Mathematics · Mathematical Physics
Point-Source Illuminance Calculator
Calculate normal illuminance from source luminous intensity toward target and source-to-target distance.
Inputs and results stay in this browser. Change one value at a time to explore the relationship.
Calculation steps
- Use c=a/b² with source luminous intensity toward target=900 and source-to-target distance=3.
- normal illuminance=100.
Understand Point-Source Illuminance
One idea, three depths
Choose how deeply to explain Point-Source Illuminance
Point-Source Illuminance: Calculate normal illuminance from source luminous intensity toward target and source-to-target distance.
Age 5Explain it to a 5-year-oldStart with a picture
Imagine using Point-Source Illuminance to answer this question: calculate normal illuminance from source luminous intensity toward target and source-to-target distance? Enter source luminous intensity toward target and source-to-target distance; the calculator shows normal illuminance. For example: source luminous intensity toward target=900 and source-to-target distance=3 produce normal illuminance=100. The answer tells you normal illuminance.
Age 15Explain it to a 15-year-oldConnect it to the formula
For a point source striking a surface normally, illuminance equals luminous intensity divided by distance squared. This page evaluates the relationship directly. The rule is c=a/b². Its input values are source luminous intensity toward target, source-to-target distance, and the main result is normal illuminance. For example: source luminous intensity toward target=900 and source-to-target distance=3 produce normal illuminance=100.
CollegeExplain it at college levelState the model precisely
This calculator evaluates the stated point-source illuminance relation over the valid real-number domain stated below. The implemented relation is c=a/b², evaluated from source luminous intensity toward target, source-to-target distance to produce normal illuminance. For a point source striking a surface normally, illuminance equals luminous intensity divided by distance squared. This page evaluates the relationship directly. Oblique incidence requires a cosine factor, and the point-source approximation fails close to an extended luminaire.
Inputs and valid domain
- source luminous intensity toward target must be a finite real number.
- source-to-target distance must be a finite real number.
Important boundary: Oblique incidence requires a cosine factor, and the point-source approximation fails close to an extended luminaire.
The formula
c=a/b²
How the calculator works through it
It substitutes source luminous intensity toward target, source-to-target distance into the formula and exposes every numerical step above. The main output is normal illuminance.
Read the result correctly
The normal illuminance is the direct answer to “calculate normal illuminance from source luminous intensity toward target and source-to-target distance.” Read it with the units shown beside the inputs; a sign, angle, percentage or rate changes what the number means.
A worked check
source luminous intensity toward target=900 and source-to-target distance=3 produce normal illuminance=100.
Where this model stops being reliable
Oblique incidence requires a cosine factor, and the point-source approximation fails close to an extended luminaire.
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 Point-Source Illuminance works. They never block the calculator, and “optional” means useful context rather than a hidden requirement.
Hard requirements
- Reading formulas and substituting values
Point-Source Illuminance uses c=a/b². 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
- Ratios, units and dimensional meaning
Tracking ratios and units keeps the Point-Source Illuminance result physically interpretable instead of merely numerical.
Review this foundation about 5 min
Optional enrichment
- Vectors and physical direction
Vector language extends Point-Source Illuminance when magnitude and direction must be treated separately.
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 source luminous intensity toward target, source-to-target distance.
- Evaluate the principal relationship: c=a/b².
- Return normal illuminance and check the domain conditions described above.
Python
from math import *
def point_source_illuminance_calculator(a, b) -> float:
return (a / (b * b))
assert abs(point_source_illuminance_calculator(900, 3) - 100) < 1e-6 * max(1.0, abs(100))
C
#include <assert.h>
#include <math.h>
double point_source_illuminance_calculator(double a, double b) {
return (a / (b * b));
}
int main(void) {
const double expected = 100;
const double actual = point_source_illuminance_calculator(900, 3);
assert(fabs(actual - expected) < 1e-6 * fmax(1.0, fabs(expected)));
}
C++
#include <cassert>
#include <cmath>
#include <numbers>
double point_source_illuminance_calculator(double a, double b) {
return (a / (b * b));
}
int main() {
constexpr double expected = 100;
const double actual = point_source_illuminance_calculator(900, 3);
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 point_source_illuminance_calculator(double a, double b)
; Linux x86-64 NASM · System V ABI · first eight doubles in xmm0–xmm7
global point_source_illuminance_calculator
section .text
point_source_illuminance_calculator:
push rbp
mov rbp, rsp
sub rsp, 32
movsd [rbp-8], xmm0
movsd [rbp-16], xmm1
movsd xmm0, [rbp-16]
mulsd xmm0, [rbp-16]
movsd [rbp-32], xmm0
movsd xmm0, [rbp-8]
divsd xmm0, [rbp-32]
movsd [rbp-24], xmm0
movsd xmm0, [rbp-24]
leave
ret
MATLAB
function result = point_source_illuminance_calculator(a, b)
result = (a / (b * b));
end
Wolfram Language
ClearAll[mwCalculate];
mwCalculate[a_, b_] := (a / (b * 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.
University Physics Volume 3
Read OpenStax University Physics: Quantum MechanicsCite this book
- APA 7
- Ling, S. J., Sanny, J., & Moebs, W. (2016). University physics volume 3. OpenStax. https://openstax.org/books/university-physics-volume-3/pages/1-introduction
- MLA 9
- Ling, Samuel J., et al. University Physics Volume 3. OpenStax, 2016, https://openstax.org/books/university-physics-volume-3/pages/1-introduction.
- Chicago author-date
- Ling, Samuel J., Jeff Sanny, and William Moebs. 2016. University Physics Volume 3. Houston, TX: OpenStax. https://openstax.org/books/university-physics-volume-3/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). Point-Source Illuminance Calculator. MW SysArc Tools. https://math.mwsysarc.com/mathematical-physics/point-source-illuminance-calculator
MLA 9
MW SysArc. “Point-Source Illuminance Calculator.” MW SysArc Tools, 21 July 2026, https://math.mwsysarc.com/mathematical-physics/point-source-illuminance-calculator. Accessed 31 Aug. 2026.
Chicago 17
MW SysArc. “Point-Source Illuminance Calculator.” MW SysArc Tools. Published July 21, 2026. Accessed August 31, 2026. https://math.mwsysarc.com/mathematical-physics/point-source-illuminance-calculator.
Harvard
MW SysArc (2026) ‘Point-Source Illuminance Calculator’, MW SysArc Tools. Published 21 July 2026. Available at: https://math.mwsysarc.com/mathematical-physics/point-source-illuminance-calculator (Accessed: 31 August 2026).
BibTeX and RIS records
BibTeX
@misc{mwsysarc_point_source_illuminance_calculator_2026,
author = {{MW SysArc}},
title = {Point-Source Illuminance Calculator},
howpublished = {MW SysArc Tools},
year = {2026},
url = {https://math.mwsysarc.com/mathematical-physics/point-source-illuminance-calculator},
note = {Published July 21, 2026; accessed August 31, 2026}
}RIS
TY - ELEC
AU - MW SysArc
TI - Point-Source Illuminance Calculator
T2 - MW SysArc Tools
PY - 2026
DA - 2026-07-21
Y2 - 2026-08-31
UR - https://math.mwsysarc.com/mathematical-physics/point-source-illuminance-calculator
N1 - Published July 21, 2026
ER -Clear answers
Frequently asked questions
What does the Point-Source Illuminance do?
Calculate normal illuminance from source luminous intensity toward target and source-to-target distance.
How does the Point-Source Illuminance work?
The calculator applies c=a/b². For a point source striking a surface normally, illuminance equals luminous intensity divided by distance squared. This page evaluates the relationship directly.
What can I learn from the Point-Source Illuminance?
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 .