🛠️ Tools

Radiography Calculators

Free interactive calculators for radiologic technology students and professionals. Covering the most commonly used formulas in clinical radiography, nuclear medicine, CT dosimetry, and ARRT exam prep. Adjust any value — results update instantly.

ARRT Prep Clinical Reference Physics Formulas Nuclear Medicine CT Dosimetry Instant Results

These interactive tools are designed to help you quickly work through the equations you'll encounter most often in radiography — from the inverse square law for radiation safety to the density maintenance formula for technique adjustment. Each calculator includes the formula reference and real-time output as you change the inputs.

📐 Inverse Square Law

I₁ / I₂ = (D₂ / D₁)²

Calculate how radiation intensity changes with distance from the source. Essential for radiation safety and technique adjustment.

Initial Intensity (I₁)

Initial Distance (D₁)

Final Distance (D₂)

30.86 mRI₂ = 100 × (40/72)² = 30.86

⚡ mAs Calculator

mAs = mA × Time (s)

Find any unknown in the exposure equation. Adjust mA or exposure time while keeping mAs constant.

Find

Time (s)

10.00 mAsmAs = 200 × 0.05 = 10.00

🔺 15% Rule (kVp)

kVp₂ = kVp₁ × 1.15 | kVp₂ = kVp₁ × 0.85

Increasing kVp by 15% doubles exposure density; decreasing by 15% halves it. Used to adjust contrast while maintaining image density.

Current kVp

Action

92.00 kVp80 × 1.15 = 92.0 kVp — doubles density

📏 Density Maintenance

mAs₂ = mAs₁ × (SID₂ / SID₁)²

Adjust mAs when changing SID to maintain consistent image density. Also known as the exposure maintenance formula.

Original mAs (mAs₁)

Original SID₁

New SID₂

12.96 mAs4.0 × (72/40)² = 12.96 mAs

🔍 Magnification Factor

MF = SID / SOD | Image Size = Object Size × MF

Calculate how much an object is magnified on the radiographic image based on SID and object-to-detector distance.

SID (cm)

SOD (cm)

Object Size (cm)

MF = 1.18×MF = 100/85 = 1.18× — image is 18% larger

⊞ Grid Ratio

Grid Ratio = h / D

Calculate grid ratio from lead strip height (h) and interspace distance (D). Higher ratios improve scatter cleanup but require more mAs.

Strip Height, h (mm)

Interspace, D (mm)

5:1 grid ratioh/D = 4.0/0.8 = 5:1

🔥 Heat Units

HU = kVp × mAs × Phase Factor

Estimate X-ray tube heat loading. Critical for avoiding tube damage during rapid-sequence or high-exposure procedures.

Generator Phase Factor

kVp

Time (s)

3,200 HU80 × (400×0.1) × 1.0 = 3,200 HU

⛔ Half-Value Layer

I = I₀ × (½)ⁿ | n = thickness / HVL

Calculate radiation attenuation through shielding material. Enter any three values to find the fourth.

Initial I₀

HVL (mm)

Thickness (mm)

Transmitted I

12.50 mR transmittedI = 100 × 0.5^(7.5/2.5) = 12.50 mR

☢️ Radioactive Half-Life

A = A₀ × 0.5^{t / T_½}

Calculate remaining activity of a radiopharmaceutical after a given decay time. Select a common isotope for preset half-life, or enter a custom value.

Isotope

Initial Activity (A₀)

Half-Life

Elapsed Time

Time Unit

25.00 mCi remainingA = 100 × 0.5^(12/6.01) = 25.00 mCi (2 half-lives)

🔄 Effective Half-Life

1/T_e = 1/T_p + 1/T_b

Calculate the effective half-life of a radiopharmaceutical from its physical and biological half-lives. Essential for nuclear medicine dosimetry.

Common Radioisotope

Physical Half-Life (Tₚ)

Biological Half-Life (Tᵦ)

3.43 hoursTₑ = (6.01 × 8) / (6.01 + 8) = 3.43 h

📉 Decay Constant & Activity

λ = ln(2) / T_½ | A = A₀ × e^−λt

Calculate the decay constant (λ) from half-life, or determine activity at any time using the exponential decay formula.

Half-Life

Time Elapsed

Initial Activity (A₀)

Time Unit

λ = 0.1153 h⁻¹ | A = 70.71 mCiλ = ln(2)/6.01 = 0.1153 h⁻¹ | A = 100 × e^(−0.1153×3) = 70.71 mCi

🔲 Geometric Unsharpness

U_g = (FS × OID) / SID

Calculate image blur from focal spot size and geometric factors. Essential for understanding spatial resolution in radiography — a must-know for the ARRT exam.

Focal Spot (FS, mm)

FS (custom mm)

SID (cm)

OID (cm)

0.10 mm unsharpnessUg = (1.0 × 10) / 100 = 0.10 mm

🎯 Subject Contrast

C = (I_max − I_min) / I_max

Calculate radiographic subject contrast from differential absorption. Higher contrast means greater visibility of detail — influenced by kVp, tissue density, and pathology.

Max Intensity (I_max)

Min Intensity (I_min)

0.55 (55% contrast)C = (100 − 45) / 100 = 0.55 (55%)

⚖️ Reciprocity Law

mA₁ × t₁ = mA₂ × t₂

Convert exposure technique when changing mA or exposure time while maintaining constant mAs. The product of mA and time stays equal regardless of which variable changes.

Find

Original mA

Original Time (s)

New mA

0.025 secondst₂ = (200 × 0.05) / 400 = 0.025 s

💡 Exposure Index (EI)

DI = 10 × log₁₀(EI_actual / EI_target)

Calculate Exposure Index and Deviation Index for digital radiography quality assurance. Target EI is typically 500 for most detectors. DI should be within ±1.0 for optimal exposure.

Actual EI

Target EI

EI = 650 | DI = +1.14 (slightly overexposed)DI = 10 × log₁₀(650/500) = +1.14

🔳 Collimation & Dose

Dose Reduction = 1 − (A_coll / A_full)

Calculate patient dose reduction from collimation. Tighter collimation reduces irradiated tissue volume and scatter, improving image quality while protecting the patient.

Collimated Field (cm²)

Full Field (cm²)

50.0% dose reductionDose = (1 − 400/800) × 100% = 50.0% reduction

🔄 CTDI & DLP (CT Dose)

DLP = CTDI_vol × Scan Length

Calculate CT dose metrics. CTDIvol represents average dose per slice; DLP (Dose-Length Product) accounts for total scan length. Used for estimating effective dose in CT.

CTDI_vol (mGy)

Scan Length (cm)

Body Region k-factor

DLP = 375.0 mGy·cm | Eff Dose = 6.4 mSvDLP = 12.5 × 30 = 375 mGy·cm | Eff = 375 × 0.017 = 6.4 mSv

🛡️ ALARA Dose Limits

NCRP Report No. 180 — Annual Limits

Quick reference for occupational and public annual effective dose limits as recommended by the NCRP. Essential for radiation safety exams and clinical practice.