x ray attenuation calculator - Aaron Graves, PhDude Replica

Interactive X-Ray Attenuation Calculator

Estimate transmitted intensity through a material using the Beer–Lambert law:

I = I₀ × e^-μx

Material preset (optional quick fill for μ at ~100 keV)

Presets are approximate and energy-dependent. Use measured or tabulated values when accuracy matters.

Initial intensity, I₀ (any positive unit)

Material thickness, x (cm)

Linear attenuation coefficient, μ (cm⁻¹)

If left blank, calculator uses (μ/ρ × density) from the next two fields.

Mass attenuation coefficient, μ/ρ (cm²/g)

Density, ρ (g/cm³)

Target transmission (%) (optional)

What this X-ray attenuation calculator does

This tool estimates how much an X-ray beam is reduced as it passes through a material. You enter the initial intensity, material thickness, and attenuation data. The calculator returns transmitted intensity, percent transmission, percent attenuation, and shielding metrics such as half-value layer (HVL) and tenth-value layer (TVL).

The core equation

Beer–Lambert attenuation law

In narrow-beam geometry, attenuation is modeled by:

I = I₀e^-μx

I₀: initial intensity before material
I: transmitted intensity after thickness x
μ: linear attenuation coefficient (cm⁻¹)
x: material thickness (cm)

If you only have mass attenuation coefficient data, use:

μ = (μ/ρ) × ρ

How to use the calculator correctly

1) Pick your attenuation input method

Use either linear attenuation coefficient μ, or provide mass attenuation coefficient μ/ρ and density ρ. If both are provided, the calculator prioritizes linear μ.

2) Keep units consistent

Thickness in cm
Linear attenuation in cm⁻¹
Mass attenuation in cm²/g
Density in g/cm³

Intensity units can be anything (counts/s, mR/h, mGy/s), as long as input and output use the same unit.

3) Understand energy dependence

Attenuation coefficients strongly depend on photon energy and material composition. A coefficient valid at one energy may be inaccurate at another. For clinical, industrial, or regulatory decisions, use data that matches your beam spectrum and geometry.

Useful outputs explained

Transmission: fraction or percent that passes through.
Attenuation: percent removed from the incident beam.
HVL: thickness that cuts intensity to 50%.
TVL: thickness that cuts intensity to 10%.

Worked example

Suppose I₀ = 1000 (arbitrary units), μ = 0.53 cm⁻¹, and x = 2 cm:

I = 1000 × e^{-(0.53 × 2)} ≈ 346

So roughly 34.6% is transmitted and 65.4% is attenuated.

Where this calculator is helpful

Radiography and shielding concept checks
Lab planning and detector count-rate estimates
Education in medical physics and radiation science
Quick sanity checks before detailed Monte Carlo modeling

Limitations and assumptions

This is a simplified narrow-beam model. It does not directly account for broad-beam buildup, scatter return, beam hardening, spectral effects, geometry-specific detector response, or layered composite transport effects. Use more detailed methods for design-grade shielding calculations.