Bubble sort, sometimes referred to as sinking sort, is a simple sorting algorithm that repeatedly steps through the input list element by element, comparing the current element with the one after it, swapping their values if needed. These passes through the list are repeated until no swaps have to be performed during a pass, meaning that the list has become fully sorted. The algorithm, which is a comparison sort, is named for the way the larger elements "bubble" up to the top of the list.

It performs poorly in real-world use and is used primarily as an educational tool. More efficient algorithms such as quicksort, timsort, or merge sort are used by the sorting libraries built into popular programming languages such as Python and Java.

The earliest description of the bubble sort algorithm was in a 1956 paper by mathematician and actuary Edward Harry Friend, Sorting on electronic computer systems, published in the third issue of the third volume of the Journal of the Association for Computing Machinery (ACM), as a "Sorting exchange algorithm." Friend described the fundamentals of the algorithm, and although initially his paper went unnoticed, some years later it was rediscovered by many computer scientists, including Kenneth E. Iverson, who coined its current name.

Bubble sort has a worst-case and average complexity of ${\displaystyle O(n^{2})}$, where ${\displaystyle n}$ is the number of items being sorted. Most practical sorting algorithms have substantially better worst-case or average complexity, often ${\displaystyle O(n\log n)}$. Even other ${\displaystyle O(n^{2})}$ sorting algorithms, such as insertion sort, generally run faster than bubble sort, and are no more complex. For this reason, bubble sort is rarely used in practice.

Like insertion sort, bubble sort is adaptive, which can give it an advantage over algorithms like quicksort. This means that it may outperform those algorithms in cases where the list is already mostly sorted (having a small number of inversions), despite the fact that it has worse average-case time complexity. For example, bubble sort is ${\displaystyle O(n)}$ on a list that is already sorted, while quicksort would still perform its entire ${\displaystyle O(n\log n)}$ sorting process.

While any sorting algorithm can be made ${\displaystyle O(n)}$ on a presorted list simply by checking the list before the algorithm runs, improved performance on almost-sorted lists is harder to replicate.

The distance and direction that elements must move during the sort determine bubble sort's performance because elements move in different directions at different speeds. An element that must move toward the end of the list can move quickly because it can take part in successive swaps. For example, the largest element in the list will win every swap, so it moves to its sorted position on the first pass even if it starts near the beginning. On the other hand, an element that must move toward the beginning of the list cannot move faster than one step per pass, so elements move toward the beginning very slowly. If the smallest element is at the end of the list, it will take ${\displaystyle n-1}$ passes to move it to the beginning. This has led to these types of elements being named rabbits and turtles, respectively, after the characters in Aesop's fable of The Tortoise and the Hare.

Various efforts have been made to eliminate turtles to improve the speed of bubble sort. Cocktail sort is a bi-directional bubble sort that goes from beginning to end, and then reverses itself, going end to beginning. It can move turtles fairly well, but it retains ${\displaystyle O(n^{2})}$ worst-case complexity. Comb sort compares elements separated by large gaps, and can move turtles extremely quickly before proceeding to smaller and smaller gaps to smooth out the list. Its average speed is comparable to faster algorithms like quicksort.