Half-Life ↔ Decay Constant
t½ = ln(2) / k. Convert between half-life and decay constant; predict remaining fraction.
Result
Loading calculator…
—
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.
Related calculators
Radioactive Decay (N = N₀ e^(−kt))
Quantity remaining after time t given decay constant k or half-life.
Atomic Mass from Isotopes Calculator
Σ (isotope mass × abundance fraction). Periodic-table atomic mass from isotope mix.
Ideal Gas Law (PV = nRT)
Solve for any of P, V, n, T given the other three. R = 8.314 J/(mol·K).
Henderson-Hasselbalch (Buffer pH)
pH = pKa + log([A⁻]/[HA]). Predict buffer pH from acid + conjugate base concentrations.
Wavelength ↔ Frequency Calculator
c = λ × ν. Wavelength in vacuum from frequency or vice versa. c = 3×10⁸ m/s.
Logarithm Calculator
log_b(x) for any base b > 0, b ≠ 1, x > 0. Common bases shown side-by-side.