Half-Life ↔ Decay Constant

t½ = ln(2) / k. Convert between half-life and decay constant; predict remaining fraction.

Result

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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

Why ln(2)?+

After one half-life: N/N₀ = ½ = e^(−kt½). Take ln: −ln(2) = −kt½ → t½ = ln(2)/k.

Carbon dating?+

Living things have constant ¹⁴C/¹²C ratio. After death, ¹⁴C decays (t½ = 5730 yr). Measure ratio → date.

Half-life examples?+

I-131: 8 days. Tc-99m: 6 hr. Ra-226: 1602 yr. U-238: 4.47 By. ¹⁴C: 5730 yr.

Drug pharmacokinetics?+

Drug elimination often follows first-order kinetics with characteristic half-life. After 5 half-lives: ~3% remaining.

Difference from radioactive-decay calc?+

Half-life calc focuses on t½/k. Decay calc takes k + t for N(t) directly. Same physics.

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