Radiation Dose Rate Calculator

Radiation Dose Rate Calculator

Cobalt-60 (1.30 R·m²/h·Ci) Cesium-137 (0.33 R·m²/h·Ci) Iridium-192 (0.48 R·m²/h·Ci) Radium-226 (0.825 R·m²/h·Ci) Americium-241 (0.0129 R·m²/h·Ci) Manual Input (Custom Γ)

Estimated Dose Rate:

0 R/h

0 mSv/h

*Calculated based on point source geometry and the inverse square law.

Understanding Radiation Dose Rate Calculations

In health physics and radiation protection, estimating the potential exposure from a gamma-emitting point source is critical for safety planning. The radiation dose rate is primarily determined by the activity of the source, the distance from that source, and the specific emission characteristics of the radionuclide (the gamma ray constant).

The Physics Formula

The standard formula used for calculating the exposure rate ($R$) at a specific distance from a point source is:

R = (Γ × A) / d²

• R: Exposure rate (Roentgens per hour, R/h).
• Γ (Gamma Constant): Specific gamma ray constant (R·m²/h·Ci). This is unique to each isotope.
• A (Activity): The strength of the radioactive source in Curies (Ci).
• d (Distance): The distance from the source in meters (m).

The Inverse Square Law

Radiation follows the Inverse Square Law. This means if you double the distance from a source, the dose rate drops by a factor of four ($2^2$). Conversely, halving the distance increases the dose rate by a factor of four. This is the most effective way to practice "Distance" in the ALARA (As Low As Reasonably Achievable) principle.

Realistic Calculation Example

Suppose you are working near a 5 Curie Cesium-137 source at a distance of 2 meters.

1. Isotope: Cs-137 (Γ = 0.33 R·m²/h·Ci)
2. Activity: 5 Ci
3. Distance: 2 meters
4. Calculation: (0.33 × 5) / (2²) = 1.65 / 4 = 0.4125 R/h

This equates to 412.5 mR/h or approximately 4.125 mSv/h.

Safety Thresholds

While radiation is a natural part of our environment, occupational limits are strictly regulated. In most jurisdictions, the annual occupational limit for radiation workers is 50 mSv (5,000 mrem) per year. Using a calculator like this helps engineers and safety officers design shielding and establish "stay times" to ensure workers do not exceed these limits.

function updateGammaConstant() { var selector = document.getElementById("isotopeSelector"); var gammaInput = document.getElementById("gammaConstant"); if (selector.value !== "custom") { gammaInput.value = selector.value; } } function calculateDoseRate() { var gamma = parseFloat(document.getElementById("gammaConstant").value); var activity = parseFloat(document.getElementById("sourceActivity").value); var distance = parseFloat(document.getElementById("sourceDistance").value); var resultDiv = document.getElementById("doseResult"); var rPerHourSpan = document.getElementById("roentgenPerHour"); var mSvPerHourSpan = document.getElementById("milliSievertPerHour"); if (isNaN(gamma) || isNaN(activity) || isNaN(distance) || distance <= 0) { alert("Please enter valid positive numbers for activity and distance."); return; } // Calculation: R = (Gamma * Activity) / (Distance^2) var doseRateR = (gamma * activity) / (distance * distance); // Conversion: 1 Roentgen is roughly 0.01 Sieverts or 10 milliSieverts var doseRateMSv = doseRateR * 10; rPerHourSpan.innerText = doseRateR.toLocaleString(undefined, {minimumFractionDigits: 4, maximumFractionDigits: 4}); mSvPerHourSpan.innerText = doseRateMSv.toLocaleString(undefined, {minimumFractionDigits: 4, maximumFractionDigits: 4}); resultDiv.style.display = "block"; // Scroll to result smoothly resultDiv.scrollIntoView({ behavior: 'smooth', block: 'nearest' }); }