Half‑Life Calculator
Select what you want to calculate, enter known values, and click Calculate.
What is Half‑Life?
Half‑life (t₁/₂) is the time required for a quantity to fall to half of its initial value. The term is most often used in nuclear physics to describe how quickly unstable atoms undergo radioactive decay, but it applies equally to any exponential decay process—from drug metabolism in the body to the fading of a glow‑in‑the‑dark sticker.
The Half‑Life Formula
N = N₀ × (1/2)t / t₁/₂
Where:
- N – remaining quantity after time t
- N₀ – initial quantity
- t – elapsed time
- t₁/₂ – half‑life of the substance
The equation shows that with every half‑life that passes, the amount left is halved. After n half‑lives, only (½)n of the original sample remains.
How to Use This Calculator
- Choose what you want to find: Remaining Quantity, Elapsed Time, or Half‑Life.
- Fill in the three known values (the field for the unknown will be locked).
- Make sure all time units are consistent (e.g., all in years, hours, or seconds).
- Click Calculate. The result appears in the highlighted field.
- Use Clear to reset all fields and start over.
Example Calculations
Example 1 – Find Remaining Quantity:
A radioactive sample starts with 200 grams and has a half‑life of 3 years. How much remains after 9 years?
Solution: N = 200 × (0.5)9/3 = 200 × 0.125 = 25 grams.
Example 2 – Find Elapsed Time:
A medication in the bloodstream has a half‑life of 4 hours. You begin with 50 mg. How long until only 10 mg remain?
Solution: t = 4 × log₂(50/10) = 4 × 2.3219 ≈ 9.29 hours.
Example 3 – Find Half‑Life:
A sample decays from 80 g to 5 g in 12 days. What is its half‑life?
Solution: t₁/₂ = 12 × ln(2) / ln(80/5) = 12 × 0.6931 / 2.7726 ≈ 3.0 days.
Applications of Half‑Life
- Carbon‑14 dating – archaeologists determine the age of organic artefacts.
- Nuclear medicine – doctors calculate when a radioactive tracer is safe.
- Pharmacokinetics – pharmacists design dosing schedules based on drug half‑life.
- Environmental science – scientists track pollutant degradation.
Mastering half‑life calculations opens the door to understanding countless natural and technological processes. Use our tool above to practice and solve your own problems instantly!
