Half-Life Calculator
Calculate exponential decay for radioactive substances and other decay processes
How to Use This Half-Life Calculator
- Select your calculation mode: Find Remaining, Find Time, or Find Half-Life
- Enter the initial quantity (starting amount of substance or material)
- Input the known values based on your selected mode
- Click Calculate to see remaining amount, elapsed half-lives, and decay constant
Example: A patient receives 100mg of a medication with a 4-hour half-life. After 12 hours: 100mg x (0.5)^(12/4) = 100mg x (0.5)^3 = 12.5mg remaining. Three half-lives have passed, leaving 12.5% of the original dose.
Tip: For quick estimates: after 7 half-lives, less than 1% of the original substance remains (0.78%).
Why Use a Half-Life Calculator?
Half-life calculations are essential in medicine, nuclear physics, archaeology, and environmental science for predicting how substances decay over time.
- Medication dosing: Calculate when drug levels drop below therapeutic threshold
- Carbon dating: Determine age of archaeological artifacts using C-14's 5,730-year half-life
- Nuclear safety: Predict when radioactive waste becomes safe (typically 10+ half-lives)
- Pharmacokinetics: Design drug dosing schedules to maintain steady-state concentrations
- Environmental cleanup: Estimate remediation timelines for contaminated sites
- Medical imaging: Plan radiotracer timing for PET scans (F-18 has 110-minute half-life)
Understanding Your Results
Results show remaining quantity, percentage remaining, and number of half-lives elapsed.
| Result | Meaning | Action |
|---|---|---|
| 50-100% remaining | Less than 1 half-life | Substance is still highly concentrated; decay is in early stages |
| 10-50% remaining | 1-3 half-lives | Significant decay has occurred; monitor if therapeutic levels matter |
| 1-10% remaining | 3-7 half-lives | Most substance has decayed; approaching negligible levels |
| Below 1% | 7+ half-lives | Substance is essentially depleted; often considered 'cleared' in medicine |
Meaning: Less than 1 half-life
Action: Substance is still highly concentrated; decay is in early stages
Meaning: 1-3 half-lives
Action: Significant decay has occurred; monitor if therapeutic levels matter
Meaning: 3-7 half-lives
Action: Most substance has decayed; approaching negligible levels
Meaning: 7+ half-lives
Action: Substance is essentially depleted; often considered 'cleared' in medicine
Note: The 'five half-lives rule' in pharmacology states that drugs reach steady state after 5 half-lives of regular dosing.
About Half-Life Calculator
Formula
N(t) = N_0 x (1/2)^(t/t_1/2) N(t) is quantity at time t, N_0 is initial quantity, and t_1/2 is the half-life. Alternatively: N(t) = N_0 x e^(-lambda x t), where lambda = ln(2)/t_1/2 is the decay constant.
Current Standards: Carbon-14 half-life: 5,730 years. Uranium-238: 4.5 billion years. Iodine-131 (medical): 8 days. Caffeine in humans: 5 hours.
Frequently Asked Questions
How is half-life used in carbon dating?
Living organisms maintain a constant C-14 ratio through respiration. After death, C-14 decays with a 5,730-year half-life while C-12 remains stable. By measuring the C-14/C-12 ratio and comparing to living organisms, scientists calculate when the organism died. This method works for organic materials up to about 50,000 years old (roughly 9 half-lives).
Why do doctors care about drug half-life?
Half-life determines dosing frequency. A drug with a 4-hour half-life might need doses every 4-6 hours to maintain therapeutic levels, while a 24-hour half-life drug can be taken once daily. After 5 half-lives, a drug reaches steady-state with regular dosing, and after stopping, 97% is eliminated in 5 half-lives.
Does half-life change based on the starting amount?
No, half-life is independent of the initial quantity. Whether you start with 100 atoms or 100 trillion atoms, half will decay in one half-life period. This is because radioactive decay is a probabilistic process where each atom has the same probability of decaying per unit time.
What's the difference between half-life and mean lifetime?
Mean lifetime (tau) is the average time an atom exists before decaying: tau = half-life / ln(2), or about 1.44 times the half-life. While half-life tells you when 50% has decayed, mean lifetime represents the statistical average 'lifespan' of individual atoms.
How many half-lives until something is completely gone?
Mathematically, exponential decay never reaches exactly zero. Practically, after 10 half-lives only 0.1% remains, and after 20 half-lives only 0.0001% remains. For regulatory purposes, radioactive materials are often considered 'decayed' after 10 half-lives.