Case 1
- Half-life
- 5730
0.0001211/t
Open with these valuesDecay Constant Calculator
0.000121per time unit
Result: 0.000121 per time unitThe decay constant is ln 2 divided by the half-life, roughly 0.693 ÷ t½. It is the chance per unit of time that any one atom decays. Carbon-14, with a half-life of 5730 years, has λ ≈ 0.000121 per year. The unit is free: λ comes out per whatever unit you entered.
Worked examples
Case 2
- Half-life
- 8.02
0.0864271/t
Open with these valuesCase 3
- Half-life
- 12.32
0.0562621/t
Open with these valuesHow it's calculated
λ = ln(2) ÷ t½
- StepEnter the half-life in any time unit — years, days, seconds.
- StepDivide ln 2, about 0.693, by that number.
- ResultRead λ per the same unit you entered.
Reference table
| Half-life | Isotope | λ (per time unit) |
|---|---|---|
| 1 | One time unit: λ is ln 2 itself | 0.693147 |
| 2 | Twice as long, half the constant | 0.346574 |
| 8.02 | Iodine-131, in days | 0.086427 |
| 12.32 | Tritium, in years | 0.056262 |
| 5730 | Carbon-14, in years | 0.000121 |
Questions
How do I calculate the decay constant?
Divide the natural logarithm of two by the half-life: λ = ln(2) ÷ t½, where ln 2 ≈ 0.693. The constant comes out in the inverse of whatever time unit you used. Carbon-14 has a half-life of 5730 years, so λ ≈ 0.000121 per year.
What is the decay constant?
The decay constant λ is the probability per unit of time that any single atom of an isotope decays. A larger λ means a faster-decaying, less stable isotope. It is the constant that links the half-life, the mean lifetime and the decay law N(t) = N₀ · e^(−λt).
How is it related to the half-life?
Inversely: λ = ln(2) ÷ t½, so a longer half-life means a smaller constant. The same equation runs backwards to recover the half-life from a known constant, t½ = ln(2) ÷ λ.
What can I do with λ once I have it?
Two things, mainly. Put it into N(t) = N₀ · e^(−λt) to get the amount left at any time, or take its reciprocal for the mean lifetime τ = 1 ÷ λ — the average time an atom survives, always about 1.44 times the half-life.
What units does the decay constant use?
Inverse time, matching whatever unit you gave the half-life in. A half-life in years gives λ per year, one in seconds gives λ per second. Keep every later time value in that same unit so the product λt stays dimensionless.
Why does the formula use ln 2?
The half-life is defined as the time for the amount to fall to one half. Setting e^(−λt) = ½ and solving gives λ · t½ = ln 2. That single constant, about 0.693, converts between half-life and decay constant in either direction.
Sources and last check
Information, not professional advice.