How to use the shielding calculator
Prepare the values for this calculation
Calculate narrow-beam monoenergetic photon attenuation using a user-entered linear attenuation coefficient, or solve the same exponential relation for thickness or coefficient. Use the formula below to check that it answers your question. Read the input units before transferring figures from a statement, measurement or dataset.
Enter and check each input
- Solve for: choose Transmitted intensity I, Thickness x, Linear attenuation coefficient μ. Match this selection to the data you enter.
- Length unit: choose centimeter (μ in cm⁻¹), inch (μ in in⁻¹). Match this selection to the data you enter.
- Incident intensity I₀: enter a value at least 1e-06. Use the unit named in the label or selected above. Do not leave this required field blank.
- Transmitted intensity I: enter a value at least 0. Use the unit named in the label or selected above. Do not leave this required field blank.
- Linear attenuation coefficient μ: enter a value at least 0. Use the unit named in the label or selected above. Do not leave this required field blank.
- Shield thickness x: enter a value at least 0. Use the unit named in the label or selected above. Do not leave this required field blank.
The input table gives a complete example. Keep units and time periods consistent across related fields.
Calculate and resolve any input error
Choose Calculate after entering the values. Changes also update the answer after a short pause. If an error appears, follow its message, correct the field and calculate again. Reset restores the example values.
Interpret the answer
Check Solved attenuation value first. With the unchanged example inputs, it is 13.53352832 intensity units. Compare the additional metrics with the primary result; each has its own label and unit.
Compare and keep a useful result
For a controlled comparison, keep every other example input unchanged and change Incident intensity I₀ from 100 to 110. The resulting Solved attenuation value is 14.88688116 intensity units. This illustrates the equation’s response to that input, rather than a forecast of real events.
Read the chart’s axis labels and data table. A scenario curve changes one stated input while holding the others fixed; it does not add external observations. Use Download graph to save an available chart as a PNG.
Use Copy result or Download CSV to keep the answer. Share tool shares the page address without placing your input values in the URL. Recheck inputs and assumptions before using the result for a decision.
Shielding Calculator formula
I=I₀e^(−μx). Thus x=ln(I₀/I)/μ and μ=ln(I₀/I)/x. This ideal narrow-beam model does not include buildup, scatter, broad-beam geometry, source spectrum or shielding-design requirements.
Inputs and units
| Input | Format / range | Example |
|---|---|---|
| Solve for | Select an option | Transmitted intensity I |
| Length unit | Select an option | centimeter (μ in cm⁻¹) |
| Incident intensity I₀ | minimum 1e-06 | 100 |
| Transmitted intensity I | minimum 0 | 10 |
| Linear attenuation coefficient μ | minimum 0 | 0.2 |
| Shield thickness x | minimum 0 | 10 |
Worked example
Using the example inputs above, the solved attenuation value is 13.53352832 intensity units.
- Solved attenuation value
- 13.53352832 intensity units
- Transmission
- 13.533528%
- Linear attenuation coefficient
- 0.2 cm⁻¹
- Thickness
- 10 cm
- Half-value layer
- 3.4657359 cm
- Tenth-value layer
- 11.51292546 cm
Results and assumptions
Ideal narrow-beam monoenergetic attenuation only. Real shielding may require energy-dependent coefficients, buildup/scatter, geometry, source terms and a qualified radiation-protection design.
Sources and method references
Fix an input or unexpected result
Incident intensity I₀ is required. Enter incident intensity i₀ using the format and bounds in the input table. Zero and an empty field are different: use zero only if it is allowed and represents your data.
If your answer differs from the example, choose Reset and compare every field, including selected units and options. Check percentage versus decimal entry and whether values describe the same period. Round only the final displayed answer when reproducing the formula.
If a discrepancy remains, report the calculator issue with the page address, non-sensitive example inputs, actual result, expected result and a reference for your calculation.