Putting numbers in order from least to greatest is the first step of almost every descriptive statistic – the median, quartiles, percentiles and the range all start from a sorted list. It is also a routine school task, where the hard part is comparing numbers written in different forms: is 2/3 bigger than 0.7? Where does −1.25 go relative to −0.5?
This calculator removes the guesswork. Type or paste your list, mixing integers, decimals, negative numbers, fractions such as 3/4 and mixed numbers such as 1 1/2. Each entry is converted to its exact decimal value and the list is sorted numerically, so the result is right even when the numbers look very different on the page.
You get the sorted list in the form you typed it, the same list as decimals, a chain written with < and = signs, a ranking table showing each value’s original position and a number line. Switch the order to greatest to least, or remove repeated values, with the two menus.
How to use the Least to Greatest Calculator
- Numbers to sort — Separate items with commas or new lines. Decimals, negatives, fractions (3/4), mixed numbers (1 1/2) and simple sums such as (2+6)/4 work. Do not use thousands separators.
- Order
- Repeated values
Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.
How it works
Each item is evaluated as a number (fractions are divided out, mixed numbers are added up), then the items are sorted by value using a stable sort, so equal values keep the order you entered them in. Duplicates are removed only if you ask.
Worked example
Sort 3/4, −0.5, 1 1/2, 2/3, 0.7, −1.25 and 2. As decimals they are 0.75, −0.5, 1.5, 0.6667, 0.7, −1.25 and 2. The two negatives come first, with −1.25 before −0.5 because it is further below zero. Among the positives, 0.6667 < 0.7 < 0.75 < 1.5 < 2, so the ordered list is −1.25, −0.5, 2/3, 0.7, 3/4, 1 1/2, 2. The range is 2 − (−1.25) = 3.25.
How the ordering works
Every entry is converted to a number before sorting: 3/4 becomes 0.75, the mixed number 1 1/2 becomes 1.5 and an expression such as (2+6)/4 becomes 2. The values are then sorted numerically – not alphabetically – so 35 comes before 305 and −8 comes before −4. Ties keep the order in which you typed them, and the ranking table shows where each entry originally stood.
| You type | Read as |
|---|---|
| 3/4 | 0.75 |
| -2/5 | −0.4 |
| 1 1/2 | 1.5 |
| (2+6)/4 | 2 |
| 45% | 0.45 |
| 2.5e3 | 2,500 |
Formula
Ascending order: x₍₁₎ ≤ x₍₂₎ ≤ … ≤ x₍ₙ₎ · fractions are compared by their decimal value (a/b = a ÷ b)
Worked example
Inputs — Numbers to sort: 3/4, -0.5, 1 1/2, 2/3, 0.7, -1.25, 2; Order: Least to greatest (ascending); Repeated values: Keep every value.
Results — Sorted list = -1.25, -0.5, 2/3, 0.7, 3/4, 1 1/2, 2; Written with inequality signs = -1.25 < -0.5 < 2/3 < 0.7 < 3/4 < 1 1/2 < 2; The same list as decimals = -1.25, -0.5, 0.666666666667, 0.7, 0.75, 1.5, 2; Number of values = 7; Smallest value = -1.25; Largest value = 2.
Key terms
- Ascending order
- Arrangement from the smallest value to the largest (least to greatest).
- Descending order
- Arrangement from the largest value to the smallest (greatest to least).
- Mixed number
- A whole number plus a proper fraction, such as 1 1/2 = 1.5.
- Stable sort
- A sort that keeps equal values in their original order.
Frequently asked questions
How do you order numbers from least to greatest?
Start with the most negative number and finish with the largest positive one. For 3/4, −0.5, 2/3 and −1.25 the order is −1.25, −0.5, 2/3, 3/4.
Which is bigger, 2/3 or 0.7?
0.7. Two thirds is 0.6667, which is smaller than 0.7000.
How do negative numbers fit in?
The further a negative number is from zero, the smaller it is: −8 < −4 < 0 < 1.5.
Can I enter fractions and mixed numbers?
Yes. Type 3/4 for a fraction and 1 1/2 (with a space) for a mixed number; separate the items with commas.
What happens to repeated numbers?
They are kept and shown with an equals sign in the inequality chain. Choose "Remove duplicates" to keep only one copy of each value.
How many numbers can I sort?
There is no fixed limit – hundreds of values sort instantly in your browser.
Is least to greatest the same as ascending order?
Yes. Greatest to least is descending order.