Half-Life Calculator

What this tool does

Calculate half-life instantly in your browser — the published formula, worked locally with no data sent anywhere. Decay is memoryless — each half-life halves whatever remains, regardless of history. Carbon dating assumes the sample's initial ¹⁴C matched the atmosphere and the system stayed closed; practical dating reaches back about 50,000 years.

How to use the Half-Life Calculator

1. Enter or select mode.
2. Enter or select starting amount n₀ (any unit — g, atoms, %).
3. Enter or select half-life (same time unit as elapsed time).
4. Enter or select elapsed time.
5. Enter or select carbon-14 remaining vs a living sample (%).
6. Read the calculated result; change any measurement to compare alternatives.

Formula

exponential decay: N(t) = N₀ × (½)^(t / T½), with decay constant λ = ln 2 / T½. Carbon dating inverts it: age = −ln(fraction remaining) / λ using the ¹⁴C half-life of 5,730 years.

mode

Mode

n0

Starting amount N₀ (any unit — g, atoms, %)

thalf

Half-life (same time unit as elapsed time)

time

Elapsed time

pct

Carbon-14 remaining vs a living sample (%)

Decay is memoryless — each half-life halves whatever remains, regardless of history. Carbon dating assumes the sample's initial ¹⁴C matched the atmosphere and the system stayed closed; practical dating reaches back about 50,000 years.

Worked example

For half-life calculator, the following measurements illustrate the exact method: Mode: decay; Starting amount N₀ (any unit — g, atoms, %): 100; Half-life (same time unit as elapsed time): 5; Elapsed time: 10; Carbon-14 remaining vs a living sample (%): 25.

Results explained

Amount remaining

Amount remaining from the formula above. Decay is memoryless — each half-life halves whatever remains, regardless of history. Carbon dating assumes the sample's initial ¹⁴C matched the atmosphere and the system stayed closed; practical dating reaches back about 50,000 years.

Amount decayed

Amount decayed from the formula above. Decay is memoryless — each half-life halves whatever remains, regardless of history. Carbon dating assumes the sample's initial ¹⁴C matched the atmosphere and the system stayed closed; practical dating reaches back about 50,000 years.

Percent remaining (%)

Percent remaining (%) from the formula above. Decay is memoryless — each half-life halves whatever remains, regardless of history. Carbon dating assumes the sample's initial ¹⁴C matched the atmosphere and the system stayed closed; practical dating reaches back about 50,000 years.

Half-lives elapsed

Half-lives elapsed from the formula above. Decay is memoryless — each half-life halves whatever remains, regardless of history. Carbon dating assumes the sample's initial ¹⁴C matched the atmosphere and the system stayed closed; practical dating reaches back about 50,000 years.

Decay constant λ (per time unit)

Decay constant λ (per time unit) from the formula above. Decay is memoryless — each half-life halves whatever remains, regardless of history. Carbon dating assumes the sample's initial ¹⁴C matched the atmosphere and the system stayed closed; practical dating reaches back about 50,000 years.

Frequently asked questions