Half-Life Calculator
Leave the field you want to calculate blank.
How Does This Calculator Work?
This calculator solves for any unknown variable in the half-life exponential decay formula. Half-life is the time it takes for a substance to reduce to half of its initial amount.
N(t) = N₀ * (1/2)(t / T)
- N(t) is the quantity remaining after time 't'.
- N₀ is the initial quantity of the substance.
- t is the total time elapsed.
- T is the half-life of the substance.
By providing any three of these four values, the calculator uses logarithmic functions to rearrange the formula and solve for the unknown variable.
The Surprising History of Radiocarbon Dating
The concept of half-life became a revolutionary tool for archaeology and geology with the invention of radiocarbon dating in the late 1940s by American chemist Willard Libby. Libby hypothesized that cosmic rays constantly create a radioactive isotope of carbon, Carbon-14, in the atmosphere.
Living organisms continuously absorb this Carbon-14. When an organism dies, it stops taking in new carbon, and the Carbon-14 it contains begins to decay with a known half-life of about 5,730 years. By measuring the ratio of remaining Carbon-14 to stable Carbon-12 in an ancient artifact (like wood, bone, or cloth), Libby realized he could accurately determine its age. This groundbreaking application of half-life principles earned him the Nobel Prize in Chemistry in 1960 and transformed our ability to date the past.
Explore More Related Tools
While you're here, check out some of our other popular math and science calculators:
- Logarithm Calculator: Essential for solving half-life equations.
- Exponent & Root Calculator: Understand the principles of exponential decay.
- Scientific Calculator: For advanced scientific calculations.
- Percentage Calculator: Calculate remaining quantity as a percentage.
- Fraction Calculator: Work with fractional half-lives.
- Ratio Calculator: Compare initial and remaining quantities.
- Statistics Calculator: Analyze data from decay experiments.
- Standard Deviation Calculator: Measure the spread of data.
- Unit Converter: Convert between different units of time.
- Age Calculator: Explore concepts of time and duration.
Frequently Asked Questions (FAQ)
Do the units matter?
Yes, but only for consistency. The units for 'Initial Quantity' and 'Remaining Quantity' must be the same (e.g., grams, %, etc.). Similarly, the units for 'Half-Life' and 'Elapsed Time' must be the same (e.g., years, seconds, etc.).
Can I calculate the age of something with this?
Yes. To find the age of an artifact (the 'Elapsed Time'), you would need to know its initial quantity of a radioactive isotope (like Carbon-14), its current remaining quantity, and the half-life of that isotope.
Does a substance ever fully decay to zero?
Theoretically, no. The half-life model describes an exponential decay process where the quantity approaches zero but never mathematically reaches it. In reality, the quantity becomes so small that it is practically undetectable and insignificant.