Half-Life Calculator

Remaining amount or required time for radioactive decay and drug metabolism

Quick Answer

Half-Life Calculator: Remaining amount or required time for radioactive decay and drug metabolism. Remaining N = N₀ × (1/2)^(t ÷ T½).

N = N₀ × (1/2)^(t/T½). After 7 half-lives less than 1% remains; after 10, less than 0.1%.

Initial amount N₀

Half-life T½

Elapsed time t

Half-life and time must use the same unit (e.g. both years).

Remaining7.203958(7.2040%)

Decayed amount92.796042

Half-lives elapsed3.80

Remaining ratio7.20%

Calculation steps

1Half-lives elapsed n = t ÷ T½ = 20 ÷ 5.27 = 3.7951
2Remaining fraction = (1/2)ⁿ = (1/2)^3.7951 = 7.2040%
3Remaining amount = 100 × 0.072040 = 7.203958

Common half-lives

C-14T½ = 5730 yr

Co-60T½ = 5.27 yr

I-131T½ = 8.02 d

CaffeineT½ = 5 h

IbuprofenT½ = 2 h

Decay is exponential, never linear: each half-life removes half of what is left, so the last few percent take longest. Rule of thumb — after 7 half-lives under 1% remains (drug considered cleared, waste considered safe); radiocarbon dating works because C-14 decays at a known 5730-year rate in dead tissue.

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How to Use

Enter known quantities: fill values and confirm units in the Half-Life Calculator.
Instant solution: unknowns solve live with the formula shown transparently.
Use constant/material tables: standard physical constants and material data are listed on this page.
Compare conditions: change inputs to compare scenarios.

Key Points

Half-Life Calculator is a free online science & engineering tool — open and use, no sign-up.
All calculations run locally in your browser; your data never leaves the device.
Key capability: Remaining amount or required time for radioactive decay and drug metabolism.
Results come with formulas and reference tables so you can verify every number.

Formula & How It Works

Half-life decay

Remaining N = N₀ × (1/2)^(t ÷ T½)

Time needed t = T½ × log₂(N₀ ÷ N)

5 half-lives ≈ 3% left (drug "cleared") · 10 half-lives < 0.1%

FAQ

How do I use the Half-Life Calculator?

Open the page and fill in the input fields — results update automatically. Remaining amount or required time for radioactive decay and drug metabolism.

Are the results accurate?

Yes. Standard formulas and conversion factors are used and verified.

Is it free? Do I need to sign up?

Completely free. No registration, login or download required.

Does it work on mobile?

Yes. The responsive design works on phones, tablets and desktops.

Is my data saved?

No. Everything runs locally in your browser.

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Source & Updates

Based on CODATA recommended constants and standard physics formulas. Last updated: 2025-07

Last updated: 2026-08-06

Formulas and content on this page are reviewed by the YiJianSuan team. For reference only — official sources prevail.

Cite this page: YiJianSuan. Half-Life Calculator[EB/OL]. https://www.yijiansuan.com/en/c/science/half-life

Results provided by this tool are for reference only and do not constitute professional advice.

Common half-lives

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How to Use

Key Points

Formula & How It Works

FAQ

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Source & Updates

Common half-lives