X-ray Absorption Calculator

X-rays are invisible rays that pass through objects. They lose energy as they travel through matter. This energy loss is called X-ray absorption. Scientists and engineers use it to study materials, check quality, or measure thickness.

We developed this X-ray absorption calculator so you can quickly find how much X-ray gets absorbed or passes through a material. It works in seconds and shows results in a clear, step-by-step format.

How X-ray Absorption Works

When an X-ray enters a material, some rays are absorbed, and some pass through. The amount that passes is called transmitted intensity. The process depends on:

• The material’s thickness
• The density of the material
• The type of material (its atomic structure)
• The energy of the X-ray

The main formula behind this calculation is based on the Beer–Lambert law.

X-ray Absorption Formula

There are two main ways to calculate X-ray absorption:

1. Using Linear Attenuation Coefficient

This method uses a property called the linear coefficient, represented as μ. It is in units of cm⁻¹.

The formula is:

I(x) = I₀ × e^(−μ × x)

Where:

• I(x) = transmitted intensity
• I₀ = initial intensity
• μ = linear attenuation coefficient
• x = thickness of the material

2. Using Mass Attenuation Coefficient

If you know the mass coefficient (μ/ρ) and the density (ρ), use this formula:

I(x) = I₀ × e^(−(μ/ρ) × ρ × x)

Where:

• μ/ρ = mass attenuation coefficient (cm²/g)
• ρ = material density (g/cm³)
• x = thickness (cm)

Both formulas give the same result. The choice depends on what data you have.

How to Use the X-ray Absorption Calculator

Using our online tool is easy. Just follow these steps:

1. Choose your calculation mode: Linear or Mass coefficient.
2. Enter the initial X-ray intensity (I₀).
3. If in linear mode, enter the linear coefficient (μ) and material thickness (x).
4. If in mass mode, enter the mass coefficient (μ/ρ), density (ρ), and thickness (x).
5. Click Calculate.

The calculator will show:

• Transmitted intensity
• Absorption percentage
• Transmission percentage
• Step-by-step explanation

You’ll instantly see how the X-ray intensity changes inside the material.

Example X-ray Absorption Calculation

Let’s say you have an X-ray beam with initial intensity I₀ = 100 units. It passes through a material 2 cm thick with a linear coefficient μ = 0.5 cm⁻¹.

Step 1: Apply the formula:

I(x) = 100 × e^(−0.5 × 2)

Step 2: Calculate exponent:

−μ × x = −0.5 × 2 = −1

Step 3: Calculate e^(−1):

e^(−1) ≈ 0.3679

Step 4: Find transmitted intensity:

I(x) = 100 × 0.3679 ≈ 36.79 units

Step 5: Calculate absorption percentage:

Absorption = ((100 − 36.79)/100) × 100 ≈ 63.21%

Step 6: Calculate transmission percentage:

Transmission = (36.79/100) × 100 ≈ 36.79%

You can do the same calculation with the mass coefficient mode if you know μ/ρ and ρ.

Why Use Our X-ray Absorption Calculator

Our tool saves you time and reduces errors. You don’t need to do complex math or use a scientific calculator. The step-by-step results show exactly how the calculation works.

This makes it perfect for:

• Students learning physics
• Engineers testing materials
• Labs measuring X-ray properties
• Anyone curious about X-ray absorption

It’s free, fast, and accurate.

Final Verdict

The X-ray absorption calculator is simple yet powerful. With it, you can quickly determine how X-rays behave in any material. You’ll see the transmitted intensity and understand absorption at a glance. It’s a must-have tool for education, research, and industry.

FAQs

What is X-ray absorption?

X-ray absorption is the loss of X-ray energy as it passes through a material.

What does the linear coefficient μ mean?

μ measures how easily a material absorbs X-rays per unit thickness.

Can I use the mass coefficient μ/ρ instead?

Yes. μ/ρ is useful when the material’s density is known.

What units should I use?

Linear μ in cm⁻¹, thickness in cm, μ/ρ in cm²/g, density in g/cm³.

Is the calculator accurate?

Yes. It uses standard physics formulas based on the Beer–Lambert law.