Calculator inputs
Saved scenarios and calculation history
Saved scenarios remain only in this browser. No database or remote service is used.
Formula used
Core absorbed-dose equations
- Dose from rate and time: D = Ḋ × t
- Dose rate: Ḋ = D ÷ t
- Exposure time: t = D ÷ Ḋ
- Energy and mass: D(Gy) = E(J) ÷ m(kg)
- Inverse square: Ḋ₂ = Ḋ₁(r₁/r₂)²
- Linear attenuation: D = D₀Be−μx
Layer, decay, and equivalent-dose equations
- Half-value layer: D = D₀(1/2)x/HVL
- Tenth-value layer: D = D₀(0.1)x/TVL
- Radioactive decay: Ḋ(t) = Ḋ₀(1/2)t/T½
- Equivalent dose: H = D × wR
- Cumulative dose: Dtotal = ΣDi
- Combined model: D = Ḋref × t × enabled correction factors
How to use this calculator
- Select the calculation mode that matches the quantity you know and the quantity you need.
- Enter numeric values without adding unit abbreviations inside number fields.
- Select a unit beside every value. Mixed units are converted internally before calculation.
- Enable optional background, distance, decay, shielding, integration, or uncertainty settings only when they are physically justified.
- Review the formula, substituted values, conversion steps, warnings, and assumptions shown with the result.
- Save, copy, print, or export the result when a record is useful.
Understanding millirad calculations
Absorbed dose and the millirad
Absorbed dose describes energy deposited by ionizing radiation in a specified mass. The gray is the SI unit and equals one joule per kilogram. The rad is a conventional absorbed-dose unit. One rad equals 0.01 gray, and one millirad equals one thousandth of a rad. Therefore, one millirad equals 0.00001 gray, 0.01 milligray, or 10 microgray. A calculator should always preserve the distinction between absorbed dose and other radiation quantities because similar-looking units can describe different physical concepts.
Choosing the correct equation
Use the dose-rate and time mode when a measured or specified dose rate remains approximately constant during an exposure. Use the inverse calculation when total dose or duration is unknown. The energy-and-mass mode applies when deposited energy and absorbing mass are directly known. Distance adjustment uses a point-source inverse-square approximation. It can fail close to an extended source, around complex geometry, or where scattering is important. Shielding calculations require coefficients or layer values that match radiation type, energy, material, and geometry.
Decay, shielding, and combined models
Radioactive decay reduces source activity and often reduces dose rate proportionally when all other conditions remain unchanged. A later exposure may require integration when its duration is not negligible compared with the half-life. Linear attenuation represents narrow-beam exponential transmission, while half-value and tenth-value layers offer convenient repeated-reduction forms. A buildup factor may approximate scattered radiation reaching the point of interest, but it should not be entered without reliable supporting data. The combined mode multiplies enabled factors, so every factor must describe the same physical scenario.
Interpreting equivalent dose
Equivalent dose applies a radiation weighting factor to absorbed dose. Its units are sievert or rem rather than gray or rad. The weighting factor is not a universal conversion constant. It depends on the radiation category, energy range, and governing standard. This calculator requires the user to enter the factor explicitly because automatic selection could encourage unsafe assumptions. Tissue weighting, effective dose, organ dose, and patient-specific risk are outside this simplified calculation.
Using results responsibly
Input quality controls result quality. Confirm calibrated measurements, unit consistency, valid geometry, source conditions, shielding data, and exposure time. Negative net dose after background subtraction usually indicates measurement uncertainty, mismatched conditions, or an incorrect background assumption. Very large or tiny outputs should be checked using scientific notation and an independent method. The calculator is suitable for education, planning discussions, and transparent arithmetic, but it cannot certify safety or compliance. Qualified radiation-safety or medical-physics personnel should review consequential decisions.
Unit conversion reference
| Unit | Meaning | Equivalent in gray | Equivalent in mrad |
|---|---|---|---|
| 1 Gy | One joule per kilogram | 1 Gy | 100,000 mrad |
| 1 mGy | One thousandth gray | 0.001 Gy | 100 mrad |
| 1 µGy | One millionth gray | 0.000001 Gy | 0.1 mrad |
| 1 rad | Conventional absorbed-dose unit | 0.01 Gy | 1,000 mrad |
| 1 mrad | One thousandth rad | 0.00001 Gy | 1 mrad |
| 1 cGy | One hundredth gray | 0.01 Gy | 1,000 mrad |
| 1 J/kg | Energy per unit mass | 1 Gy | 100,000 mrad |
Validation, assumptions, and safeguards
- Zero mass is rejected because energy divided by zero is undefined.
- Zero reference or new distance is rejected in inverse-square calculations.
- Negative time, mass, distance, energy, thickness, and dose-rate values are rejected.
- Shielding transmission percentages must remain between zero and one hundred.
- Half-life, half-value layer, and tenth-value layer must be greater than zero.
- Every unit is checked against a fixed allowlist before calculation.
- Scientific notation is supported in standard number fields.
- Displayed precision is limited to fourteen decimal places.
- CSRF protection is included for form submissions.
- All submitted text is escaped before display.
- Cumulative exposure entries are limited to one hundred rows.
- Activity units are not treated as absorbed-dose units.
- Roentgen is not converted to mrad with a universal factor.
- mrad is never silently treated as mrem.
- The equivalent-dose mode requires an explicit weighting factor.
- Combined calculations display each multiplier separately.
- Background subtraction warns when the resulting net dose is negative.
- Local history can be cleared without contacting a server.
Glossary
- Absorbed dose
- Radiation energy deposited per unit mass.
- Gray
- SI absorbed-dose unit equal to one joule per kilogram.
- Rad
- Conventional absorbed-dose unit equal to 0.01 gray.
- Millirad
- One thousandth of a rad.
- Dose rate
- Absorbed dose accumulated per unit time.
- Equivalent dose
- Absorbed dose modified by a radiation weighting factor.
- Half-life
- Time required for a radioactive quantity to decrease by half.
- Linear attenuation coefficient
- Exponential attenuation constant per unit material thickness.
- Half-value layer
- Material thickness reducing intensity to one half under stated conditions.
- Tenth-value layer
- Material thickness reducing intensity to one tenth under stated conditions.
- Buildup factor
- A model factor accounting for scattered radiation in some shielding calculations.
- Point source
- An approximation where source dimensions are small relative to distance.
- Background subtraction
- Removal of a separately measured background contribution.
- Uncertainty
- A quantified range associated with measurement or model limitations.
- Transmission
- The fraction of radiation remaining after a barrier or process.
- ALARA
- A radiation-protection principle emphasizing reasonably minimized exposure.
Frequently asked questions
Is one mrad equal to one mrem?
No universal equality applies. mrad is absorbed dose, while mrem is equivalent dose. A weighting factor and applicable radiation-protection convention are required.
Can curies or becquerels be converted directly to mrad?
No. Activity alone does not determine absorbed dose. Radiation yield, energy, geometry, distance, duration, absorption, shielding, and other factors are needed.
Can milliroentgen be converted directly to millirad?
Not with one universal factor. Exposure in air and absorbed dose in a material are different quantities. Conversion depends on radiation energy and absorbing medium.
Why does distance use a squared ratio?
For an ideal point source spreading uniformly, radiation is distributed over an area that grows with the square of distance. Real sources may not satisfy this approximation.
Why are shielding coefficients not built in?
Attenuation data depend strongly on radiation type, energy, material composition, density, geometry, and scatter conditions. Unverified presets could produce misleading results.
When should decay be integrated over exposure time?
Integration is useful when the exposure duration is not negligible compared with the half-life. For very short exposure durations, using the starting rate is often numerically similar.
What does a negative background-subtracted dose mean?
It usually means the measured background contribution exceeds the gross result. Review uncertainty, timing, detector response, and whether both measurements are comparable.
Does the calculator establish a safe exposure level?
No. It calculates quantities from entered values. Safety limits and compliance decisions require applicable rules, calibrated instruments, documented procedures, and qualified review.
Can this be used for radiation therapy?
No. Treatment planning and clinical dosimetry require validated medical systems, commissioned equipment, patient-specific information, and qualified medical-physics oversight.
Where is calculation history stored?
History is stored locally in the current browser using localStorage. It is not sent to a database by this application.
Technical implementation notes
This single PHP file is designed for PHP 8.0 and later. It uses strict typing, server-side validation, allowlisted units, CSRF protection, escaped output, responsive CSS, browser-local history, client-side CSV and JSON exports, and a dependency-free canvas chart. No database connection is required. No external assets are loaded, which reduces deployment complexity and avoids failures caused by unavailable libraries or blocked content-delivery networks.
For deployment, save the file with a .php extension on a PHP-enabled server. Confirm that sessions are enabled and that the server can write session data. The calculator does not write user files on the server. Local scenario storage is handled by the browser. Production deployments should still use HTTPS, secure session-cookie settings, routine server updates, error logging, and standard web-application hardening.