ChemBench

Radioactive Decay Calculator

How much is left, given the half-life?

Initial amount

Half-life (years)

Elapsed time (years)

Remaining amount

What you entered

Initial amount: 100Half-life (years): 5730Elapsed time (years): 11460

1
Number of half-lives elapsed
11460 ÷ 5730= 2
2
N = N₀ × (½)^(t ÷ half-life)
100 × (½)^2= 25

Result

Remaining amount: 25

After 11460 years, 25 out of the original 100 remains.

How much remains after each half-life

Every half-life removes half of whatever is left. Starting from 100 units, the sequence is 50, 25, 12.5, and so on, regardless of the isotope.

Half-lives elapsed	Time (carbon-14, 5,730 yr)	Remaining from 100
0	0 years	100.000
0.5	2,865 years	70.711
1	5,730 years	50.000
2	11,460 years	25.000
3	17,190 years	12.500
4	22,920 years	6.250

Carbon-14 dating becomes unreliable beyond about 50,000 years, roughly nine half-lives, because too little activity remains to measure. Half a half-life leaves 70.7%, which is 1 over the square root of 2, not 75%.

Every half-life cuts the amount in half

Radioactive decay follows N = N₀ × (½)^(t/half-life) — after one half-life, half remains; after two, a quarter; after three, an eighth, and so on, regardless of the starting amount.

The basis of carbon dating

Carbon-14 dating uses exactly this formula, working backward from the fraction of carbon-14 remaining in an organic sample to determine how many half-lives (and therefore how many years) have passed since the organism died.

Frequently asked questions

I have 100 g of a substance with a half-life of 8 days — how much is left after 24 days?

24 days = 3 half-lives. Remaining = 100 × (1/2)³ = 100 × 0.125 = 12.5 g.

How do I use this for carbon dating?

Carbon-14 has a half-life of 5,730 years. If a sample has 25% of its original C-14, it has gone through 2 half-lives: 2 × 5,730 = 11,460 years old. Enter the known fraction remaining and the half-life to calculate elapsed time.

What is the difference between half-life and decay constant?

They are inversely related: decay constant λ = ln(2)/half-life. The half-life is more intuitive for communication, but the decay constant appears in the exponential decay equation N = N₀e^(-λt).

Can I use this for non-radioactive exponential decay?

Yes. The same math applies to drug elimination from the body, population decline, and capacitor discharge — any process where the rate of decrease is proportional to the current amount.