Calculators Directory
Browse all 28 specialized computational tools designed for radiation protection officers, health physicists, and radiochemists. Filter by domain, toggle compact list mode on mobile, or search across equations, variables, and isotopes.
All Calculators
Ẋ = 6 × C × E × N 6CEN Rule of Thumb
Estimates unshielded gamma exposure rate at 1 foot (30.48 cm) from a point source given activity in Curies, photon energy in MeV, and photon yield per disintegration.
f_DAC = C / DAC; CEDE = H_DAC-h × 2.5 mrem/DAC-hr Airborne Derived Air Concentration (DAC) & Committed Dose
Converts air particulate filter measurements to air concentration, fraction of DAC, worker DAC-hours, and Committed Effective Dose Equivalent (CEDE) under 10 CFR 20.
t = Allowable Dose / Exposure Rate ALARA Stay Time & Dose Accumulation
Calculates maximum worker stay time for an RWP dose limit, projected dose for a planned task duration, or maximum permissible exposure rate for a shift.
E_D = E_α × [4.0015 / (M_P − 4.0015)]; S_i = E_α / (W_air × R_air) Alpha Heavy Daughter Recoil & Specific Ionization
Evaluates two-body conservation of linear momentum in alpha decay to determine daughter nucleus recoil energy, velocity, and linear ion pair density along the track in air.
R_air = 0.318 × E^(1.5); R_m = R_air × (ρ_air / ρ_m) × √(A_m / A_air) Alpha Particle Range & Bragg-Kleeman Stopping
Calculates monoenergetic alpha particle penetration distance in standard air and converts it to soft tissue depth to assess whether alphas penetrate the 70 µm epidermal stratum corneum.
Φ(d) = 0.5 × A_s × f_self × max(0, 1 − d / R_air) Alpha Surface Contamination Flux & Skin Dose
Evaluates planar 2π surface alpha contamination emission, air standoff attenuation cutoff, detector mylar window transmission, and shallow tissue basal dose.
A₂(t) = A₁(0) × [λ₂ / (λ₂ − λ₁)] × (e^(−λ₁ t) − e^(−λ₂ t)) + A₂(0) e^(−λ₂ t) Bateman Parent-Daughter Decay Kinetics & Equilibrium
Solves coupled Bateman differential equations for parent-daughter radioactive decay chains, modeling transient equilibrium, secular equilibrium, and generator milking cycles.
R = 0.412 × E^(1.265 − 0.0954 ln E) (Katz-Penfold) / 0.542 E − 0.133 (Feather) Beta Particle Maximum Range & Stopping Thickness
Calculates continuous-slowing-down approximation (CSDA) maximum range and shield thickness required to stop 100% of primary beta particles across various absorbers.
Ḣ_p(0.07) = 300 × A × [e^(−μ_air × d) / d²] Beta Skin & Shallow Dose Rate (Hp(0.07))
Models shallow contact and standoff equivalent dose rates to the skin basal layer (ICRP 70 µm depth) from beta point sources accounting for geometric falloff and air attenuation.
1 / T_eff = 1 / T_p + 1 / T_b ⟹ T_eff = (T_p × T_b) / (T_p + T_b) Biological & Effective Half-Life
Calculates composite effective clearance half-life T_eff combining physical radiological decay T_p and physiological metabolic clearance T_b, and evaluates whole-body retention.
f_brem = 3.5 × 10⁻⁴ × Z_eff × E_max Bremsstrahlung Radiation Yield & Power
Estimates the fraction of beta kinetic energy converted into penetrating Bremsstrahlung photons and calculates total radiated photon power to design graded shields.
I = I₀ × B(μx) × e^(−μx); B(μx) = 1 + b(μx) Broad-Beam Gamma Shielding & Buildup Factor
Models broad-beam gamma shielding barriers including Compton scattered secondary photon buildup B(µx) and iteratively solves for required barrier thickness.
a = (ln 2 × N_A) / (T_½ × M); m = A₀ / a Carrier-Free Specific Activity & Radioisotope Mass
Calculates theoretical carrier-free specific activity in Ci/g and Bq/g and determines the physical mass corresponding to a given radioactivity level.
L_C = 1.645 σ_0; L_D = 2.71 + 3.29 σ_0; MDA = L_D / (t_s × ε × Y) Currie Detection Limits & Minimum Detectable Activity (MDA)
Applies standard Currie (1968) and MARLAP / ISO 11929 hypothesis testing statistics (α = β = 0.05) to evaluate instrument critical decision levels and minimum detectable activity.
Non-Paralyzable: n = m / (1 − m τ); Paralyzable: m = n e^(−n τ) Detector Dead-Time & Pulse Pileup Loss Correction
Quantifies detector recovery time pulse pileup counting losses and reconstructs true incident interaction rates using both non-paralyzable and paralyzable saturation models.
X = K × (kVp / 100)² × mAs × (d_ref / SSD)² × 2^(−Δt / HVL_Al) Diagnostic & Industrial X-Ray Tube Output
Estimates diagnostic and industrial X-ray tube workload output exposure in mR and entrance surface air kerma in mGy based on peak kilovoltage, tube current-time product, aluminum filtration, and distance.
ξ = 1 + [α ln α / (1 − α)]; N_coll = ln(E₀ / E_th) / ξ Fast Neutron Elastic Scattering & Moderation
Models two-body s-wave elastic scattering kinematics in nuclear reactors and laboratory moderators to determine average logarithmic energy decrement ξ and collisions to thermalize.
CEDE = I × e(50); ALI = 0.05 Sv / e(50) Internal Intake & Committed Dose (CEDE & ALI)
Calculates 50-year Committed Effective Dose Equivalent (CEDE) and Annual Limit on Intake (ALI) percentages for worker inhalation and ingestion intakes using ICRP 68/119 dose coefficients.
d ≤ L/2: I₂ = I₁(d₁/d₂) | d > L/2: (L/2d₂)² Line Source Geometry (Piping & Rods)
Models exposure rates around radioactive piping, coolant headers, and fuel rods where close-in intensity drops linearly (1/d) before transitioning toward inverse-square (1/d²) beyond half the pipe length.
R_n = R_g − R_b; σ_Rn = √[(R_g / t_g) + (R_b / t_b)] Net Count Rate & Propagated Poisson Uncertainty
Propagates Poisson counting statistics for sample and background measurements, computing 1σ (68.3%) and 2σ (95.4%) confidence limits and coefficient of variation (%CV).
Ḣ*(10) = Φ × h_Φ*(10, E_n) × 3.6 × 10⁻⁶ mSv/hr Neutron Fluence-to-Dose Equivalent (ICRP 74)
Converts thermal, epithermal, fast, and fusion neutron flux to ambient dose equivalent rate H*(10) and mrem/hr using ICRP 74 and NCRP 112 conversion coefficients.
d ≤ 0.1R: I₀ | 0.1R–0.7R: I₀/3 | d > 0.7R: (I₀/3)(0.7R/d)² Plane & Disk Source (Spills & Walls)
Evaluates dose rates above circularly distributed floor spills, sumps, or contaminated walls across contact, transition, and far-field elevation zones.
I₁ × D₁² = I₂ × D₂² Point Source (Inverse Square Law)
Calculates exposure rate at a new distance or determines the required standoff distance to reach a target dose rate boundary from an isotropic point source.
A(t) = A₀ × (1/2)^(t / T₁/₂) Radioactive Decay & Half-Life
Calculates remaining activity after elapsed time, initial source activity, radionuclide half-life, or required hold time for decay-in-storage disposal.
C(t) = (A₀ / V) × e^(−(λ_rad + Q / V) t) Radioactive Dilution & Chamber Clearance
Models static tank dilution and continuous flow ventilation washout clearance, predicting concentration decay and required turnover times for hot cell re-entry.
C_dpm = (R_gross − R_bkg) / [ε_det × E_wipe × (A_wipe / 100)] Removable Surface Contamination (Wipe / Smear)
Standardizes contamination surveys per 10 CFR 20 and DOT 49 CFR 173, converting laboratory smear counts into dpm/100 cm² and Bq/cm² to verify regulatory release limits.
I = I₀ × (0.5)^(N_HVL) Shielding Attenuation (HVL & TVL)
Calculates transmitted dose rate behind lead, steel, tungsten, concrete, or water shielding barriers, or determines the number of HVLs and TVLs required to reach a target dose rate.
A = N × σ × Φ × (1 − e^(−λ t_irr)) × e^(−λ t_cool) Thermal Neutron Activation & Saturation
Calculates neutron capture (n,γ) radioisotope production, saturation activity limits in reactor flux traps, and residual activity after decay cooling.
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Governing Equations & Validity Regimes
| Calculator | Domain | Governing Equation | Primary Application & Assumptions |
|---|---|---|---|
| 6CEN Rule of Thumb | Photon & External | Ẋ = 6 × C × E × N | Estimates unshielded gamma exposure rate at 1 foot (30.48 cm) from a point source given activity in Curies, photon energy in MeV, and photon yield per disintegration. |
| Airborne Derived Air Concentration (DAC) & Committed Dose | Contamination & Internal | f_DAC = C / DAC; CEDE = H_DAC-h × 2.5 mrem/DAC-hr | Converts air particulate filter measurements to air concentration, fraction of DAC, worker DAC-hours, and Committed Effective Dose Equivalent (CEDE) under 10 CFR 20. |
| ALARA Stay Time & Dose Accumulation | Photon & External | t = Allowable Dose / Exposure Rate | Calculates maximum worker stay time for an RWP dose limit, projected dose for a planned task duration, or maximum permissible exposure rate for a shift. |
| Alpha Heavy Daughter Recoil & Specific Ionization | Alpha & Heavy Ions | E_D = E_α × [4.0015 / (M_P − 4.0015)]; S_i = E_α / (W_air × R_air) | Evaluates two-body conservation of linear momentum in alpha decay to determine daughter nucleus recoil energy, velocity, and linear ion pair density along the track in air. |
| Alpha Particle Range & Bragg-Kleeman Stopping | Alpha & Heavy Ions | R_air = 0.318 × E^(1.5); R_m = R_air × (ρ_air / ρ_m) × √(A_m / A_air) | Calculates monoenergetic alpha particle penetration distance in standard air and converts it to soft tissue depth to assess whether alphas penetrate the 70 µm epidermal stratum corneum. |
| Alpha Surface Contamination Flux & Skin Dose | Alpha & Heavy Ions | Φ(d) = 0.5 × A_s × f_self × max(0, 1 − d / R_air) | Evaluates planar 2π surface alpha contamination emission, air standoff attenuation cutoff, detector mylar window transmission, and shallow tissue basal dose. |
| Bateman Parent-Daughter Decay Kinetics & Equilibrium | Contamination & Internal | A₂(t) = A₁(0) × [λ₂ / (λ₂ − λ₁)] × (e^(−λ₁ t) − e^(−λ₂ t)) + A₂(0) e^(−λ₂ t) | Solves coupled Bateman differential equations for parent-daughter radioactive decay chains, modeling transient equilibrium, secular equilibrium, and generator milking cycles. |
| Beta Particle Maximum Range & Stopping Thickness | Beta & Electron | R = 0.412 × E^(1.265 − 0.0954 ln E) (Katz-Penfold) / 0.542 E − 0.133 (Feather) | Calculates continuous-slowing-down approximation (CSDA) maximum range and shield thickness required to stop 100% of primary beta particles across various absorbers. |
| Beta Skin & Shallow Dose Rate (Hp(0.07)) | Beta & Electron | Ḣ_p(0.07) = 300 × A × [e^(−μ_air × d) / d²] | Models shallow contact and standoff equivalent dose rates to the skin basal layer (ICRP 70 µm depth) from beta point sources accounting for geometric falloff and air attenuation. |
| Biological & Effective Half-Life | Advanced Photon & X-Ray | 1 / T_eff = 1 / T_p + 1 / T_b ⟹ T_eff = (T_p × T_b) / (T_p + T_b) | Calculates composite effective clearance half-life T_eff combining physical radiological decay T_p and physiological metabolic clearance T_b, and evaluates whole-body retention. |
| Bremsstrahlung Radiation Yield & Power | Beta & Electron | f_brem = 3.5 × 10⁻⁴ × Z_eff × E_max | Estimates the fraction of beta kinetic energy converted into penetrating Bremsstrahlung photons and calculates total radiated photon power to design graded shields. |
| Broad-Beam Gamma Shielding & Buildup Factor | Advanced Photon & X-Ray | I = I₀ × B(μx) × e^(−μx); B(μx) = 1 + b(μx) | Models broad-beam gamma shielding barriers including Compton scattered secondary photon buildup B(µx) and iteratively solves for required barrier thickness. |
| Carrier-Free Specific Activity & Radioisotope Mass | Advanced Photon & X-Ray | a = (ln 2 × N_A) / (T_½ × M); m = A₀ / a | Calculates theoretical carrier-free specific activity in Ci/g and Bq/g and determines the physical mass corresponding to a given radioactivity level. |
| Currie Detection Limits & Minimum Detectable Activity (MDA) | Counting Statistics | L_C = 1.645 σ_0; L_D = 2.71 + 3.29 σ_0; MDA = L_D / (t_s × ε × Y) | Applies standard Currie (1968) and MARLAP / ISO 11929 hypothesis testing statistics (α = β = 0.05) to evaluate instrument critical decision levels and minimum detectable activity. |
| Detector Dead-Time & Pulse Pileup Loss Correction | Counting Statistics | Non-Paralyzable: n = m / (1 − m τ); Paralyzable: m = n e^(−n τ) | Quantifies detector recovery time pulse pileup counting losses and reconstructs true incident interaction rates using both non-paralyzable and paralyzable saturation models. |
| Diagnostic & Industrial X-Ray Tube Output | Advanced Photon & X-Ray | X = K × (kVp / 100)² × mAs × (d_ref / SSD)² × 2^(−Δt / HVL_Al) | Estimates diagnostic and industrial X-ray tube workload output exposure in mR and entrance surface air kerma in mGy based on peak kilovoltage, tube current-time product, aluminum filtration, and distance. |
| Fast Neutron Elastic Scattering & Moderation | Neutron & Activation | ξ = 1 + [α ln α / (1 − α)]; N_coll = ln(E₀ / E_th) / ξ | Models two-body s-wave elastic scattering kinematics in nuclear reactors and laboratory moderators to determine average logarithmic energy decrement ξ and collisions to thermalize. |
| Internal Intake & Committed Dose (CEDE & ALI) | Contamination & Internal | CEDE = I × e(50); ALI = 0.05 Sv / e(50) | Calculates 50-year Committed Effective Dose Equivalent (CEDE) and Annual Limit on Intake (ALI) percentages for worker inhalation and ingestion intakes using ICRP 68/119 dose coefficients. |
| Line Source Geometry (Piping & Rods) | Photon & External | d ≤ L/2: I₂ = I₁(d₁/d₂) | d > L/2: (L/2d₂)² | Models exposure rates around radioactive piping, coolant headers, and fuel rods where close-in intensity drops linearly (1/d) before transitioning toward inverse-square (1/d²) beyond half the pipe length. |
| Net Count Rate & Propagated Poisson Uncertainty | Counting Statistics | R_n = R_g − R_b; σ_Rn = √[(R_g / t_g) + (R_b / t_b)] | Propagates Poisson counting statistics for sample and background measurements, computing 1σ (68.3%) and 2σ (95.4%) confidence limits and coefficient of variation (%CV). |
| Neutron Fluence-to-Dose Equivalent (ICRP 74) | Neutron & Activation | Ḣ*(10) = Φ × h_Φ*(10, E_n) × 3.6 × 10⁻⁶ mSv/hr | Converts thermal, epithermal, fast, and fusion neutron flux to ambient dose equivalent rate H*(10) and mrem/hr using ICRP 74 and NCRP 112 conversion coefficients. |
| Plane & Disk Source (Spills & Walls) | Photon & External | d ≤ 0.1R: I₀ | 0.1R–0.7R: I₀/3 | d > 0.7R: (I₀/3)(0.7R/d)² | Evaluates dose rates above circularly distributed floor spills, sumps, or contaminated walls across contact, transition, and far-field elevation zones. |
| Point Source (Inverse Square Law) | Photon & External | I₁ × D₁² = I₂ × D₂² | Calculates exposure rate at a new distance or determines the required standoff distance to reach a target dose rate boundary from an isotropic point source. |
| Radioactive Decay & Half-Life | Photon & External | A(t) = A₀ × (1/2)^(t / T₁/₂) | Calculates remaining activity after elapsed time, initial source activity, radionuclide half-life, or required hold time for decay-in-storage disposal. |
| Radioactive Dilution & Chamber Clearance | Advanced Photon & X-Ray | C(t) = (A₀ / V) × e^(−(λ_rad + Q / V) t) | Models static tank dilution and continuous flow ventilation washout clearance, predicting concentration decay and required turnover times for hot cell re-entry. |
| Removable Surface Contamination (Wipe / Smear) | Contamination & Internal | C_dpm = (R_gross − R_bkg) / [ε_det × E_wipe × (A_wipe / 100)] | Standardizes contamination surveys per 10 CFR 20 and DOT 49 CFR 173, converting laboratory smear counts into dpm/100 cm² and Bq/cm² to verify regulatory release limits. |
| Shielding Attenuation (HVL & TVL) | Photon & External | I = I₀ × (0.5)^(N_HVL) | Calculates transmitted dose rate behind lead, steel, tungsten, concrete, or water shielding barriers, or determines the number of HVLs and TVLs required to reach a target dose rate. |
| Thermal Neutron Activation & Saturation | Neutron & Activation | A = N × σ × Φ × (1 − e^(−λ t_irr)) × e^(−λ t_cool) | Calculates neutron capture (n,γ) radioisotope production, saturation activity limits in reactor flux traps, and residual activity after decay cooling. |