Calculate mass density, mass absorption coefficient, or attenuation coefficient from any 2 values with unit conversions in g/cm³, cm²/g, and cm⁻¹.
Mass Absorption Coefficient Formula
The calculator uses the relationship between attenuation coefficient, mass density, and mass absorption coefficient.
\mu_m = \frac{\mu}{\rho}\mu = \rho \mu_m
\rho = \frac{\mu}{\mu_m}- μm = mass absorption coefficient, usually in cm²/g, m²/kg, or in²/lb
- μ = attenuation coefficient, usually in cm⁻¹, m⁻¹, or in⁻¹
- ρ = mass density, usually in g/cm³, kg/m³, or lb/ft³
If you leave the mass absorption coefficient blank, the calculator divides the attenuation coefficient by the mass density.
If you leave the attenuation coefficient blank, the calculator multiplies mass density by the mass absorption coefficient.
If you leave the mass density blank, the calculator divides the attenuation coefficient by the mass absorption coefficient.
The calculator converts all entered values to base units first: g/cm³ for density, cm²/g for mass absorption coefficient, and cm⁻¹ for attenuation coefficient. It then converts the result back to the unit you selected.
Supported Unit Conversions
These are the main conversion factors used before applying the formula.
| Quantity | Entered Unit | Base Unit Conversion |
|---|---|---|
| Mass density | kg/m³ | 1 kg/m³ = 0.001 g/cm³ |
| Mass density | lb/ft³ | 1 lb/ft³ ≈ 0.0160185 g/cm³ |
| Mass absorption coefficient | m²/kg | 1 m²/kg = 0.1 cm²/g |
| Mass absorption coefficient | in²/lb | 1 in²/lb ≈ 0.00064516 cm²/g |
| Attenuation coefficient | m⁻¹ | 1 m⁻¹ = 0.01 cm⁻¹ |
| Attenuation coefficient | in⁻¹ | 1 in⁻¹ = 2.54 cm⁻¹ |
Typical Density Values for Reference
| Material | Approximate Density | Equivalent Density |
|---|---|---|
| Air at sea level | 0.001225 g/cm³ | 1.225 kg/m³ |
| Water | 1.00 g/cm³ | 1000 kg/m³ |
| Aluminum | 2.70 g/cm³ | 2700 kg/m³ |
| Iron | 7.87 g/cm³ | 7870 kg/m³ |
| Lead | 11.34 g/cm³ | 11340 kg/m³ |
Example Problems
Example 1: Calculate attenuation coefficient
You have a material with a density of 2.70 g/cm³ and a mass absorption coefficient of 0.075 cm²/g.
\mu = \rho \mu_m
\mu = 2.70 \times 0.075 = 0.2025\ \text{cm}^{-1}The attenuation coefficient is 0.2025 cm⁻¹.
Example 2: Calculate mass absorption coefficient with metric units
You have an attenuation coefficient of 15 m⁻¹ and a density of 1000 kg/m³.
First convert to base units:
- 15 m⁻¹ = 0.15 cm⁻¹
- 1000 kg/m³ = 1 g/cm³
\mu_m = \frac{0.15}{1} = 0.15\ \text{cm}^2/\text{g}Convert the result to m²/kg:
0.15\ \text{cm}^2/\text{g} \times 10 = 1.5\ \text{m}^2/\text{kg}The mass absorption coefficient is 1.5 m²/kg.
FAQ
What is the difference between attenuation coefficient and mass absorption coefficient?
The attenuation coefficient measures how strongly a material reduces radiation intensity per unit length. Its units are inverse length, such as cm⁻¹ or m⁻¹.
The mass absorption coefficient normalizes that effect by density. Its units are area per mass, such as cm²/g or m²/kg. This makes it easier to compare materials without the result depending directly on density.
Why does mass density affect the attenuation coefficient?
Higher density usually means more mass in the same volume. For the same mass absorption coefficient, a denser material gives a larger attenuation coefficient because the radiation interacts with more material per unit distance.
Can the mass absorption coefficient change?
Yes. The mass absorption coefficient depends on the material and the type or energy of the radiation. For example, a value for one photon energy should not be reused for a different energy unless the data source says it is valid.
