Half-life calculator (radioactive decay)
Pick what you are looking for, then fill in the other three values. Times must share one unit (years, hours…), and amounts too (grams, %, atoms…).
Result
25Amount left N
- Number of half-lives elapsed
- 2
- Share left
- 25%
- Decay constant λ (per time unit)
- 0.13862944
- Mean lifetime τ = 1 ÷ λ
- 7.213475
- After 1 half-life(s), at t = 5: 50 left.
- After 2 half-life(s), at t = 10: 25 left.
- After 3 half-life(s), at t = 15: 12.5 left.
- After 4 half-life(s), at t = 20: 6.25 left.
- After 5 half-life(s), at t = 25: 3.125 left.
Inputs
- I am looking for
- Amount left
- Starting amount N₀
- 100
- Time elapsed t
- 10
- Half-life T½
- 5
How it is calculated
N = N₀ × (1/2)^(t ÷ T½).
Result
Amount left N
- Number of half-lives elapsed
- 2
- Share left
- 25%
- Decay constant λ (per time unit)
- 0.13862944
How it is calculated
- N = N₀ × (1/2)^(t ÷ T½).
- t = T½ × ln(N₀ ÷ N) ÷ ln 2.
- T½ = t × ln 2 ÷ ln(N₀ ÷ N).
- N₀ = N ÷ (1/2)^(t ÷ T½). Constant λ = ln 2 ÷ T½.
Example
100 g, half-life 5 years, after 10 years: 2 half-lives, 100 ÷ 4 = 25 g left. λ ≈ 0.138629 per year.
Good to know
- Pure exponential model: fits radioactivity, drug elimination or any decay of this kind.
- The amount left must be smaller than the starting amount to find the time or the half-life.
- The tool does not convert units: use the same time unit everywhere.
Frequently asked questions
What is this tool used for?
Pick what you are looking for, then fill in the other three values. Times must share one unit (years, hours…), and amounts too (grams, %, atoms…).
How is the result calculated?
N = N₀ × (1/2)^(t ÷ T½).
What should I check before using the result?
Pure exponential model: fits radioactivity, drug elimination or any decay of this kind.