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Calcimator

Radiation Dose Rate Calculator

Calculate radiation dose rate from source activity and distance using the inverse square law.

About this calculator

This calculator applies the classic point-source dose rate equation, D = (A × Γ) / d², where A is source activity in gigabecquerels, Γ is the isotope's specific gamma constant (a fixed property of each radionuclide — Co-60's 0.351 mSv·m²/(GBq·hr) is roughly four times Cs-137's 0.0842), and d is distance from the source in meters. Because dose rate falls off with the square of distance, doubling your distance from a source cuts dose rate to a quarter, not half — the inverse square law is the single most powerful, cost-free radiation protection tool available, which is why the calculator also solves the equation backward to report the distance at which dose rate drops to the public limit (1 mSv/yr, assuming 2,000 hours/year of exposure) and the occupational limit (20 mSv/yr under the same assumption). Total dose is just dose rate multiplied by exposure time, and the calculator converts between mSv, μSv, and mrem for convenience since different regulatory contexts and older instrumentation favor different units.

The two "exceeds limit" flags extrapolate your instantaneous dose rate out to a full 2,000-hour occupational year, so they're a useful early-warning check rather than an actual annual dose record. Critically, this model assumes an idealized bare point source in air: it ignores buildup factors from scattered radiation, any intervening shielding or structures, and the finite size and geometry of real sources, all of which change the actual dose rate a worker experiences at close range or behind partial shielding.

Inputs

Bq
mSv·m²/(GBq·hr)
ft
hours

Results

Dose Rate

12.99 mSv/hr

Total Dose

12.99 mSv

Dose Rate12,987 μSv/hr
Total Dose1,298.7 mrem
Public Limit Distance161.16 m
Occupational Limit Distance36.04 m
Exceeds Occupational Limit1
Exceeds Public Limit1
Total Dose Usv12,987
How to Use This Calculator
  1. Enter Source Activity, Gamma Constant (Γ), and Distance from Source.
  2. Set Exposure Time.
  3. Review Dose Rate (mSv/hr) and Total Dose (mSv).
  4. Use Dose Rate (μSv/hr) and Total Dose (mrem) to inform your decision.
  5. Use the chart to visualize the results and explore different scenarios by adjusting inputs.

How the result changes with Distance from Source

Distance from SourceDose RateTotal Dose
0.551.95 mSv/hr51.95 mSv
0.7523.09 mSv/hr23.09 mSv
1.55.77 mSv/hr5.77 mSv
2.52.08 mSv/hr2.08 mSv

What each input means

Source Activity
Radioactive source activity in becquerels. 1 Ci = 3.7×10¹⁰ Bq.
Gamma Constant (Γ)
Specific gamma ray constant for the isotope. Cs-137: 0.0842, Co-60: 0.351, Ir-192: 0.130.
Distance from Source
Distance from the point source in meters.
Exposure Time
Duration of exposure in hours.

What each result means

Public Limit Distance
Distance for 1 mSv/yr (general public limit)
Occupational Limit Distance
Distance for 20 mSv/yr (occupational limit)
Exceeds Occupational Limit
1 = Yes (>20 mSv/yr at 2000 hr/yr), 0 = No
Exceeds Public Limit
1 = Yes (>1 mSv/yr at 2000 hr/yr), 0 = No

How this is calculated

Worked example, using the default values

  1. Identify Input Parameters
    4 parameters
    Source Activity = 37000000000, Gamma Constant (Γ) = 0.351, Distance from Source = 1, Exposure Time = 1 = 4 input(s) provided
  2. Calculate Dose Rate
    Dose Rate = dr
    12.987 = 12.987
  3. Calculate Total Dose
    Total Dose
    12.987 = 12.987
  4. Calculate Dose Rate
    Dose Rate
    12987 = 12987
  5. Calculate Total Dose
    Total Dose
    1298.7 = 1298.7

Engine last updated . Checked against 4 independently-derived tests — how we verify calculators. Built by Paul Gunder, a software engineer, not a licensed financial, medical, or legal professional.

Frequently Asked Questions

Why does doubling my distance from the source cut dose rate to a quarter instead of half?

Dose rate here is proportional to 1/d² (the inverse square law), not 1/d, because the same amount of radiation is spreading out over a spherical surface whose area grows with the square of distance. So doubling distance quadruples that surface area, spreading the same energy over four times the space and cutting dose rate to one-fourth — tripling distance cuts it to one-ninth, and so on.

How does the calculator determine the "safe distance" for the general public?

It solves the dose rate equation backward: instead of computing dose rate at a given distance, it takes the public dose-rate target (derived from 1 mSv/year assuming 2,000 hours of annual exposure) and solves for the distance at which A×Γ/d² equals that target, which works out to d = √(A×Γ / target rate). The occupational limit distance uses the same approach with the higher 20 mSv/year target.

What is the gamma constant and why does it differ between isotopes like Cs-137 and Co-60?

The gamma constant (Γ) is a fixed physical property of each radionuclide describing how much dose rate its gamma emissions produce at a given activity and distance — it depends on the isotope's specific gamma-ray energies and emission probabilities per decay. Co-60 emits two relatively high-energy gammas per decay, giving it a constant (0.351 mSv·m²/(GBq·hr)) roughly four times higher than Cs-137's (0.0842), meaning equal activities of Co-60 produce substantially more dose rate at the same distance.

Does this calculator account for shielding between me and the source?

No — it models an idealized bare point source in air with no intervening material, so it ignores any shielding, walls, or structures between you and the source, as well as buildup effects from scattered radiation and the finite size of real sources. If shielding is present, use the Radiation Shielding calculator to estimate its attenuation separately, since this dose-rate model will overstate actual exposure whenever real shielding exists.

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