About the Range Calculator
The range is the simplest way to describe how spread out a set of numbers is: the difference between the largest and the smallest value. It answers everyday questions directly — how far temperatures swung in a day, how much prices differed between shops, how wide the gap was between the best and worst test scores. It is usually the first measure of spread taught in statistics, and a quick first look at any data set.
This range calculator finds the range of any list of numbers, along with the minimum, maximum and midrange, the range as a percentage of the mean, and the sorted values so you can check the result at a glance.
How to Use the Range Calculator
Enter your numbers, separated by commas, spaces or new lines. Negative numbers and decimals are fine.
The range appears with the minimum, maximum, midrange and sorted list.
The Formulas
range = maximum − minimum
midrange = (maximum + minimum) ÷ 2Step-by-Step Example
The values 3, 7, 2, 9, 12, 5.
Sorted: 2, 3, 5, 7, 9, 12
Minimum: 2
Maximum: 12
Range: 12 − 2 = 10
Midrange: (12 + 2) ÷ 2 = 7The range is 10 and the midrange 7. The mean of the six values is 6.33, a little below the midrange because the values are not evenly spread.
With negative values: daily temperatures of −5, −2, 3 and 8 °C have a range of 8 − (−5) = 13 degrees. Subtracting a negative number adds it.
Strengths of the Range
The range is quick to find, easy to explain and in the same units as the data. For small samples it gives a fair sense of spread, which is why control charts in manufacturing often track the range of small samples of parts. It is also the natural measure for questions that really are about the extremes: the lowest and highest prices, the coldest and warmest days, the tallest and shortest players.
Weaknesses of the Range
The range depends on only two values, the most extreme ones, and ignores everything in between. A single unusual value can make it enormous. For 2, 3, 5, 7, 9 and 120, the range is 118, although five of the six values lie within 7 of each other. The range also tends to grow as more data is collected, because a larger sample is more likely to include extreme values, so ranges from samples of different sizes are not directly comparable.
Better Measures of Spread
When extreme values are a concern, the interquartile range — the spread of the middle half of the data — gives a more stable picture, because it ignores the lowest and highest quarters. The standard deviation uses every value and is the standard measure for most statistical work. Reporting the range alongside one of these gives both the full extent of the data and its typical spread.
The Midrange
The midrange, halfway between the minimum and maximum, is a quick estimate of the centre of the data. It works well for symmetric data without outliers, but like the range it relies only on the extremes, so the mean or median is usually a better measure of the typical value.
Range in Everyday Life
Weather forecasts give the day's temperature range. Price comparison sites show the range of prices for a product. Teachers report the range of marks in a class. In sport, the range of a team's scores over a season shows how consistent they were. In each case, pairing the range with an average — "scores ranged from 54 to 97, with a median of 78" — gives a clearer picture than either figure alone.
Range and Standard Deviation
For roughly bell-shaped data, the range and the standard deviation are linked by a useful rule of thumb: the range is usually about four standard deviations for moderate samples, and closer to six for very large ones. Dividing the range by four therefore gives a quick estimate of the standard deviation when nothing else is available. For the example data, 10 ÷ 4 = 2.5, close to the sample standard deviation of about 3.8 — rough, but useful as a check that a calculated standard deviation is in the right ballpark, and a reminder that the two measures describe the same spread in different ways.
Understanding Your Result
The headline is the range.
The minimum and maximum line gives the two extreme values and the number of values.
The midrange line gives the midpoint of the extremes and the mean for comparison.
The relative range line expresses the range as a percentage of the mean.
The sorted values line lists the data in order, so you can spot outliers.
When Should You Use This Calculator?
Use it for homework on measures of spread.
Use it to summarise temperatures, prices, scores or times.
Use it to spot unusual values at either end of a data set.
Use it for quick checks of consistency in small samples.
Common Mistakes
Forgetting to find the true minimum and maximum. Sort the data first.
Mishandling negative numbers. Subtracting a negative minimum adds its size.
Reading too much into one extreme value. Check whether an outlier is a mistake.
Comparing ranges from different sample sizes. Larger samples tend to have larger ranges.
Confusing range with interquartile range. The IQR covers only the middle half.