- Percent, modulo, E notation (1.5E3), constants π and e, and Ans for the previous answer.
- Memory keys MC, MR, M+, M− and MS.
- A live typeset preview of the input, and a result display in large tabular figures.
- Optional fraction form of the result: 0.625 shown as 5/8 as well.
- History with click-to-reuse, a clear button and a copy button for the result.
Formulas
Both are built from factorials.
nCr(n, r) = n! ÷ (r! × (n − r)!)
nPr(n, r) = n! ÷ (n − r)!Worked examples
nCr(10,3) gives 120
10!/(3!×7!).
nPr(5,2) gives 20
5 × 4.
nCr(52,5) gives 2598960
Five-card poker hands from a 52-card deck.
nCr(10,3)+nPr(5,2) gives 140
120 + 20.
Privacy: how it works
- Every calculation runs in your browser tab. The history is saved in this browser only (local storage) and is never sent to Ulkaa or anyone else. Clear it with one button, or clear your browser data.
Tips
- log means base 10 and ln means natural log. Use log(x,b) for any other base.
- Percent turns the number before it into a hundredth, so 200×10% is 20. Write mod for a remainder: 10 mod 3 is 1.
- Factorial works for whole numbers up to 170 and gives an error beyond, because the result no longer fits in a number.
- If the keypad is in the way on a phone, tap the keyboard button beside the expression to type with the device keyboard.
- tan(90°) has no value, and the calculator says so instead of showing a huge number.
Frequently asked questions
Is it really free?
Yes. There is no price, no trial and no credit card. Ulkaa Tool does the work with your own device, so there is no server bill to pass on to you.
Do I need an account?
No. There is no sign-up and no login. Open the page and use it. An Ulkaa account is not needed for anything on this tool.
Does it run in my browser?
Yes. Your calculations are processed by code running in your browser tab, on your own device.
Is my data uploaded?
No. Your calculations are never sent to Ulkaa or to anyone else. You can check this yourself by watching the Network tab in your browser developer tools while you use the tool.
What is the difference between nCr and nPr?
nCr ignores order and nPr counts it. Choosing the letters A and B is one combination but two permutations, AB and BA.
Can r be larger than n?
No. You cannot choose more items than you have, so the calculator reports an error rather than a number.
More Scientific Calculator pages
- Scientific CalculatorA full scientific keypad with degrees, radians and gradians, memory, history and a live formula preview.
- Scientific Calculator in Degree ModeSin, cos and tan in degrees, with exact answers at the common angles.
- Scientific Calculator in Radian ModeTrigonometry in radians, with π as a key and inverse functions that return radians.
- Scientific Calculator in Gradian ModeTrigonometry in gradians, also called gons or grades, where a full turn is 400.
- Scientific Calculator With Fraction ResultsType a calculation and see the answer as a decimal and, when it has a simple form, as a fraction.
- Factorial CalculatorPress x! after a number to multiply it by every whole number below it.
- Exponent and Root CalculatorUse xʸ for powers and √, ∛ and ⁿ√ for roots, in one expression.
- Logarithm CalculatorCalculate log base 10, natural log ln and logarithms to any base.