What is the inverse square law in radiation?

For a point source, dose rate falls with the square of distance: Ḣ₂ = Ḣ₁ × (d₁ ÷ d₂)². Doubling the distance cuts the rate to one quarter and tripling it to one ninth, so 2 mSv/h at 1 m becomes 0.5 mSv/h at 2 m and 0.22 mSv/h at 3 m. It holds once you are a few source diameters away and there is no shielding or scatter.

How far away do I need to be to reach a target dose rate?

Rearrange the inverse-square law: d₂ = d₁ × √(Ḣ₁ ÷ Ḣ₂). If a source reads 2 mSv/h at 1 m, the distance for 20 µSv/h (0.02 mSv/h) is 1 × √(2 ÷ 0.02) = 10 m. The inverse-square tool on this page does this calculation.

What is the gamma constant of Cs-137 and Co-60?

Unger and Trubey (ORNL/RSIC-45) give 0.382 rem/h at 1 m per curie for Cs-137 (with its Ba-137m daughter) and 1.37 rem/h for Co-60, which is 0.103 and 0.370 µSv·m²/(MBq·h). So 1 GBq of Co-60 gives about 370 µSv/h at 1 m. Exposure-rate tables list about 0.33 and 1.3 R/h per Ci at 1 m; the quantities differ, so do not mix them.

How do I work out total dose from a dose rate?

Multiply the dose rate by the time spent in the field, in matching units. 2 mSv/h for 30 minutes is 2 × 0.5 = 1 mSv. For short-lived sources, include decay: 740 MBq of Tc-99m at 1 m gives 24.5 µSv/h at the start, but over 2 hours the dose is 43.8 µSv rather than 49.1 µSv because the activity falls by 21%.

Stay time is how long you can remain in a radiation field before reaching a dose budget: stay time = allowed dose ÷ dose rate. With a 1 mSv budget at 0.25 mSv/h the stay time is 4 hours. Time, distance and shielding are the three basic ways to reduce dose.

How do mSv and mrem relate?

1 mSv equals 100 mrem, so 2 mSv/h is 200 mrem/h and 100 mSv is 10,000 mrem. The rem is still common in the United States; the sievert is the SI unit used internationally.

Can I convert this result to gray or rad?

Not from the information entered here. Gray/rad describe absorbed dose; sievert/rem describe dose equivalent or related protection quantities. NIST warns that the unit name alone does not define the quantity, so this tool does not silently equate them.

Can this calculate an X-ray tube dose rate?

No. X-ray tube output depends on kVp, tube current (mA), filtration and geometry, not on radionuclide activity. This calculator only applies the gamma point-source formula for a radionuclide.

Is this accurate for all radiation sources?

No. It is an idealized gamma point-source model. It excludes shielding, scatter, buildup, extended-source geometry, beta and neutron fields, and internal or patient dosimetry. A patient who received a radiopharmaceutical gives a lower rate than the bare-source constant because the body attenuates photons. Use a qualified health or medical physicist for real decisions.

Radiation Dose Rate Calculator

Pick an isotope or enter a documented gamma constant, then activity, distance and time to estimate dose-equivalent rate and total dose for an ideal unshielded point source, including decay. Separate tools scale a measured rate to a new distance and give the stay time for a dose budget.

For an ideal unshielded gamma point source, dose rate = activity × gamma constant ÷ distance², and total dose = dose rate × exposure time.

Source Parameters

Isotope preset

Gamma dose-rate constant (Γ)

Use the value and dose quantity stated by your reference. rem·m²/(Ci·h) equals mrem·m²/(mCi·h).

Source Activity

Distance from Source

Exposure Time

Half-life (optional — accounts for decay)

Display Unit

Dose Rate

—

mSv/h

Total Accumulated Dose

—

mSv

Calculation audit

Ideal unshielded point source; no legal-limit comparison is made.

All Unit Conversions

Unit	Dose Rate	Total Dose

Enter source parameters and click Calculate to see results.

Inverse-Square Distance Tool

Scale a measured dose rate to another distance (any rate unit; distances in the same unit): Ḣ₂ = Ḣ₁ × (d₁ ÷ d₂)².

Measured rate Ḣ₁

At distance d₁

New distance d₂

Target rate (optional)

Rate at d₂—

Distance for target rate—

Stay Time for a Dose Budget

Stay time = dose budget ÷ dose rate (constant rate). Uses the rate from the calculator above, or type one.

Dose rate (mSv/h)

Dose budget

Stay time—

Educational estimate only. Do not use for medical treatment, shielding design, emergency response, worker release, or regulatory compliance. The model assumes an unshielded point source and omits scatter, buildup and source geometry. Consult a qualified health or medical physicist.

Gamma Dose-Rate Constants for Common Isotopes

Unshielded point source in air. Specific gamma-ray dose constants from Unger & Trubey (ORNL/RSIC-45), half-lives from NNDC.

Isotope	Half-life	rem·m²/(Ci·h)	µSv·m²/(MBq·h)	µSv/h at 1 m, 1 GBq	Typical use
Co-60	5.2714 y	1.370	0.3703	370	Industrial radiography, teletherapy, check sources
Cs-137	30.08 y	0.382	0.1032	103	Includes Ba-137m; gauges, calibration sources
Ir-192	73.829 d	0.592	0.1599	160	Industrial radiography, HDR brachytherapy
Na-22	2.6018 y	1.339	0.3620	362	PET calibration and check sources
F-18	109.77 min	0.695	0.1879	188	PET imaging (FDG)
I-131	8.0252 d	0.283	0.0765	76	Thyroid therapy
Tc-99m	6.0067 h	0.123	0.0332	33	Nuclear medicine imaging

Conversion: 1 rem·m²/(Ci·h) = 10,000 µSv ÷ 37,000 MBq = 0.2703 µSv·m²/(MBq·h). Values count photons down to 10 keV and are conservative; tables based on newer ICRP 107 emission data (Smith & Stabin, 2012) and exposure-rate constants in R are lower, by about 5% for Co-60, 14% for Cs-137 and more for low-energy emitters such as Tc-99m. Use the constant your procedure specifies.

Source list: Gamma Ray Dose Constants (RadResponder ROSS toolkit); units per the NIST Guide to the SI.

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Quick answer

For an ideal unshielded gamma point source, dose rate = activity × gamma constant ÷ distance², and total dose = dose rate × exposure time. Doubling the distance cuts the rate to one quarter.

Example: With an example gamma constant of 0.1 µSv·m²/(MBq·h), 400 MBq at 2 m gives 400 × 0.1 ÷ 2² = 10 µSv/h, so 3 hours adds up to 30 µSv (0.03 mSv, or 3 mrem).

Pick an isotope or enter your gamma constant, activity, distance and time to get the rate and total dose in µSv, mSv and mrem.

Summary

This educational calculator applies the inverse-square point-source model Ḣ = A × Γ / r². Pick one of seven common gamma emitters (constants from Unger & Trubey, ORNL/RSIC-45) or enter a gamma constant from your own reference in µSv·m²/(MBq·h) or rem·m²/(Ci·h). An optional half-life integrates decay during the exposure. Two extra tools scale a measured dose rate to another distance (inverse-square law) and convert a dose budget into a stay time. It does not model shielding, scatter, buildup, source geometry or patient dose.

How it works

Choose an isotope preset, or enter a gamma dose-rate constant from a documented source and pick its unit.
Enter the source activity in MBq, mCi, GBq or Ci, the distance from the source and the exposure time.
The calculator applies the ideal point-source equation: dose-equivalent rate Ḣ = A × Γ ÷ r².
Without a half-life, total dose H = Ḣ × t. With a half-life T½, H = Ḣ × τ × (1 − e^(−t/τ)), where τ = T½ ÷ ln 2 is the mean life.
To rescale a survey-meter reading, enter the rate at one distance to get the rate at another: Ḣ₂ = Ḣ₁ × (d₁ ÷ d₂)².
Enter a dose budget to get the stay time = budget ÷ dose rate.

Use cases

Academic and training exercises on inverse square law calculations.
Checking hand calculations for Cs-137, Co-60 or Ir-192 check sources.
Estimating how far to stand from a source to reach a target dose rate.
Planning stay time for a dose budget in a training scenario.
Converting a dose-equivalent estimate between µSv, mSv and mrem.

Frequently Asked Questions

Last updated: 2026-10-09 · Reviewed by Nham Vu