Big O Complexity Visualizer

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Calculate and compare growth rates of different algorithms as input size increases.

Algorithm Input

Input Size (n)

Complexity Comparison

100

Linear O(n)

Number of operations relative to input size n.

Constant O(1)1

Logarithmic O(log n)6.64

Linearithmic O(n log n)664

Quadratic O(n²)10,000

Relative Performance Gap

O(log n)7 ops

O(n)100 ops

O(n log n)664 ops

O(n²)10,000 ops

About this calculator

What is Big O Notation?

Big O notation is a mathematical notation used to describe the limiting behavior of a function when the argument tends towards a particular value or infinity. In computer science, it is used to classify algorithms according to how their run time or space requirements grow as the input size grows.

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Pro Tips

Always focus on the highest-order term (ignore constants).
O(1) is the fastest complexity (Constant time).
Big O represents the 'Worst Case' scenario for an algorithm.

Fun Facts

"Binary Search is O(log n), making it efficient even for billions of elements."
"QuickSort is O(n log n) on average, which is why it's the default sort in many libraries."
"The Traveling Salesperson Problem has no known polynomial time solution (it's NP-hard), often exceeding O(2ⁿ)."

Formula: T(n) = O(f(n))