Point Source Dose Rate Calculator

Compute gamma dose rate from a radioactive point source at any distance, or find the safe separation distance for a given dose rate limit, using the inverse square law.

☢️ Point Source Dose Rate Calculator
Isotope
Specific Gamma Constant (Γ)
μSv·m²/(MBq·h)
Source Activity
Distance from Source1.00 m
m
0.1 m20 m
Isotope
Specific Gamma Constant (Γ)
μSv·m²/(MBq·h)
Source Activity
Target Dose Rate Limit
Dose Rate at Distance
—
Weekly Dose (40 h/wk)
—
Annual Dose (2,000 h/yr)
—
Safe Distance
—
Distance (cm)
—
Distance (feet)
—
A × Γ Product
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☢️ What is the Point Source Dose Rate Calculator?

Point source dose rate is the gamma radiation dose rate produced at a given distance from a radioactive source, computed using the inverse square law and the specific gamma constant of the isotope. The fundamental formula is H_dot = (A × Gamma) / d², where H_dot is the dose rate in microsieverts per hour, A is the source activity in megabecquerels, Gamma is the specific gamma constant of the isotope in µSv·m²/(MBq·h), and d is the distance from the source center in meters.

This calculator serves three important professional communities. Radiation protection officers use it to establish controlled and supervised area boundaries around radioactive sources in hospitals, nuclear power plants, and research facilities. Nuclear medicine physicists use it to estimate dose rates around patients who have received diagnostic or therapeutic radiopharmaceuticals, and to design waiting areas that comply with regulatory limits. Industrial radiographers use it to calculate exclusion zones around Ir-192 or Se-75 sources used for nondestructive testing of welds and pipelines.

The inverse square law is one of the most powerful principles in radiation protection because distance is free. Doubling the separation from a source reduces the dose rate to one-quarter. Tripling the distance reduces it to one-ninth. This calculator also includes a Safe Distance mode that solves the formula in reverse: given a source activity, isotope, and a target dose rate limit (such as the 2.5 µSv/h boundary between supervised and uncontrolled areas per IAEA GSR Part 3), it computes the minimum separation distance.

The calculator covers 13 clinically and industrially important isotopes with pre-tabulated specific gamma constants from IAEA Nuclear Data Section publications. For isotopes not in the library, users can enter a custom Gamma value obtained from IAEA TECDOC-1040, NIST, or equivalent national nuclear data files. Activity is accepted in SI units (MBq, GBq) or legacy Curie-based units (Ci, mCi, µCi) with automatic conversion.

📐 Formula

Ḣ  =  (A × Γ) ÷ d²
Ḣ = dose rate (µSv/h)
A = source activity (MBq)
Γ = specific gamma constant (µSv·m²/(MBq·h)), isotope dependent
d = distance from source center (m)
dsafe  =  √( A × Γ ÷ Ḣtarget )
dsafe = minimum safe distance (m)
Ḣtarget = maximum allowable dose rate (µSv/h)
Example: Co-60 source at 1,000 MBq, target 2.5 µSv/h: d = sqrt(1000 × 0.3099 / 2.5) = sqrt(123.96) = 11.13 m

📖 How to Use This Calculator

Steps

1
Select calculation mode: Choose Dose Rate to compute the dose rate at a specific distance, or Safe Distance to find the minimum separation for a dose rate limit.
2
Choose an isotope: Select from the dropdown; the specific gamma constant (Gamma) fills in automatically. For unlisted isotopes, choose Custom and enter the Gamma value from IAEA TECDOC-1040 or NIST tables.
3
Enter source activity: Type the activity and select units. The calculator accepts MBq, GBq, Bq, kBq, Ci, mCi, and µCi and converts all values to MBq internally.
4
Set distance or dose rate limit: In Dose Rate mode, enter the distance (use the slider for quick exploration of the inverse square law). In Safe Distance mode, type the regulatory dose rate limit and select its unit.
5
Read the results: Dose Rate mode shows the dose rate plus weekly and annual dose estimates with a regulatory context note. Safe Distance mode shows the minimum distance in meters, centimeters, and feet.

💡 Example Calculations

Example 1 — Co-60 Industrial Source at 1 Meter

Co-60 source, 100 MBq activity, 1 meter distance

1
Identify values: A = 100 MBq, Gamma (Co-60) = 0.3099 µSv·m²/(MBq·h), d = 1 m.
2
Apply formula: H_dot = (100 × 0.3099) / 1² = 30.99 / 1 = 30.99 µSv/h.
3
Derived doses: Weekly (40 h) = 30.99 × 40 = 1,239.6 µSv/wk. Annual (2,000 h) = 30.99 × 2,000 / 1,000 = 61.98 mSv/yr. This exceeds the 20 mSv/yr occupational limit, so the area requires controls.
Dose Rate = 30.99 µSv/h
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Example 2 — Tc-99m Nuclear Medicine Patient at 2 Meters

Tc-99m patient, 555 MBq (standard bone scan dose), 2 meter separation

1
Identify values: A = 555 MBq, Gamma (Tc-99m) = 0.0206 µSv·m²/(MBq·h), d = 2 m.
2
Apply formula: H_dot = (555 × 0.0206) / 2² = 11.433 / 4 = 2.858 µSv/h.
3
At 2.858 µSv/h this is just above the 2.5 µSv/h public area boundary. Increasing to 2.3 m gives (555 × 0.0206) / 2.3² = 2.16 µSv/h, safely below the limit.
Dose Rate = 2.858 µSv/h
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Example 3 — I-131 Therapy Source Close Range

I-131 therapy patient, 3,700 MBq (100 mCi), 0.5 meter distance

1
Identify values: A = 3,700 MBq (100 mCi), Gamma (I-131) = 0.0590 µSv·m²/(MBq·h), d = 0.5 m.
2
Apply formula: H_dot = (3,700 × 0.0590) / 0.5² = 218.3 / 0.25 = 873.2 µSv/h = 0.873 mSv/h.
3
This exceeds 500 µSv/h: a radiation area. The patient should be isolated in a shielded room. At 2 meters the dose rate falls to 873.2 / (2/0.5)² = 873.2 / 16 = 54.6 µSv/h, still a controlled area.
Dose Rate = 873.2 µSv/h (0.873 mSv/h)
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Example 4 — Safe Distance for Co-60 Radiotherapy Source

Co-60 source, 1 GBq activity, target dose rate limit = 2.5 µSv/h (public area)

1
Convert: A = 1 GBq = 1,000 MBq. Gamma (Co-60) = 0.3099. Target = 2.5 µSv/h.
2
Compute A × Gamma: 1,000 × 0.3099 = 309.9 µSv·m²/h.
3
Safe distance: d = sqrt(309.9 / 2.5) = sqrt(123.96) = 11.134 m. This is the minimum separation for unrestricted public access from an unshielded 1 GBq Co-60 source.
Safe Distance = 11.134 m (1113.4 cm, 36.53 ft)
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❓ Frequently Asked Questions

What is the inverse square law for gamma radiation dose rate?+
The inverse square law states that the dose rate from a point source decreases with the square of the distance. If you double your distance from a source, the dose rate drops to one-quarter (1/2² = 1/4). If you triple the distance, it drops to one-ninth (1/3² = 1/9). Physically this occurs because gamma radiation travels outward spherically, and the area of a sphere grows as 4πd². The same total radiation energy spreads over an ever-growing area, reducing the intensity per unit area as 1/d².
What is the specific gamma constant and how is it measured?+
The specific gamma constant Gamma (µSv·m²/(MBq·h)) represents the dose rate at 1 meter from a 1 MBq unshielded point source. It is computed from nuclear data: Gamma = (E_i × I_i × µ_en/rho)_tissue summed over all gamma rays emitted by the isotope, where E_i is photon energy, I_i is emission probability, and µ_en/rho is the mass energy-absorption coefficient in tissue at that energy. Values are tabulated in IAEA TECDOC-1040 and are based on evaluated nuclear data files (ENSDF, JEFF, ENDF). The constant is specific to the isotope and does not depend on source geometry.
How accurate is the point source formula for real-world sources?+
The formula is accurate to within a few percent when the measurement distance is at least 3 times the largest source dimension and the geometry is open (no significant scatter from walls or floors). For compact sources like sealed radioactive sources (needles, seeds, pellets), the point source approximation is valid at distances as short as 5 cm. For extended sources such as Tc-99m-labeled patients, contaminated surfaces, or reactor cores, the formula overestimates the dose rate at short range and must be replaced by extended-source integration. Scatter buildup causes the formula to underestimate dose rate in enclosed spaces.
What regulatory dose rate limits apply to controlled and supervised areas?+
IAEA Basic Safety Standards (GSR Part 3, 2014) define area classifications by dose rate. A dose rate above 3/5 of the hourly occupational limit designates a controlled area. For a 20 mSv/yr occupational limit with 2,000 h/yr occupancy, this threshold is approximately 12 µSv/h. Areas where dose rates exceed 1 mSv/h are high radiation areas requiring strict access control. National regulations vary: the US NRC uses 0.05 mSv/h (5 mR/h) to designate a radiation area. Always use your country's specific regulatory thresholds.
How do I calculate dose rate from a source that is decaying over time?+
The activity A(t) decreases exponentially as A(t) = A₀ × exp(-0.693t / T½), where A₀ is the initial activity, t is elapsed time, and T½ is the half-life. The dose rate at time t is then H_dot(t) = (A₀ × exp(-0.693t / T½) × Gamma) / d². For I-131 (T½ = 8.02 days), a 3,700 MBq source decays to 1,850 MBq after 8 days, halving the dose rate. Use the Radioactive Decay Calculator on this site to find A(t), then enter the decayed activity here to compute the dose rate at any future time.
Why does Co-60 have such a high specific gamma constant compared to Tc-99m?+
Co-60 emits two high-energy gamma rays (1.17 MeV and 1.33 MeV) essentially simultaneously with nearly 100% emission probability each, giving Gamma = 0.3099 µSv·m²/(MBq·h). Tc-99m emits a single 140 keV gamma with 89% probability. The dose rate from a gamma ray scales roughly with photon energy (through the mass energy-absorption coefficient), so Co-60's gammas are far more penetrating and deposit more energy per photon. Additionally, Tc-99m's 140 keV gamma is partially attenuated by tissue and clothing, while Co-60's MeV gammas penetrate almost anything. The Gamma ratio of 15 explains why a 1 GBq Co-60 source requires 15 times more distance than a 1 GBq Tc-99m source to achieve the same dose rate.
How do I compute dose rate from a mixture of isotopes?+
For a mixture of n isotopes at the same location, compute the dose rate from each isotope separately and sum: H_total = (A₁ × Gamma₁ + A₂ × Gamma₂ + ... + Aₙ × Gammaₙ) / d². For a source containing both Cs-137 (500 MBq, Gamma = 0.0772) and Co-60 (100 MBq, Gamma = 0.3099) at 1 meter: H = (500 × 0.0772 + 100 × 0.3099) / 1 = (38.6 + 30.99) / 1 = 69.59 µSv/h. The higher-energy Co-60 contributes nearly as much dose rate as 5 times more Cs-137 activity.
What is the relationship between dose rate in µSv/h and mR/h?+
The roentgen (R) is an older unit of radiation exposure in air. For gamma rays in soft tissue, 1 R ≈ 8.77 mGy ≈ 8.77 mSv (for Sv/Gy quality factor of 1). Therefore 1 mR/h ≈ 8.77 µSv/h. Many older survey meters are calibrated in mR/h. To convert: divide mR/h by 8.77 to get µSv/h, or multiply µSv/h by 0.114 to get mR/h. This conversion is approximate because it depends slightly on photon energy. The SI units µSv and mSv are preferred in modern practice per ICRU and IAEA recommendations.
How does shielding interact with the inverse square law in dose rate calculations?+
Shielding and distance provide multiplicative dose reduction. A shield of material with linear attenuation coefficient µ (cm⁻¹) and thickness x (cm) reduces the dose rate by the factor exp(-µx) in narrow-beam geometry. The combined formula is H_shield = (A × Gamma / d²) × exp(-µx). For example, 2 cm of lead (µ = 1.278 cm⁻¹ at Co-60) gives exp(-2.556) = 0.077, a 13-fold reduction. Combined with doubling the distance (4-fold reduction), total attenuation is 4 × 13 = 52-fold. Distance and shielding are both essential tools in the radiation protection hierarchy: time, distance, and shielding.
What is the A times Gamma product shown in the Safe Distance results?+
The A × Gamma product (in µSv·m²/h) is the dose rate strength of the source at 1 meter from the unshielded point source. It equals the dose rate measured at exactly 1 m. Knowing this single number lets you instantly compute the dose rate at any other distance as H = (A × Gamma) / d², or the safe distance for any limit as d = sqrt(A × Gamma / H_limit). For example, a Co-60 source with A × Gamma = 310 µSv·m²/h produces 310 µSv/h at 1 m, 77.5 µSv/h at 2 m, and 34.4 µSv/h at 3 m.
How does the dose rate calculation apply to nuclear medicine patient release?+
After administration of radiopharmaceuticals, regulatory agencies specify release criteria based on the dose rate at a defined distance. The US NRC (10 CFR 35.75) allows patient release when the effective dose equivalent to any individual from the patient is not likely to exceed 5 mSv (0.5 rem). In practice, many facilities use a dose rate criterion of 70 µSv/h at 1 meter (measured with a survey meter) as a surrogate. For Tc-99m at this threshold: solving 70 = A × 0.0206 / 1 gives A = 3,398 MBq. Patients with less than this activity can be released. For I-131, the threshold is much more stringent due to the longer half-life (8 days vs. 6 hours for Tc-99m).
Can this calculator be used for neutron sources?+
No. This calculator applies only to gamma-ray emitting point sources using the specific gamma constant formalism. Neutron dose rates require different data: the neutron dose rate constant depends on the neutron energy spectrum and the fluence-to-dose conversion factors from ICRP Publication 74. Neutrons also have quality factors greater than 1 (typically 5 to 20 depending on energy), so the same fluence produces higher effective dose than for gamma rays. For neutron sources such as californium-252 or americium-beryllium, consult NCRP Report 38 or use a Monte Carlo transport code such as MCNP or OpenMC.
Tags: Point Source Dose Rate Calculator Inverse Square Law Radiation Specific Gamma Constant Calculator Radiation Protection Distance Gamma Dose Rate Formula Nuclear Medicine Dose Rate Calculator Formula Free Online

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What is the point source dose rate formula H_dot = A × Gamma / d²?

This formula applies the inverse square law to gamma-emitting point sources. H_dot is the dose rate in µSv/h, A is the source activity in MBq, Gamma is the specific gamma constant in µSv·m²/(MBq·h), and d is the distance from the source in meters. The formula states that dose rate decreases with the square of distance: doubling the distance reduces the dose rate by a factor of four. It is valid for unshielded point sources in open geometry.

What is the specific gamma constant and where do these values come from?

The specific gamma constant Gamma (also called the gamma-ray dose rate constant) represents the dose rate produced per unit activity at 1 meter from an unshielded point source. It accounts for all gamma rays emitted by the isotope, weighted by their emission probability and energy. Values come from IAEA Nuclear Data Section reports and national nuclear data files. For Co-60, Gamma is 0.3099 µSv·m²/(MBq·h); for Tc-99m it is 0.0206 µSv·m²/(MBq·h), a factor of 15 lower, reflecting Tc-99m's single 140 keV gamma versus Co-60's two high-energy gammas.

How do I convert between activity units like MBq, GBq, Ci, and mCi?

The becquerel (Bq) is the SI unit: 1 Bq equals one nuclear disintegration per second. 1 MBq = 1,000,000 Bq. The curie (Ci) is the historical unit: 1 Ci = 3.7 × 10¹⁰ Bq = 37,000 MBq. So 1 mCi = 37 MBq and 1 µCi = 0.037 MBq. For medical isotopes: a typical diagnostic Tc-99m dose of 555 MBq equals 15 mCi. A Co-60 therapy source of 370 GBq equals 10 Ci.

What dose rate limits apply in radiation protection?

IAEA Basic Safety Standards (GSR Part 3, 2014) classify areas by dose rate. A dose rate above 2 mSv/h designates a high radiation area. Above 100 mSv/h is a very high radiation area. For occupational workers, the annual effective dose limit is 20 mSv/year (averaged over 5 years). For members of the public it is 1 mSv/year. These translate to roughly 10 µSv/h and 0.5 µSv/h respectively at 2,000 hours per year. Always apply the ALARA principle to keep doses as low as reasonably achievable.

How does doubling the distance affect the dose rate?

Doubling the distance from a point source reduces the dose rate to one-quarter of its original value (since dose rate is proportional to 1/d²). Tripling the distance gives one-ninth the dose rate. This is the inverse square law: the same gamma radiation spreads over a sphere whose area grows as d². Practical implication: increasing distance is the most effective and least costly protective measure. Moving from 0.5 m to 1 m reduces dose rate by 75%; moving from 1 m to 2 m reduces it by another 75%.

When does the point source approximation fail?

The formula breaks down when the measurement distance d is less than roughly 3 times the largest dimension of the source. At close range to an extended source (such as a radiotherapy unit, a contaminated surface, or a large tank), you must use extended-source geometry integrals. The formula also ignores scatter buildup, which causes the actual dose rate to be higher than the bare formula predicts at distances where scatter from walls and floors contributes. Shielding calculations should use buildup factors from ANSI/ANS-6.4.3 or Monte Carlo codes.

Why do nuclear medicine isotopes have low specific gamma constants?

Most diagnostic nuclear medicine isotopes are selected precisely because they produce low external dose rates. Tc-99m emits only a single 140 keV gamma with 89% probability, giving Gamma = 0.0206 µSv·m²/(MBq·h). Ga-67 emits low-energy gammas at 93, 184, and 300 keV, giving Gamma = 0.0214. In contrast, therapy isotopes like I-131 have higher Gamma (0.0590) due to a 364 keV gamma. High-energy sources like Co-60 (1.17 and 1.33 MeV gammas, both near 100% emission probability) have the highest Gamma values at 0.3099.

How do I calculate the dose rate from a shielded source?

Shielding attenuates the dose rate by an exponential factor. For a shield with linear attenuation coefficient µ (cm⁻¹) and thickness x (cm), the shielded dose rate is H_shield = (A × Gamma / d²) × exp(-µx) × B, where B is the buildup factor. In narrow-beam geometry, B = 1. For typical room shielding, use B values from the gamma-ray attenuation calculator or NCRP Report 151 tables. For a quick estimate without buildup, the unshielded formula overestimates dose rate, making it conservative for safety calculations.

What is the occupancy factor and how does it change the required safe distance?

The occupancy factor T accounts for the fraction of time a location is actually occupied. NCRP Report 151 defines T from 1/40 (seldom-occupied areas like stairwells) to 1 (continuously occupied offices). The design dose rate limit is divided by T to give an effective limit. For a supervised area with T = 0.25, the effective limit is 4 times higher, reducing the required distance by a factor of 2 (since d scales as the square root of dose rate). Apply occupancy factors in compliance with your national regulatory requirements.

How do I add the dose rates from multiple sources?

For n point sources with activities A₁, A₂, ..., Aₙ at distances d₁, d₂, ..., dₙ from the point of interest, the total dose rate is the sum: H_total = A₁Γ₁/d₁² + A₂Γ₂/d₂² + ... + AₙΓₙ/dₙ². If all sources are the same isotope at the same distance, the formula simplifies to H_total = Γ/d² × (A₁ + A₂ + ... + Aₙ). For sources of different isotopes at different locations, compute each contribution separately and sum.

What does the A times Gamma product represent in the safe distance result?

The product A × Gamma (in µSv·m²/h) is the dose rate strength of the source at 1 meter. It equals the dose rate you would measure exactly 1 meter from the unshielded source. The safe distance formula is simply d_safe = sqrt(A × Gamma / H_target), so knowing this product lets you quickly compute the safe distance for any target dose rate: d = sqrt(product / H_target). A larger A × Gamma product means a stronger source that requires greater distance or more shielding.

How accurate is this calculator for medical physics and industrial radiography applications?

The calculator uses IAEA-tabulated specific gamma constants and the inverse square law, which is accurate to within a few percent for point sources in open geometry at distances greater than about 3 times the source diameter. For medical physics applications (nuclear medicine, brachytherapy), the formula provides a first-order estimate; detailed dosimetry requires vendor-specific source data and TG-43 formalism for brachytherapy sources. For industrial radiography, the formula is commonly used for exclusion zone calculations and is conservative (it ignores shielding by the source container and jig).

📌 Quick Tips

💡The inverse square law applies only to unshielded point sources in open geometry. For extended sources, distributed sources, or sources inside containers, the formula gives an overestimate of distance at close range and an underestimate of shielding effectiveness.
💡The specific gamma constant Γ is an isotope property, not an energy property. It is pre-integrated over all gamma energies emitted by that isotope. For mixtures of isotopes, compute each dose rate separately and sum them.
💡IAEA Basic Safety Standards classify areas by dose rate: below 1 µSv/h is typically unrestricted, 1-20 µSv/h is supervised, above 20 µSv/h is controlled. National regulations vary, so always consult your Radiation Protection Officer.
💡To estimate dose for a specific task duration, multiply the dose rate in µSv/h by the time in hours. A dose rate of 10 µSv/h for a 6-minute procedure gives 1 µSv total effective dose.
💡The safe distance formula assumes 100% occupancy. Apply an occupancy factor T (0.025 to 1) to reduce the required distance for areas that are not continuously occupied.