How long until something loses half its value? This half-life calculator tells you how many periods it takes for a quantity to decay to 50% of its starting value given a constant rate of decline.
Half-Life Calculator
Using the half-life calculator
Enter the Rate per period as a percentage. For decay, use a negative rate (e.g., -5 for 5% decline per period). The calculator instantly shows how many periods until the quantity reaches half its original value.
The period can be whatever timeframe matches your rate: years, months, days – the math works the same.
The half-life formula
The formula for half-life is:
t_{1/2} = \frac{\ln(0.5)}{\ln(1 + r)} = \frac{-\ln(2)}{\ln(1 + r)}Where r is the rate per period as a decimal (e.g., -5% = -0.05).
Since ln(0.5) = -ln(2), the half-life formula is essentially the doubling time formula with a sign flip.
Example: depreciation at 15% per year
How long until a car loses half its value at 15% annual depreciation?
t_{1/2} = \frac{\ln(0.5)}{\ln(1 - 0.15)} = \frac{-0.693}{-0.163} \approx 4.27 \text{ years}At 15% depreciation, your car loses half its value in about 4.3 years.
The Rule of 70 for decay
Just like the Rule of 72 for doubling, there's a quick approximation for half-life:
\text{Half-life} \approx \frac{70}{\text{decay rate \%}}At 10% decay, half-life is roughly 70 / 10 = 7 periods. At 5% decay, about 70 / 5 = 14 periods. The shorthand works best between roughly 5 and 15%.
We use 70 instead of 72 because ln(2) × 100 ≈ 69.3, and for decay (where the base is less than 1), the approximation works slightly better with 70.
Applications of half-life
Half-life appears in many contexts:
- Radioactive decay: The original use – how long until half the atoms decay ☢️. (You figure out how it relates to new versions of Half Life coming out!).
- Asset depreciation: Cars, equipment, and other depreciating assets.
- Drug metabolism: How long until half a medication leaves your system.
- Population decline: Species or regional population decreases.
- Market share erosion: How fast a company loses ground to competitors. Relatively, that is - the market could be expanding, of course.
Half-life vs. doubling time
Half-life and doubling time are roughly – but not perfectly – mirror images. If something grows at +7% per period, it doubles in about 10.2 periods. If it declines at -7% per period, it halves in about 9.6 periods.
(Vaseline on the mirror, I guess.)
The asymmetry exists because the math of exponential change isn't symmetric: losing 7% of 100 gives you 93, but gaining 7% of 93 only gives you 99.5 – not quite back to 100.
