DecayCalculator.com

Radioactive decay is the process by which an unstable atomic nucleus loses energy by emitting radiation. In nuclear medicine, radiopharmaceuticals — drugs labelled with radioactive isotopes — are injected into patients for diagnostic scans or therapeutic treatments. Because these isotopes decay over time, their activity (the rate of radioactive emission) decreases continuously. Technicians and physicists must account for this decay when preparing doses: the activity in a vial at the time of calibration will be different from the activity at the time of administration, sometimes by a significant margin depending on the isotope and elapsed time.

The standard formula is A(t) = A₀ × e^−λt, where A₀ is the initial activity, λ is the decay constant (λ = ln(2) / T½), and t is the elapsed time. Our Decay Calculator handles this automatically — just select the isotope, enter the reference activity and calibration time, and set the target time. The calculator also shows a time-activity curve so you can visualise how the activity evolves over a ±48 hour window.

Technetium-99m (Tc-99m) has a half-life of approximately 6.01 hours, which makes it ideal for nuclear medicine. It is short enough that the patient's radiation exposure is limited, but long enough to allow time for radiopharmaceutical preparation, quality control, and the imaging procedure itself. It also emits gamma rays at an energy (140 keV) that is well-suited to gamma camera detection. Tc-99m is the most widely used diagnostic radioisotope in the world, used in bone scans, cardiac perfusion imaging, renal studies, and many other applications.

These are three different ways of quantifying radiation exposure, each more clinically meaningful than the last. Absorbed dose (measured in Gray, Gy) is the raw physical energy deposited per unit mass of tissue. Equivalent dose (measured in Sievert, Sv) adjusts for the biological effectiveness of different radiation types — for example, alpha particles cause more damage per unit of absorbed dose than X-rays. Effective dose (also in Sv) goes one step further and accounts for the varying radiosensitivity of different organs and tissues, allowing a single number to represent the overall health risk from a non-uniform exposure. Our Dose Converter handles all three conversions using ICRP 103 weighting factors.

The tissue weighting factors (w_T) defined in ICRP Publication 103 (2007) represent the relative contribution of each organ or tissue to the total radiation detriment from uniform whole-body exposure. Tissues with higher w_T values — such as bone marrow, lung, stomach, and colon (each w_T = 0.12) — are more radiosensitive and contribute more to the overall effective dose. The sum of all w_T values equals 1.00. These factors are used to calculate effective dose: E = Σ(w_T × H_T), where H_T is the equivalent dose to each tissue.

Use our Activity Concentration Calculator. You need to know the concentration of activity in the vial at a reference time (e.g. at the time of elution or delivery), the time at which you will perform the extraction, and the activity you want to administer. The calculator first corrects the concentration for radioactive decay between the reference time and the extraction time, then divides the desired activity by this corrected concentration to give the volume in mL. This is a calculation performed routinely in nuclear medicine departments, particularly for Tc-99m preparations.

These calculators are designed to support and verify manual calculations performed by trained professionals. They use accurate half-life data from the IAEA and NNDC and follow established formulas and international standards. However, they are intended for educational and verification purposes — they do not replace your institution's validated procedures, local regulations, or professional judgment. Always confirm doses and volumes using your institution's approved methods before administration.