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Radioactive Half-Life Calculator - t½

Calculate radioactive half-life, decay constant, remaining quantity, elapsed time, and activity. Physics calculator for nuclear chemistry, radiometric dating, pharmacology, and health physics. Supports Carbon-14 dating and medical isotope decay calculations.

Radioactive Half-Life Formula

N = N₀ × (½)ⁿ | t½ = ln(2) / λ | N = N₀ × e^(-λt)

Variables:

  • NRemaining Amount
    Amount of remaining radioactive substance(e.g.: N = 50 atoms)
  • N₀Initial Amount
    Initial amount of radioactive substance(e.g.: N₀ = 100 atoms)
  • t½Half-Life
    Time required for half of the substance to decay(e.g.: t½ = 5,700 years (C-14))
  • nNumber of Half-Lives
    How many half-lives have occurred(e.g.: n = 2 (2 t½))
  • λDecay Constant
    Radioactive decay rate(e.g.: λ = 0.1217 /year)
  • tTime
    Time elapsed(e.g.: t = 10 years)

How to Use the KalkuLab Half-Life Calculator

  1. 1

    Select Calculation Mode

    Choose one of 4 modes: Remaining After n Half-Lives, General Decay, Calculate Half-Life, or Number of Half-Lives

  2. 2

    Enter Input Values

    Input the known values according to the selected mode

  3. 3

    Calculate Result

    Click calculate to get the result

  4. 4

    Analyze Results

    View remaining amount, percentage, and other decay information

Examples

Carbon-14 Remaining After 2 Half-Lives

Problem:

If there are initially 1000 C-14 atoms, how many remain after 2 half-lives?

Solution:
  1. 1.Given: N₀ = 1000 atoms, n = 2
  2. 2.Formula: N = N₀ × (½)ⁿ
  3. 3.Calculate: N = 1000 × (½)²
  4. 4.Result: N = 1000 × ¼ = 250 atoms
Result:250 atoms

After 2 half-lives, only 25% of the original C-14 remains

Calculate Half-Life from Decay Constant

Problem:

If the decay constant λ = 0.1217/year, what is the half-life?

Solution:
  1. 1.Given: λ = 0.1217/year
  2. 2.Formula: t½ = ln(2) / λ
  3. 3.Calculate: t½ = 0.693 / 0.1217
  4. 4.Result: t½ = 5.69 years
Result:5.69 years

The half-life of this element is 5.69 years

Frequently Asked Questions

What is radioactive half-life?
Half-life is the time required for half of the initial amount of a radioactive substance to decay into a more stable isotope through radioactive decay.
Why is radioactive decay stochastic?
Radioactive decay is random at the individual atom level, but follows predictable statistical patterns for large numbers of atoms. You cannot predict when a specific atom will decay.
What are real-world applications of half-life?
Used in radiocarbon dating (C-14), nuclear medicine (cancer treatment), industrial tracing, and geological research (determining rock age).
Is half-life the same for all isotopes?
No. Each radioactive isotope has a different half-life, from microseconds (very unstable isotopes) to billions of years (such as U-238).
What is the relationship between half-life and decay constant?
Half-life (t½) is inversely proportional to the decay constant (λ). The larger λ, the faster the decay and the smaller t½. Formula: t½ = ln(2) / λ

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References