Half-Life Calculator
Solve for Nₜ, N₀, time, or half-life · Decay chart · Step-by-step solution
☢️ Enter any three values - remaining quantity, initial quantity, time, and half-life - to solve for the fourth. Or use a Quick-Load isotope.
Half-Life · Mean Lifetime · Decay Constant Converter
Enter any one value to convert to the other two. The three constants describe the same decay process from different perspectives.
The Half-Life Formula
Half-life describes how a quantity undergoing exponential decay decreases over time. After each half-life period, the remaining quantity is halved. The three equivalent forms of the decay equation connect the four key variables:
Rearranging for each unknown:
All four forms are algebraically equivalent. The relationships between the three decay constants are:
Percent Remaining After N Half-Lives
The fraction remaining after N half-lives is (1/2)ᴺ. The table below shows how rapidly the quantity decreases:
| Half-Lives | Fraction | Percent Remaining | Percent Decayed |
|---|---|---|---|
| 0 | 1/1 | 100% | 0% |
| 1 | 1/2 | 50.000% | 50.000% |
| 2 | 1/4 | 25.000% | 75.000% |
| 3 | 1/8 | 12.500% | 87.500% |
| 4 | 1/16 | 6.250% | 93.750% |
| 5 | 1/32 | 3.125% | 96.875% |
| 7 | 1/128 | 0.781% | 99.219% |
| 10 | 1/1024 | 0.0977% | 99.902% |
| 20 | 1/1,048,576 | 0.0001% | ~100% |
Common Isotopes and Their Half-Lives
| Isotope | Half-Life | Decay Type | Primary Use / Context |
|---|---|---|---|
| Carbon-14 (¹⁴C) | 5,730 years | Beta (β⁻) | Archaeological and geological dating up to ~50,000 years |
| Tritium (³H) | 12.32 years | Beta (β⁻) | Luminescent watch dials, nuclear weapons triggers |
| Iodine-131 (¹³¹I) | 8.02 days | Beta + gamma | Thyroid cancer treatment, thyroid function imaging |
| Fluorine-18 (¹⁸F) | 109.8 minutes | Positron (β⁺) | PET scan tracer (FDG glucose analog) |
| Cesium-137 (¹³⁷Cs) | 30.17 years | Beta + gamma | Industrial gauging, Chernobyl/Fukushima contamination marker |
| Strontium-90 (⁹⁰Sr) | 28.8 years | Beta (β⁻) | Nuclear fallout, bone-seeking like calcium |
| Radium-226 (²²⁶Ra) | 1,600 years | Alpha | Historical use in luminous paints, sealed source radiotherapy |
| Radon-222 (²²²Rn) | 3.82 days | Alpha | Building air quality concern, lung cancer risk from accumulation |
| Plutonium-239 (²³⁹Pu) | 24,100 years | Alpha | Nuclear weapons, MOX fuel, long-term waste disposal concern |
| Uranium-238 (²³⁸U) | 4.47 billion years | Alpha | Uranium-lead geological dating, nuclear fuel |
| Potassium-40 (⁴⁰K) | 1.25 billion years | Beta + electron capture | Potassium-argon geological dating, natural radiation source in body |
| Uranium-235 (²³⁵U) | 703.8 million years | Alpha | Fissile material in nuclear reactors and weapons |
Carbon-14 Dating
Radiocarbon dating uses the known half-life of carbon-14 (5,730 years) to determine the age of organic materials. The method relies on the fact that cosmic rays continuously produce carbon-14 in the upper atmosphere by bombarding nitrogen-14 atoms. This carbon-14 is incorporated into carbon dioxide, absorbed by plants through photosynthesis, and then passes up the food chain to animals.
The ratio of carbon-14 to carbon-12 in a living organism remains approximately constant because the organism continuously exchanges carbon with the environment. Once the organism dies, it stops absorbing new carbon, and the carbon-14 that was present begins to decay at the known rate of t½ = 5,730 years.
The practical upper limit for carbon-14 dating is about 50,000 years, at which point the remaining carbon-14 concentration is too small to measure accurately. For older materials (millions to billions of years), geologists use isotopes with much longer half-lives, such as potassium-40 to argon-40 (1.25 billion years) and uranium-238 to lead-206 (4.47 billion years).