Half-Life ↔ Decay Constant
t½ = ln(2) / k. Convert between half-life and decay constant; predict remaining fraction.
Result
k
1.2097e-4
Fraction remaining after t = 5730: 50.0000%.
- Half-life t½5,730.000000
- Decay constant k1.209681e-4
- Elapsed time t5730
- Half-lives elapsed1.0000
- Fraction remaining0.50000000
- % remaining50.0000%
Step-by-step
- t½ × k = ln(2) ≈ 0.6931.
- k = ln(2) / t½ = 1.2097e-4.
- N(t)/N₀ = e^(−kt) = e^(−0.6931) = 50.0000%.
How to use this calculator
- Pick t½ or k as input.
- Set elapsed time to predict remaining fraction.
About this calculator
Half-life is the time for half a quantity to decay (radioactive nuclei, drug clearance, etc.). Related to decay constant by t½ × k = ln(2) ≈ 0.6931. After n half-lives, fraction remaining = (1/2)ⁿ. Common: ¹⁴C t½ = 5730 yr (carbon dating). U-238: 4.5 billion yr (Earth age). Tc-99m (medical imaging): 6 hours.
Frequently asked
After one half-life: N/N₀ = ½ = e^(−kt½). Take ln: −ln(2) = −kt½ → t½ = ln(2)/k.
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