Big O Complexity Calculator

Enter a value of N and compare how O(1), O(log N), O(N), O(N log N), O(N²) and O(2^N) algorithms scale, with an interactive chart and plain-English explanations.

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N (input size): 20

O(1)

1 ops

Constant time — the number of operations doesn't change with input size, like accessing an array element by index.

O(log N)

4 ops

Logarithmic time — operations grow slowly as input grows, like binary search on a sorted array.

O(N)

20 ops

Linear time — operations grow proportionally with input size, like a single loop over an array.

O(N log N)

86 ops

Linearithmic time — typical of efficient sorting algorithms like merge sort or quicksort.

O(N^2)

400 ops

Quadratic time — operations grow with the square of input size, common in nested loops.

O(2^N)

1,048,576 ops

Exponential time — operations double with each additional input element, common in brute-force recursive algorithms.

How to Use the Big O Complexity Calculator

1Enter a value for N.
2Compare the resulting operation counts for each complexity class.
3Read the explanation of what each complexity class means in practice.

Frequently Asked Questions

What does N represent?+

N is the size of the input — for example, the number of items in an array.

Why do some values get extremely large?+

Exponential complexities like O(2^N) grow so fast that for even moderate N they represent astronomically large operation counts — that's the point of the comparison.

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