X-Ray Attenuation Calculator
Through 6.93 cm of tissue with μ = 0.2 cm⁻¹, a beam of intensity 100 falls to 25.0074: two half-value layers of 3.47 cm each.
Soft tissue about 0.2 cm⁻¹, bone about 0.5 cm⁻¹ near 60 keV.
25.0073601112094
Full answer, then cut to fewer decimals (not rounded):
- 25.0073601112094
- 25.007360111209
- 25.00736011120
- 25.0073601112
- 25.007360111
- 25.00736011
- 25.0073601
- 25.007360
- 25.00736
- 25.0073
- 25.007
- 25.00
- 25.0
- Transmission I/I₀
- 25.00736011 %
- Half-value layer ln 2/μ
- 3.465735903 cm
- Tenth-value layer ln 10/μ
- 11.51292546 cm
Step-by-step solution
- Convert units: μ = 0.2 cm⁻¹ = 20 m⁻¹; x = 6.93 cm = 0.0693 m
- I = I₀ × e^(−μ × x)
- I = 100 × e^(−20 × 0.0693)
- I = 25.00736011
X-Ray Attenuation Formula
I = I₀ e^(−μx)
μ linear attenuation coefficient; HVL = ln 2/μ; TVL = ln 10/μ
Worked Example
A beam through 6.93 cm of soft tissue with μ = 0.2 cm⁻¹:
- Convert units: μ = 0.2 cm⁻¹ = 20 m⁻¹; x = 6.93 cm = 0.0693 m
- I = I₀ × e^(−μ × x)
- I = 100 × e^(−20 × 0.0693)
- I = 25.00736011
Half-value layer ln 2/μ: 3.465735903 cm · Tenth-value layer ln 10/μ: 11.51292546 cm
GATE tip
CT numbers come from μ: HU = 1000(μ − μ_water)/μ_water, giving water 0, air −1000 and dense bone about +1000.
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Doppler Ultrasound Calculator
Δf = 2 f₀ v cos θ / c
c ≈ 1540 m/s in soft tissue; θ the angle between beam and flow
Example: A 5 MHz probe aligned with blood moving at 20 cm/s: Doppler shift Δf = 1298.7 Hz.
Frequently asked questions
What is the half-value layer?
The thickness that halves the beam: HVL = 0.693/μ. It describes beam quality; harder (higher energy) beams have larger HVLs.
What about the mass attenuation coefficient?
μ/ρ (cm²/g) removes the density dependence; multiply by the density to get μ for a given material.
Sources
- The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
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APA
Scientific Converters. (2026, October 15). X-Ray Attenuation Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/x-ray-attenuation-calculator/
IEEE
Scientific Converters, "X-Ray Attenuation Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/x-ray-attenuation-calculator/