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.
☢️ 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
Try this example →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
Try this example →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)
Try this example →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) = 11.13 m. This is the minimum separation for unrestricted public access from an unshielded 1 GBq Co-60 source.
Safe Distance = 11.13 m (1,113 cm, 36.52 ft)
Try this example →❓ 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.