Range and Midrange Calculator
Get range, midrange, and half range from low and high values in one step.
What it does
Range and midrange summarize a data set with only two numbers, the smallest and the largest. Range tells how wide the span is. Midrange tells where the center of that span sits. Together they give a fast picture before you compute mean or median.
The tool above takes low and high and returns range, midrange, and half range. The defaults 12 and 38 match the worked example, so the page opens already calculated. Change either box to update all three results at once.
Teachers use range to introduce spread, and shops use it for tolerances. If a part must span 12 to 38 mm, range 26 mm is the total allowance and midrange 25 mm is the nominal center. Half range 13 mm is the plus or minus amount around that center.
These measures react strongly to extremes. One far outlier stretches range and pulls midrange with it, while mean and median move less. That sensitivity is both the point and the warning: use range for a quick span check, then confirm with sturdier summaries when outliers are possible.
This page shows formulas, a full hand checked example at 12 and 38, a reference table, and practice checks that run through the tool.
How to use
- Find the lowest value in your data and type it as Low value.
- Find the highest value and type it as High value.
- Check that high is at least as large as low, or the tool reports an error.
- Read Range as high minus low.
- Read Midrange as the point halfway between low and high.
- Use Half range as the plus or minus tolerance around midrange.
Formula
- low
- Smallest value observed.
- high
- Largest value observed.
- midrange
- Center of the extremes, not the median.
All three outputs share the input units. If inputs are mm, outputs are mm. When low equals high, range is 0 and midrange equals that single value.
Worked example
Example: low 12, high 38
A quiz section scores between 12 and 38 points. Here is the full path to the three answers.
- Write the inputs: low = 12, high = 38.
- Range: 38 minus 12 = 26.
- Midrange: (12 + 38) / 2 = 50 / 2 = 25.
- Half range: 26 / 2 = 13.
- Check: midrange minus half range is 25 minus 13 = 12, the low.
- Check: midrange plus half range is 25 plus 13 = 38, the high.
Reference table
| Output | Formula | Use |
|---|---|---|
| Range | High minus low | Total span and variability |
| Midrange | (Low + high) / 2 | Center of the span |
| Half range | Range / 2 | Plus or minus tolerance |
| Low = high | Range 0 | No spread, single value |
Limits
- Uses only extremes, so one outlier can dominate both outputs.
- Does not describe shape, skew, or gaps inside the span.
- Needs ordered low and high. Reversed inputs trigger an error.
- For large data with outliers, pair with quartiles or SD.
Common mistakes
- Swapping low and high, which the tool rejects instead of guessing.
- Reading midrange as median. Median uses all values, midrange uses two.
- Reporting range without units, so 26 could mean points, mm, or dollars.
- Trusting range alone for skewed data with a far tail value.
- Rounding low and high before subtracting, which shifts range by the rounding.
Try it yourself
Quick checks. Answers sit tucked under each question.
Low 5, high 15?
Range 10, midrange 10, half range 5.
Low 100, high 160?
Range 60, midrange 130, half range 30.
Questions
What is range?
High minus low. It is the simplest measure of spread.
What is midrange?
(Low + high) / 2. It marks the center of the span.
Range or standard deviation?
Range is fast and uses two values. SD uses all values and resists single outliers better.
Can range be zero?
Yes, when low equals high. All values are then the same.
Can range be negative?
No, when high is at least low. Reversed inputs are an entry error.
Why does one outlier change range so much?
Range reads only extremes, so a new extreme resets both range and midrange at once.