Mathematics · Statistics
Square-Root-of-Time Value-at-Risk Scale Calculator
Calculate scaled var magnitude from one-period var magnitude and square root of target period count.
Inputs and results stay in this browser. Change one value at a time to explore the relationship.
Calculation steps
- Use c=ab with one-period VaR magnitude=12 and square root of target period count=3.1622776601683795.
- scaled VaR magnitude=37.94733192202055.
Understand Square-Root-of-Time Value-at-Risk Scale
One idea, three depths
Choose how deeply to explain Square-Root-of-Time Value-at-Risk Scale
Square-Root-of-Time Value-at-Risk Scale: Calculate scaled var magnitude from one-period var magnitude and square root of target period count.
Age 5Explain it to a 5-year-oldStart with a picture
Imagine using Square-Root-of-Time Value-at-Risk Scale to answer this question: calculate scaled var magnitude from one-period var magnitude and square root of target period count? Enter one-period VaR magnitude and square root of target period count; the calculator shows scaled VaR magnitude. For example: one-period VaR magnitude=12 and square root of target period count=3.1622776601683795 produce scaled VaR magnitude=37.94733192202055. The answer tells you scaled VaR magnitude.
Age 15Explain it to a 15-year-oldConnect it to the formula
Under independent identically distributed normal-return assumptions, VaR scales by square root of time. This page evaluates the relationship directly. The rule is c=ab. Its input values are one-period VaR magnitude, square root of target period count, and the main result is scaled VaR magnitude. For example: one-period VaR magnitude=12 and square root of target period count=3.1622776601683795 produce scaled VaR magnitude=37.94733192202055.
CollegeExplain it at college levelState the model precisely
This calculator evaluates the stated square-root-of-time value-at-risk scale relation over the valid real-number domain stated below. The implemented relation is c=ab, evaluated from one-period VaR magnitude, square root of target period count to produce scaled VaR magnitude. Under independent identically distributed normal-return assumptions, VaR scales by square root of time. This page evaluates the relationship directly. Serial dependence, changing volatility, fat tails, and compounding can invalidate this approximation.
Inputs and valid domain
- one-period VaR magnitude must be a finite real number.
- square root of target period count must be a finite real number.
Important boundary: Serial dependence, changing volatility, fat tails, and compounding can invalidate this approximation.
The formula
c=ab
How the calculator works through it
It substitutes one-period VaR magnitude, square root of target period count into the formula and exposes every numerical step above. The main output is scaled VaR magnitude.
Read the result correctly
The scaled VaR magnitude is the direct answer to “calculate scaled var magnitude from one-period var magnitude and square root of target period count.” Read it with the units shown beside the inputs; a sign, angle, percentage or rate changes what the number means.
A worked check
one-period VaR magnitude=12 and square root of target period count=3.1622776601683795 produce scaled VaR magnitude=37.94733192202055.
Where this model stops being reliable
Serial dependence, changing volatility, fat tails, and compounding can invalidate this approximation.
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 Square-Root-of-Time Value-at-Risk Scale works. They never block the calculator, and “optional” means useful context rather than a hidden requirement.
Hard requirements
- Reading formulas and substituting values
Square-Root-of-Time Value-at-Risk Scale uses c=ab. 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 Square-Root-of-Time Value-at-Risk Scale 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 Square-Root-of-Time Value-at-Risk Scale 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 one-period VaR magnitude, square root of target period count.
- Evaluate the principal relationship: c=ab.
- Return scaled VaR magnitude and check the domain conditions described above.
Python
from math import *
def value_at_risk_horizon_scale_calculator(a, b) -> float:
return (a * b)
assert abs(value_at_risk_horizon_scale_calculator(12, 3.1622776601683795) - 37.94733192202055) < 1e-6 * max(1.0, abs(37.94733192202055))
C
#include <assert.h>
#include <math.h>
double value_at_risk_horizon_scale_calculator(double a, double b) {
return (a * b);
}
int main(void) {
const double expected = 37.94733192202055;
const double actual = value_at_risk_horizon_scale_calculator(12, 3.1622776601683795);
assert(fabs(actual - expected) < 1e-6 * fmax(1.0, fabs(expected)));
}
C++
#include <cassert>
#include <cmath>
#include <numbers>
double value_at_risk_horizon_scale_calculator(double a, double b) {
return (a * b);
}
int main() {
constexpr double expected = 37.94733192202055;
const double actual = value_at_risk_horizon_scale_calculator(12, 3.1622776601683795);
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 value_at_risk_horizon_scale_calculator(double a, double b)
; Linux x86-64 NASM · System V ABI · first eight doubles in xmm0–xmm7
global value_at_risk_horizon_scale_calculator
section .text
value_at_risk_horizon_scale_calculator:
push rbp
mov rbp, rsp
sub rsp, 32
movsd [rbp-8], xmm0
movsd [rbp-16], xmm1
movsd xmm0, [rbp-8]
mulsd xmm0, [rbp-16]
movsd [rbp-24], xmm0
movsd xmm0, [rbp-24]
leave
ret
MATLAB
function result = value_at_risk_horizon_scale_calculator(a, b)
result = (a * b);
end
Wolfram Language
ClearAll[mwCalculate];
mwCalculate[a_, b_] := (a * b);
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). Square-Root-of-Time Value-at-Risk Scale Calculator. MW SysArc Tools. https://math.mwsysarc.com/statistics/value-at-risk-horizon-scale-calculator
MLA 9
MW SysArc. “Square-Root-of-Time Value-at-Risk Scale Calculator.” MW SysArc Tools, 21 July 2026, https://math.mwsysarc.com/statistics/value-at-risk-horizon-scale-calculator. Accessed 31 Aug. 2026.
Chicago 17
MW SysArc. “Square-Root-of-Time Value-at-Risk Scale Calculator.” MW SysArc Tools. Published July 21, 2026. Accessed August 31, 2026. https://math.mwsysarc.com/statistics/value-at-risk-horizon-scale-calculator.
Harvard
MW SysArc (2026) ‘Square-Root-of-Time Value-at-Risk Scale Calculator’, MW SysArc Tools. Published 21 July 2026. Available at: https://math.mwsysarc.com/statistics/value-at-risk-horizon-scale-calculator (Accessed: 31 August 2026).
BibTeX and RIS records
BibTeX
@misc{mwsysarc_value_at_risk_horizon_scale_calculator_2026,
author = {{MW SysArc}},
title = {Square-Root-of-Time Value-at-Risk Scale Calculator},
howpublished = {MW SysArc Tools},
year = {2026},
url = {https://math.mwsysarc.com/statistics/value-at-risk-horizon-scale-calculator},
note = {Published July 21, 2026; accessed August 31, 2026}
}RIS
TY - ELEC
AU - MW SysArc
TI - Square-Root-of-Time Value-at-Risk Scale Calculator
T2 - MW SysArc Tools
PY - 2026
DA - 2026-07-21
Y2 - 2026-08-31
UR - https://math.mwsysarc.com/statistics/value-at-risk-horizon-scale-calculator
N1 - Published July 21, 2026
ER -Clear answers
Frequently asked questions
What does the Square-Root-of-Time Value-at-Risk Scale do?
Calculate scaled var magnitude from one-period var magnitude and square root of target period count.
How does the Square-Root-of-Time Value-at-Risk Scale work?
The calculator applies c=ab. Under independent identically distributed normal-return assumptions, VaR scales by square root of time. This page evaluates the relationship directly.
What can I learn from the Square-Root-of-Time Value-at-Risk Scale?
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 .