Half-Life Calculator

Using the Half-Life Calculator allows nuclear physicists, pharmacologists, and radiologists to accurately model exponential decay. Follow these steps:

Step 1: Determine your calculation goal. Select whether you want to find the Remaining Quantity after a period, the Time required to reach a specific quantity, or the Half-Life itself given two measured quantities.

Step 2: Enter the Initial Quantity (N₀). This is the starting amount of the radioactive substance or drug dose at Time = 0.

Step 3: Enter the Half-Life (t½). This is the fixed, constant duration it takes for exactly half of the substance to decay or be eliminated.

Step 4: Enter the Time Elapsed. This is how long after the initial dose or measurement you want to evaluate.

Step 5: Click the "Calculate" button.

Step 6: Review the output showing the exact Remaining Quantity and the percentage remaining. The calculator will model the exponential decay curve precisely.

The Half-Life formula is a specific application of exponential decay mathematics. It is fundamentally different from simple linear subtraction — the amount decaying per period is always proportional to how much remains.

The core formula is: N(t) = N₀ × (½)^(t ÷ t½)

Where: N(t) = Quantity remaining after time t N₀ = Initial quantity at time zero t = Time elapsed t½ = Half-life (the time constant for this specific substance)

Example — Carbon-14 Dating: Carbon-14 has a half-life of 5,730 years. An ancient bone sample started with 100 grams of C-14. After 11,460 years (exactly two half-lives): N = 100 × (0.5)^(11460 ÷ 5730) = 100 × (0.5)² = 100 × 0.25 = 25 grams. After two half-lives, exactly 25% of the original C-14 remains, allowing archaeologists to date ancient artifacts with remarkable precision.

The Half-Life Calculator is an essential tool in nuclear physics, radiological medicine, archaeology, and pharmacology. The "half-life" concept describes a universal law of exponential decay: for any unstable radioactive isotope or drug molecule, there is a fixed constant time period after which exactly half of it will have transformed or been eliminated, regardless of how much was present to begin with. This mathematical consistency makes half-life extraordinarily powerful. Archaeologists use Carbon-14 half-life to date organic artifacts up to 50,000 years old. Nuclear engineers use Uranium-238 half-life (4.5 billion years) to date geological formations. Pharmacologists use drug half-lives to calculate safe dosing intervals that maintain therapeutic blood levels without toxic accumulation.