Ascending Order Calculator

If you have a list of numbers and need to know what is their ascending order, this calculator is the tool you need. Inside the boxes, insert your numbers, and their ascending order will immediately display. More fields will appear if you need more (up to 50 numbers!)

If you want to learn more, keep reading this article, where we explain what ascending order means and its different algorithms.

Ascending order means sorting different numbers from the least to the greatest. For example, the ordering of the set {5, 8, 1, 2, 5, 6} in ascending order results in {1, 2, 5, 5, 6, 8}.

The previous list of numbers is short and easy, but manually sorting long and complicated sets can take years for a human. Therefore, we need computer algorithms that do it more efficiently.

There exist different algorithms to calculate the ascending order of a set of numbers, among which we can find:

• Insertion sort;
• Bubble sort; and
• Merge sort.

This calculator uses bubble sort, which is probably the most common sorting algorithm:

• This algorithm shifts positions from left to right, selecting pairs of adjacent numbers and checking if those pairs of numbers are in ascending order. If they're not in order, it switches them.
• Once it reaches the end of the array, it restarts from the beginning.
• The algorithm stops when it doesn't perform any switch during the passage over the array.

For example, let's use the bubble sort method for the set {5,8,1,2,5,6}:

1. First pair of elements: {5,8}. It's in order: move on.
2. Second pair: {8,1}. Not ordered; switch it: {1,8}.
3. Next pair: {8,2}. Switch it: {2,8}.
4. Next one: {8,5}. Switch it: {5,8}.
5. Next one: {8,6}. Switch it: {6,8}.

The resulting set from the previous steps is {5,1,2,5,6,8}. If you repeat the procedure for this new set, you'll obtain the final ordered list: {1,2,5,5,6,8}.

You can look at our ordering numbers calculator article to learn more about the other sorting algorithms.

And what about descending order?

The procedure for descending order is almost the same. The only difference is that now we switch the pair if the opposite occurs: if the first number is the smallest one. You can learn more in our greatest to least calculator.

Try our other descending and ascending order calculators:

• The least to greatest calculator;
• The least to greatest decimals calculator;
• The order from least to greatest calculator; and
• The ordering decimals calculator.

The ascending vs. descending order difference is simple:

• Ascending order: it means sorting from least to greatest (e.g., {1,2,3,4,5,6,6});
• Descending order: we sort the numbers from greatest to least (e.g., {6,6,5,4,3,2,1});

The algorithm for both types of sorting is the same, and the only difference is how we order the numbers during the algorithm execution (from least to greatest or from greatest to least).

To order 4/8, 1/3, and 2/3 from least to greatest:

1. Convert the fractions into equivalent fractions with the same denominators.
   • 4/8 = 12/24;
   • 1/3 = 8/24; and
   • 2/3 = 16/24.
2. The greater for two fractions with equal denominators will be the one with the greater numerator. Therefore: 8/24 < 12/24 < 16/24.
3. Finally, convert each fraction into its original form. The order of the fractions from least to greatest is 1/3 < 4/8 < 2/3.

To sort 1, 2, 5, 6, 5, and 8 with bubble sort:

1. Take the first pair of elements: {1,2}. It's in order; move on.
2. Take the second pair: {2,5}. It's in order; move on.
3. The next pair is {5,6}; leave it.
4. Next one, {6,5}: switch it ({5,6}).
5. The next pair is {6,8}; leave it.

The result is: {1,2,5,5,6,8}.