Calculator
Formula used
I = I0 × e-μx
μ = ln(I0 / I) / x
μ = ln(2) / HVL
μ = ln(10) / TVL
μ = (μ/ρ) × ρ
HVL = ln(2) / μ
TVL = ln(10) / μ
Mean free path = 1 / μ
The coefficient depends on the material and radiation energy. Keep units consistent before interpreting shielding thickness or transmission results.
How to use this calculator
- Choose the method that matches your available data.
- Select a length unit for thickness-based inputs and outputs.
- Enter measured intensity values, HVL, TVL, or mass attenuation data.
- Optionally add an evaluation thickness to estimate transmission at another depth.
- Submit the form to view the coefficient, shielding metrics, graph, and export options.
Example data table
| Material | Energy label | μ (1/cm) | Thickness (cm) | Transmission fraction | Attenuation (%) |
|---|---|---|---|---|---|
| Lead | Low-energy example | 1.250 | 1.0 | 0.2865 | 71.35 |
| Concrete | Shield wall example | 0.180 | 10.0 | 0.1653 | 83.47 |
| Aluminum | Beam filter example | 0.420 | 2.0 | 0.4317 | 56.83 |
| Water | Reference medium | 0.095 | 5.0 | 0.6219 | 37.81 |
| Steel | Industrial barrier example | 0.650 | 3.0 | 0.1423 | 85.77 |
These rows are illustrative examples only. Real attenuation values vary with beam energy, material composition, and measurement conditions.
Frequently asked questions
1. What does the linear attenuation coefficient represent?
It measures how quickly a beam loses intensity while passing through a material. Larger values mean stronger attenuation and less transmitted radiation for the same thickness.
2. Why does radiation energy matter?
Attenuation changes with photon or particle energy. A material may shield well at one energy and less effectively at another, so energy-specific data is important.
3. What is the difference between linear and mass attenuation coefficients?
The linear coefficient uses inverse length units. The mass attenuation coefficient normalizes attenuation by density, which helps compare materials before converting to a linear coefficient.
4. What is an HVL?
The half-value layer is the thickness required to reduce beam intensity to half its original value. It is directly related to the attenuation coefficient.
5. What is a TVL?
The tenth-value layer is the thickness required to reduce intensity to one-tenth of the initial value. It is useful for stronger shielding comparisons.
6. Can I use any length unit?
Yes. Choose millimeters, centimeters, or meters, then keep every thickness entry in that same unit. The coefficient output updates to the matching inverse unit.
7. Why is transmitted intensity not always required?
Some methods start from HVL, TVL, or mass attenuation data. In those cases, the coefficient can be found directly, then transmission can be estimated for any chosen thickness.
8. Are these results enough for final shielding design?
They are useful for estimation and learning, but final shielding design should also consider buildup, scattered radiation, beam spectrum, geometry, and accepted safety standards.