How to Calculate Dose Rate from Activity

Dose Rate from Activity Calculator

— Custom / Manual Entry — Cobalt-60 (0.306 mSv·m²/h per GBq) Iridium-192 (0.081 mSv·m²/h per GBq) Cesium-137 (0.077 mSv·m²/h per GBq) Radium-226 (0.147 mSv·m²/h per GBq) Gold-198 (0.040 mSv·m²/h per GBq)

Calculation Results

The estimated Dose Rate is: 0.00 mSv/h

Equates to: 0 μSv/h

How to Calculate Dose Rate from Activity

In radiation protection and industrial radiography, calculating the dose rate from a known radioactive source activity is fundamental for safety planning. The calculation relies on the relationship between the source's strength, the specific properties of the radionuclide, and the distance from the point of interest.

The Dose Rate Formula

The standard formula used to determine the dose rate at a specific distance from a point source is:

D = (Γ × A) / d²

Where:

  • D = Dose Rate (usually in mSv/h)
  • Γ (Gamma Constant) = The specific gamma ray constant for the isotope (mSv·m²/h per GBq)
  • A = Activity of the radioactive source (GBq)
  • d = Distance from the source (meters)

Understanding the Inverse Square Law

A critical component of this calculation is , which represents the Inverse Square Law. This law dictates that the intensity of radiation decreases inversely with the square of the distance from the source. For example, if you double your distance from a source (e.g., from 1 meter to 2 meters), the dose rate decreases by a factor of four (2²), not two.

Common Isotope Gamma Constants

The specific gamma ray constant (Γ) is unique to each radioisotope and represents the dose rate at 1 meter from a source of 1 GBq. Common values include:

Isotope Gamma Constant (mSv·m²/h/GBq)
Cobalt-60 (Co-60)0.306
Iridium-192 (Ir-192)0.130
Cesium-137 (Cs-137)0.077
Radium-226 (Ra-226)0.223

Practical Example Calculation

Suppose you are working with a 50 GBq Cobalt-60 source and you are standing 4 meters away. To find the dose rate:

  1. Identify the constant for Co-60: 0.306 mSv·m²/h/GBq.
  2. Multiply constant by activity: 0.306 × 50 = 15.3.
  3. Calculate distance squared: 4² = 16.
  4. Divide the product by distance squared: 15.3 / 16 = 0.956 mSv/h.

In this scenario, an unshielded worker would receive nearly 1 mSv every hour at that distance.

function applyPreset() { var select = document.getElementById("isotopeSelect"); var gammaInput = document.getElementById("gammaInput"); if (select.value !== "") { gammaInput.value = select.value; } } function calculateDoseRate() { var activity = parseFloat(document.getElementById("activityInput").value); var gamma = parseFloat(document.getElementById("gammaInput").value); var distance = parseFloat(document.getElementById("distanceInput").value); var resultArea = document.getElementById("resultArea"); var doseRateDisplay = document.getElementById("doseRateResult"); var microDisplay = document.getElementById("microResult"); if (isNaN(activity) || isNaN(gamma) || isNaN(distance) || distance <= 0) { alert("Please enter valid positive numbers for Activity, Gamma Constant, and Distance."); return; } // Formula: D = (Gamma * Activity) / d^2 var doseRate = (gamma * activity) / (distance * distance); var microSieverts = doseRate * 1000; doseRateDisplay.innerHTML = doseRate.toLocaleString(undefined, {minimumFractionDigits: 4, maximumFractionDigits: 4}); microDisplay.innerHTML = microSieverts.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 2}); resultArea.style.display = "block"; resultArea.scrollIntoView({ behavior: 'smooth', block: 'nearest' }); }

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