Half-Life Calculator
After 11,460 years, two half-lives, 100 g of carbon-14 decays to 25 g, from N = N₀(½)^(t/T½).
Use the same time unit as the half-life, or pick units for both.
Carbon-14: 5730 years; iodine-131: 8.02 days.
25
- Fraction remaining N/N₀
- 0.25
- Half-lives elapsed t/T½
- 2
- Decay constant λ = ln 2 / T½
- 0.0001209680943 s⁻¹
- Mean lifetime τ = T½ / ln 2
- 0.0002619540961 years
Step-by-step solution
- N = N₀ × (½)^(t ÷ T½)
- N = 100 × (½)^(11460 ÷ 5730)
- N = 25
Half-Life Formula
N = N₀ (½)^(t / T½)
N amount left, N₀ initial amount, t elapsed time, T½ half-life; λ = ln 2 / T½
Worked Example
100 g of carbon-14 (half-life 5730 years) after 11,460 years:
- N = N₀ × (½)^(t ÷ T½)
- N = 100 × (½)^(11460 ÷ 5730)
- N = 25
Half-lives elapsed t/T½: 2 · Decay constant λ = ln 2 / T½: 0.0001209680943 s⁻¹ · Mean lifetime τ = T½ / ln 2: 0.0002619540961 years
Half-lives to know
Carbon-14: 5730 years; iodine-131: 8.02 days; cobalt-60: 5.27 years; uranium-238: 4.47 billion years. After 10 half-lives less than 0.1 % remains.
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Frequently asked questions
How does carbon dating work?
Living things keep the C-14 level of the atmosphere; after death it decays with a 5730-year half-life. Measuring the fraction left and choosing “time elapsed” gives the age.
Does it work for drugs and other decays?
Yes, for anything that decays exponentially: drug elimination, capacitor discharge or cooling under some conditions, as long as the half-life is constant.
Sources
- The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
Cite this page
APA
Scientific Converters. (2026, October 15). Half-Life Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/half-life-calculator/
IEEE
Scientific Converters, "Half-Life Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/half-life-calculator/