How it works
Calculate radioactive decay, half-life, or remaining quantity.
Input query strings and outputs
Use an input name in this page’s URL as ?name=value, and join additional inputs with &. Portable shared links may instead use the compact ?ac= state parameter.
Input query strings
5-
?initial=Initial Quantity (N₀)Number · Optional · Default: 100
-
?halfLife=Half-Life (t½)Number · Optional · Default:
-
?time=Elapsed Time (t)Number · Optional · Default: 10
-
?remaining=Remaining Quantity (Nₜ)Number · Optional · Default: 50
-
?mode=ModeChoice · Optional · Default: find-remaining
Outputs
1-
resultResultText · Primary output
result contains the calculator’s complete rendered result area, including its visible result cards, tables, charts, and messages.
Calculate radioactive decay and substance persistence
Description
The Half-Life Calculator is a scientific tool for modeling exponential decay. It is used to determine how long it takes for a substance (like a radioactive isotope or a pharmaceutical drug) to decrease to half of its initial amount. The tool can either find the Remaining Quantity after a specific time or calculate the Half-Life of a substance based on observed decay data.
Inputs
- Mode Selection: Choose “Find Remaining” or “Find Half-Life”.
- Initial Quantity ($N_0$): The starting amount of the substance.
- Elapsed Time ($t$): The duration of the decay process.
- Variable Field (depending on mode):
- Half-Life ($t_{1/2}$): Required if finding the remaining quantity.
- Remaining Quantity ($N_t$): Required if calculating the half-life.
Outputs
- Result: Either the final quantity remaining or the calculated half-life period.
Chart
- N/A: This tool provides precise numeric decay values.
“Good to Know”
- Exponential Decay: Half-life is a constant. After one half-life, 50% remains. After two, 25% remains. After three, 12.5% remains, and so on.
- Pharmacokinetics: Doctors use half-life to determine how long a medicine stays in the body and how often a patient needs a dose.
- Carbon Dating: Scientists use the known half-life of Carbon-14 (about 5,730 years) to determine the age of ancient organic materials.
Examples
Example 1: Finding Remaining Substance
- Input: Mode: Remaining, Initial: 100g, Half-Life: 5 days, Time: 10 days
- Output: 25.0000g (Exactly 2 half-lives have passed)
Example 2: Calculating Half-Life
- Input: Mode: Half-Life, Initial: 100g, Remaining: 10g, Time: 24 hours
- Output: 7.2246 hours
Example 3: Long-term Persistence
- Input: Mode: Remaining, Initial: 500, Half-Life: 10, Time: 100
- Output: 0.4883 (After 10 half-lives, less than 0.1% remains)