Exposure Rate Calculator

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Radiation Exposure Rate Calculator

Iridium-192 (Ir-192) Cobalt-60 (Co-60) Cesium-137 (Cs-137) Custom Isotope
Unit: R·ft²/hr·Ci
Unit: Curies (Ci)
Unit: Feet (ft)
Calculated Exposure Rate:
0.00 R/hr
(0 mR/hr)

How to Calculate Radiation Exposure Rate

In industrial radiography, health physics, and non-destructive testing (NDT), determining the exposure rate from a radioactive source is critical for safety and compliance. This calculation typically utilizes the Inverse Square Law combined with the specific properties of the radioactive isotope being used.

The Exposure Rate Formula

The standard formula for calculating the exposure rate in air from a point source is:

E = (Γ × A) / d²

Where:

  • E = Exposure Rate (typically measured in Roentgens per hour, R/hr)
  • Γ (Gamma) = The specific Gamma Ray Constant for the isotope (R·ft²/hr·Ci)
  • A = Activity of the source (Curies, Ci)
  • d = Distance from the source (Feet, ft)

Common Gamma Constants

The Gamma constant (Γ) represents the radiation intensity inherent to specific isotopes. This calculator uses the standard industrial radiography units of R·ft²/hr·Ci:

  • Iridium-192 (Ir-192): Approximately 5.2 (Used often in pipeline NDT)
  • Cobalt-60 (Co-60): Approximately 14.5 (High energy, used for thick materials)
  • Cesium-137 (Cs-137): Approximately 3.3 (Common in calibration equipment)

The Inverse Square Law Explained

The distance variable in the denominator is squared (d²), representing the Inverse Square Law. This physical principle states that radiation intensity is inversely proportional to the square of the distance from the source.

Practically, this means:

  • Doubling the distance (e.g., moving from 10ft to 20ft) reduces the exposure rate by a factor of 4 (to 25% of the original).
  • Halving the distance (e.g., moving from 10ft to 5ft) increases the exposure rate by a factor of 4.

This is why distance is often cited as the most effective tool for reducing radiation dose to personnel, alongside time and shielding.

Example Calculation

Let's calculate the exposure rate for a standard industrial radiography scenario:

  • Source: Iridium-192
  • Activity: 50 Curies
  • Distance: 100 feet (barrier boundary)

Using the formula: (5.2 × 50) / 100²

1. Numerator: 5.2 × 50 = 260

2. Denominator: 100 × 100 = 10,000

3. Result: 260 / 10,000 = 0.026 R/hr (or 26 mR/hr)

function updateGammaConstant() { var select = document.getElementById("isotopeSelect"); var gammaInput = document.getElementById("gammaConstant"); var selectedValue = select.value; if (selectedValue !== "custom") { gammaInput.value = selectedValue; } else { gammaInput.value = ""; gammaInput.focus(); } } function calculateExposureRate() { // Get Input Values var gamma = parseFloat(document.getElementById("gammaConstant").value); var activity = parseFloat(document.getElementById("sourceActivity").value); var distance = parseFloat(document.getElementById("distanceFromSource").value); // Output Elements var resultBox = document.getElementById("ercResult"); var resultText = document.getElementById("resultValue"); var resultSub = document.getElementById("resultValueMr"); // Validation if (isNaN(gamma) || isNaN(activity) || isNaN(distance)) { alert("Please enter valid numbers for all fields."); return; } if (distance <= 0) { alert("Distance must be greater than zero."); return; } // Calculation: (Gamma * Activity) / (Distance ^ 2) var exposureRateR = (gamma * activity) / (distance * distance); // Convert to mR/hr for secondary display (1 R = 1000 mR) var exposureRateMr = exposureRateR * 1000; // Formatting // If the number is very small, use more decimals, otherwise standard 2-3 var displayR = exposureRateR < 0.01 ? exposureRateR.toFixed(5) : exposureRateR.toFixed(3); var displayMr = exposureRateMr.toFixed(1); // Display Results resultBox.style.display = "block"; resultText.innerHTML = displayR + " R/hr"; resultSub.innerHTML = "(" + displayMr + " mR/hr)"; }

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