Mathematics · Statistics
Range Calculator
Find the minimum, maximum and range of six entered observations.
Inputs and results stay in this browser. Change one value at a time to explore the relationship.
Calculation steps
- Minimum = 2.
- Maximum = 14.
- Range = 14 − 2 = 12.
Understand Data range
One idea, three depths
Choose how deeply to explain Data range
Data range: Find the minimum, maximum and range of six entered observations.
Age 5Explain it to a 5-year-oldStart with a picture
Imagine using Data range to answer this question: find the minimum, maximum and range of six entered observations? Enter Value 1, Value 2, Value 3, and 3 other inputs; the calculator shows Range. For example: For 2, 4, 7, 9, 10 and 14, the range is 14 − 2 = 12. The answer tells you Range.
Age 15Explain it to a 15-year-oldConnect it to the formula
Range measures the full observed spread using the two extreme values. The rule is Range = maximum − minimum. Its input values are Value 1, Value 2, Value 3, Value 4, Value 5, Value 6, and the main result is Range. For example: For 2, 4, 7, 9, 10 and 14, the range is 14 − 2 = 12.
CollegeExplain it at college levelState the model precisely
This calculator evaluates the stated data range relation over the valid real-number domain stated below. The implemented relation is Range = maximum − minimum, evaluated from Value 1, Value 2, Value 3, Value 4, Value 5, Value 6 to produce Range. Range measures the full observed spread using the two extreme values. Range is sensitive to outliers and does not describe how values are distributed between the extremes.
Inputs and valid domain
- Value 1 must be a finite real number.
- Value 2 must be a finite real number.
- Value 3 must be a finite real number.
- Value 4 must be a finite real number.
- Value 5 must be a finite real number.
- Value 6 must be a finite real number.
Important boundary: Range is sensitive to outliers and does not describe how values are distributed between the extremes.
The formula
Range = maximum − minimum
How the calculator works through it
It substitutes Value 1, Value 2, Value 3, Value 4, Value 5, Value 6 into the formula and exposes every numerical step above. The main output is Range, accompanied by Minimum, Maximum.
Read the result correctly
The Range is the direct answer to “find the minimum, maximum and range of six entered observations.” Read it with the units shown beside the inputs; a sign, angle, percentage or rate changes what the number means.
A worked check
For 2, 4, 7, 9, 10 and 14, the range is 14 − 2 = 12.
Where this model stops being reliable
Range is sensitive to outliers and does not describe how values are distributed between the extremes.
Learn it by changing one value
Begin with the worked example, then change one value while keeping the others fixed. Compare the new result and calculation steps to identify which part of the formula changed.
Dictionary terms behind this calculator
Before studying the codeWhat you should know firstUse the calculator immediately, or check the foundations before reading the implementation.
These foundations help you understand why Data range works. They never block the calculator, and “optional” means useful context rather than a hidden requirement.
Hard requirements
- Reading formulas and substituting values
Data range uses Range = maximum − minimum. You need to recognise what each side represents before substituting the stated inputs or rearranging the relationship.
Review this foundation about 4 min
Strong support
- Averages and representative values
Representative values help you judge what the Data range inputs summarise and what the result can legitimately describe.
Review this foundation about 5 min
Optional enrichment
- Spread and measurement variation
Variation is not always part of the Data range formula, but it helps you judge how stable a reported result may be.
Review this foundation about 6 min
Mathematics → algorithm → program
Implement this calculation in code
These are direct reference implementations of the calculator's principal relationship and first output. They run locally and include a small known-answer check where the language supports it.
Algorithm
- Read Value 1, Value 2, Value 3, Value 4, Value 5, Value 6.
- Evaluate the principal relationship: Range = maximum − minimum.
- Return Range and check the domain conditions described above.
Python
from math import *
def data_range(v1, v2, v3, v4, v5, v6) -> float:
return (max(max(max(v1, v2), max(v3, v4)), max(v5, v6)) - min(min(min(v1, v2), min(v3, v4)), min(v5, v6)))
assert abs(data_range(2, 4, 7, 9, 10, 14) - 12) < 1e-6 * max(1.0, abs(12))
C
#include <assert.h>
#include <math.h>
double data_range(double v1, double v2, double v3, double v4, double v5, double v6) {
return (fmax(fmax(fmax(v1, v2), fmax(v3, v4)), fmax(v5, v6)) - fmin(fmin(fmin(v1, v2), fmin(v3, v4)), fmin(v5, v6)));
}
int main(void) {
const double expected = 12;
const double actual = data_range(2, 4, 7, 9, 10, 14);
assert(fabs(actual - expected) < 1e-6 * fmax(1.0, fabs(expected)));
}
C++
#include <cassert>
#include <cmath>
#include <numbers>
double data_range(double v1, double v2, double v3, double v4, double v5, double v6) {
return (std::fmax(std::fmax(std::fmax(v1, v2), std::fmax(v3, v4)), std::fmax(v5, v6)) - std::fmin(std::fmin(std::fmin(v1, v2), std::fmin(v3, v4)), std::fmin(v5, v6)));
}
int main() {
constexpr double expected = 12;
const double actual = data_range(2, 4, 7, 9, 10, 14);
assert(std::fabs(actual - expected) < 1e-6 * std::fmax(1.0, std::fabs(expected)));
}
Linux x86-64 assembly
x86-64 NASM · System V ABI · Linux · SSE2 with libm where required
; double data_range(double v1, double v2, double v3, double v4, double v5, double v6)
; Linux x86-64 NASM · System V ABI · first eight doubles in xmm0–xmm7
extern fmax
extern fmin
global data_range
section .text
data_range:
push rbp
mov rbp, rsp
sub rsp, 144
movsd [rbp-8], xmm0
movsd [rbp-16], xmm1
movsd [rbp-24], xmm2
movsd [rbp-32], xmm3
movsd [rbp-40], xmm4
movsd [rbp-48], xmm5
movsd xmm0, [rbp-8]
movsd xmm1, [rbp-16]
call fmax wrt ..plt
movsd [rbp-80], xmm0
movsd xmm0, [rbp-24]
movsd xmm1, [rbp-32]
call fmax wrt ..plt
movsd [rbp-88], xmm0
movsd xmm0, [rbp-80]
movsd xmm1, [rbp-88]
call fmax wrt ..plt
movsd [rbp-72], xmm0
movsd xmm0, [rbp-40]
movsd xmm1, [rbp-48]
call fmax wrt ..plt
movsd [rbp-96], xmm0
movsd xmm0, [rbp-72]
movsd xmm1, [rbp-96]
call fmax wrt ..plt
movsd [rbp-64], xmm0
movsd xmm0, [rbp-8]
movsd xmm1, [rbp-16]
call fmin wrt ..plt
movsd [rbp-120], xmm0
movsd xmm0, [rbp-24]
movsd xmm1, [rbp-32]
call fmin wrt ..plt
movsd [rbp-128], xmm0
movsd xmm0, [rbp-120]
movsd xmm1, [rbp-128]
call fmin wrt ..plt
movsd [rbp-112], xmm0
movsd xmm0, [rbp-40]
movsd xmm1, [rbp-48]
call fmin wrt ..plt
movsd [rbp-136], xmm0
movsd xmm0, [rbp-112]
movsd xmm1, [rbp-136]
call fmin wrt ..plt
movsd [rbp-104], xmm0
movsd xmm0, [rbp-64]
subsd xmm0, [rbp-104]
movsd [rbp-56], xmm0
movsd xmm0, [rbp-56]
leave
ret
MATLAB
function result = data_range(v1, v2, v3, v4, v5, v6)
result = (max(max(max(v1, v2), max(v3, v4)), max(v5, v6)) - min(min(min(v1, v2), min(v3, v4)), min(v5, v6)));
end
Wolfram Language
ClearAll[mwCalculate];
mwCalculate[v1_, v2_, v3_, v4_, v5_, v6_] := (Max[Max[Max[v1, v2], Max[v3, v4]], Max[v5, v6]] - Min[Min[Min[v1, v2], Min[v3, v4]], Min[v5, v6]]);
Continue in mathematical software
The downloaded file includes your current inputs and first calculated result. It is created locally.
Floating-point answers can differ slightly by language, compiler and processor. Compare within a suitable tolerance rather than assuming every decimal representation will be identical.
Supporting sourcesAcademic referencesPrimary standards, textbooks and complete citations
Standards, reading and academic references
Use the calculator as the worked interaction, then consult the primary standards and academic textbooks listed below. MW SysArc links to the original sources; the explanation on this page is original and does not reproduce them.
Introductory Statistics 2e
Read the free OpenStax statistics textbookCite this book
- APA 7
- Illowsky, B., & Dean, S. (2023). Introductory statistics 2e. OpenStax. https://openstax.org/books/introductory-statistics-2e/pages/1-introduction
- MLA 9
- Illowsky, Barbara, and Susan Dean. Introductory Statistics 2e. OpenStax, 2023, https://openstax.org/books/introductory-statistics-2e/pages/1-introduction.
- Chicago author-date
- Illowsky, Barbara, and Susan Dean. 2023. Introductory Statistics 2e. Houston, TX: OpenStax. https://openstax.org/books/introductory-statistics-2e/pages/1-introduction.
OpenStax entries are free to read online. Follow the licence shown on each linked source before redistributing or adapting its content.
Reuse the page responsiblyCite this pageAPA, MLA, Chicago, Harvard, BibTeX and RIS
These formats cite this calculator page itself. They are separate from the academic references above, which support the mathematical method and terminology.
APA 7
MW SysArc. (2026, July 21). Range Calculator. MW SysArc Tools. https://math.mwsysarc.com/statistics/range-calculator
MLA 9
MW SysArc. “Range Calculator.” MW SysArc Tools, 21 July 2026, https://math.mwsysarc.com/statistics/range-calculator. Accessed 31 Aug. 2026.
Chicago 17
MW SysArc. “Range Calculator.” MW SysArc Tools. Published July 21, 2026. Accessed August 31, 2026. https://math.mwsysarc.com/statistics/range-calculator.
Harvard
MW SysArc (2026) ‘Range Calculator’, MW SysArc Tools. Published 21 July 2026. Available at: https://math.mwsysarc.com/statistics/range-calculator (Accessed: 31 August 2026).
BibTeX and RIS records
BibTeX
@misc{mwsysarc_data_range_2026,
author = {{MW SysArc}},
title = {Range Calculator},
howpublished = {MW SysArc Tools},
year = {2026},
url = {https://math.mwsysarc.com/statistics/range-calculator},
note = {Published July 21, 2026; accessed August 31, 2026}
}RIS
TY - ELEC
AU - MW SysArc
TI - Range Calculator
T2 - MW SysArc Tools
PY - 2026
DA - 2026-07-21
Y2 - 2026-08-31
UR - https://math.mwsysarc.com/statistics/range-calculator
N1 - Published July 21, 2026
ER -Clear answers
Frequently asked questions
What does the Data range do?
Find the minimum, maximum and range of six entered observations.
How does the Data range work?
The calculator applies Range = maximum − minimum. Range measures the full observed spread using the two extreme values.
What can I learn from the Data range?
It connects the mathematical rule to your chosen numbers and shows each calculation step. Change one input at a time to see how the result responds.
Does MW SysArc receive or store what I enter?
No. The calculation runs locally in your browser. MW SysArc does not receive or store your calculation inputs.
How should I use the result?
Use the steps to understand the method, then verify important school or professional work using the notation and rounding rules required in your setting.
Last reviewed . Calculations tested .