Mathematics · Mathematical Physics

Point-Source Radiation Dose Rate Calculator

Calculate idealized dose rate from source dose-rate distance-squared coefficient and source-to-point distance.

Runs locally
Your numbers

Inputs and results stay in this browser. Change one value at a time to explore the relationship.

Your inputCalculatedPassed forward in chains
idealized dose rate15

Calculation steps

  1. Use c=a/b² with source dose-rate distance-squared coefficient=240 and source-to-point distance=4.
  2. idealized dose rate=15.

Understand Point-Source Radiation Dose Rate

One idea, three depths

Choose how deeply to explain Point-Source Radiation Dose Rate

Point-Source Radiation Dose Rate: Calculate idealized dose rate from source dose-rate distance-squared coefficient and source-to-point distance.

Age 5Explain it to a 5-year-oldStart with a picture

Imagine using Point-Source Radiation Dose Rate to answer this question: calculate idealized dose rate from source dose-rate distance-squared coefficient and source-to-point distance? Enter source dose-rate distance-squared coefficient and source-to-point distance; the calculator shows idealized dose rate. For example: source dose-rate distance-squared coefficient=240 and source-to-point distance=4 produce idealized dose rate=15. The answer tells you idealized dose rate.

Age 15Explain it to a 15-year-oldConnect it to the formula

An unshielded isotropic point-source dose rate equals its distance-squared coefficient divided by distance squared. This page evaluates the relationship directly. The rule is c=a/b². Its input values are source dose-rate distance-squared coefficient, source-to-point distance, and the main result is idealized dose rate. For example: source dose-rate distance-squared coefficient=240 and source-to-point distance=4 produce idealized dose rate=15.

CollegeExplain it at college levelState the model precisely

This calculator evaluates the stated point-source radiation dose rate relation over the valid real-number domain stated below. The implemented relation is c=a/b², evaluated from source dose-rate distance-squared coefficient, source-to-point distance to produce idealized dose rate. An unshielded isotropic point-source dose rate equals its distance-squared coefficient divided by distance squared. This page evaluates the relationship directly. Source extent, buildup, attenuation, scatter, shielding, occupancy, energy spectrum, and near-field geometry invalidate the simple model.

Inputs and valid domain

  • source dose-rate distance-squared coefficient must be a finite real number.
  • source-to-point distance must be a finite real number.

Important boundary: Source extent, buildup, attenuation, scatter, shielding, occupancy, energy spectrum, and near-field geometry invalidate the simple model.

The formula

c=a/b²

How the calculator works through it

It substitutes source dose-rate distance-squared coefficient, source-to-point distance into the formula and exposes every numerical step above. The main output is idealized dose rate.

Read the result correctly

The idealized dose rate is the direct answer to “calculate idealized dose rate from source dose-rate distance-squared coefficient and source-to-point 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 dose-rate distance-squared coefficient=240 and source-to-point distance=4 produce idealized dose rate=15.

Where this model stops being reliable

Source extent, buildup, attenuation, scatter, shielding, occupancy, energy spectrum, and near-field geometry invalidate the simple model.

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 Radiation Dose Rate 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 Radiation Dose Rate 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 Radiation Dose Rate result physically interpretable instead of merely numerical.

    Review this foundation about 5 min

Optional enrichment

Learn the missing foundationsI already know these — show the code

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

  1. Read source dose-rate distance-squared coefficient, source-to-point distance.
  2. Evaluate the principal relationship: c=a/b².
  3. Return idealized dose rate and check the domain conditions described above.
Python
            from math import *

def point_source_radiation_dose_rate_calculator(a, b) -> float:
    return (a / (b * b))

assert abs(point_source_radiation_dose_rate_calculator(240, 4) - 15) < 1e-6 * max(1.0, abs(15))
          
Current calculator valuesUpdates when you change an input above.
              
            
C
            #include <assert.h>
#include <math.h>

double point_source_radiation_dose_rate_calculator(double a, double b) {
    return (a / (b * b));
}

int main(void) {
    const double expected = 15;
    const double actual = point_source_radiation_dose_rate_calculator(240, 4);
    assert(fabs(actual - expected) < 1e-6 * fmax(1.0, fabs(expected)));
}
          
Current calculator valuesUpdates when you change an input above.
              
            
C++
            #include <cassert>
#include <cmath>
#include <numbers>

double point_source_radiation_dose_rate_calculator(double a, double b) {
    return (a / (b * b));
}

int main() {
    constexpr double expected = 15;
    const double actual = point_source_radiation_dose_rate_calculator(240, 4);
    assert(std::fabs(actual - expected) < 1e-6 * std::fmax(1.0, std::fabs(expected)));
}
          
Current calculator valuesUpdates when you change an input above.
              
            
Linux x86-64 assembly

x86-64 NASM · System V ABI · Linux · SSE2 with libm where required

            ; double point_source_radiation_dose_rate_calculator(double a, double b)
; Linux x86-64 NASM · System V ABI · first eight doubles in xmm0–xmm7
global point_source_radiation_dose_rate_calculator
section .text

point_source_radiation_dose_rate_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
          
Current calculator valuesUpdates when you change an input above.
              
            
MATLAB
            function result = point_source_radiation_dose_rate_calculator(a, b)
    result = (a / (b * b));
end
          
Current calculator valuesUpdates when you change an input above.
              
            
Wolfram Language
            ClearAll[mwCalculate];
mwCalculate[a_, b_] := (a / (b * b));
          
Current calculator valuesUpdates when you change an input above.
              
            

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 Mechanics
Cite 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 Radiation Dose Rate Calculator. MW SysArc Tools. https://math.mwsysarc.com/mathematical-physics/point-source-radiation-dose-rate-calculator

MLA 9

MW SysArc. “Point-Source Radiation Dose Rate Calculator.” MW SysArc Tools, 21 July 2026, https://math.mwsysarc.com/mathematical-physics/point-source-radiation-dose-rate-calculator. Accessed 31 Aug. 2026.

Chicago 17

MW SysArc. “Point-Source Radiation Dose Rate Calculator.” MW SysArc Tools. Published July 21, 2026. Accessed August 31, 2026. https://math.mwsysarc.com/mathematical-physics/point-source-radiation-dose-rate-calculator.

Harvard

MW SysArc (2026) ‘Point-Source Radiation Dose Rate Calculator’, MW SysArc Tools. Published 21 July 2026. Available at: https://math.mwsysarc.com/mathematical-physics/point-source-radiation-dose-rate-calculator (Accessed: 31 August 2026).

BibTeX and RIS records

BibTeX

@misc{mwsysarc_point_source_radiation_dose_rate_calculator_2026,
  author = {{MW SysArc}},
  title = {Point-Source Radiation Dose Rate Calculator},
  howpublished = {MW SysArc Tools},
  year = {2026},
  url = {https://math.mwsysarc.com/mathematical-physics/point-source-radiation-dose-rate-calculator},
  note = {Published July 21, 2026; accessed August 31, 2026}
}

RIS

TY  - ELEC
AU  - MW SysArc
TI  - Point-Source Radiation Dose Rate Calculator
T2  - MW SysArc Tools
PY  - 2026
DA  - 2026-07-21
Y2  - 2026-08-31
UR  - https://math.mwsysarc.com/mathematical-physics/point-source-radiation-dose-rate-calculator
N1  - Published July 21, 2026
ER  -

Clear answers

Frequently asked questions

What does the Point-Source Radiation Dose Rate do?

Calculate idealized dose rate from source dose-rate distance-squared coefficient and source-to-point distance.

How does the Point-Source Radiation Dose Rate work?

The calculator applies c=a/b². An unshielded isotropic point-source dose rate equals its distance-squared coefficient divided by distance squared. This page evaluates the relationship directly.

What can I learn from the Point-Source Radiation Dose Rate?

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 .

MW SysArc Certified