Carbon Dating: Reading the Carbon-14 Clock

While an organism is alive it keeps its carbon-14 topped up by exchange with the atmosphere. When it dies the exchange stops and the carbon-14 decays, so the surviving fraction dates the death: age = (T / ln 2) · ln(N0 / N), where T is the half-life of carbon-14. Set what the laboratory measured, what the atmosphere held when the organism died, and how precise the measurement was. The panel reports the radiocarbon age — years before 1950, on the assumption that the atmosphere always held the 1950 level, which it did not. Turning that into a calendar date needs a published calibration curve, and this lab does not carry one.

Half-lives elapsed1.000 half-lives

Mean lifetime tau8,223 yearsmean lifetime: T divided by ln(2)

Decay constant0.00012160 per yeardecay constant: ln(2) divided by T

Practical limit of the methodabout 50,000 yearswhere the reading runs into laboratory background

The other two half-livesSame measurement on the other two half-lives: 5730 y: 5,730 · 5568 y: 5,570 radiocarbon years.

What the half-life means hereEach 5,700 years halves what is left: after 1.000 half-lives, 50.00 % of the starting carbon-14 is still there.

What the reading meansRadiocarbon years, not calendar years: the atmosphere has not always held exactly the 1950 level, so a published calibration curve is needed to turn this into a calendar date.

Fixed by the physics: age = -(T / ln 2) ln(f), with f the measured level divided by the atmospheric level when the organism died. Published half-lives: 5700 y (currently recommended) · 5730 y (Cambridge) · 5568 y (Libby, kept by convention so reported ages stay comparable). A radiocarbon age is not a calendar age.

Radiocarbon age age = -(T / ln 2) ln(f)

5,700 radiocarbon years BP

5,660 to 5,740 radiocarbon years BP

Uncertainty in the age

± 41 years

one standard deviation from the measurement alone

Carbon-14 remaining f = pMC / atmosphere

50.00 %

of the carbon-14 it started with

Half-life in use

5700 years

the currently recommended value

Measured carbon-1450.0 pMC

percent of the 1950 modern standard

Atmosphere when it died100 pMC

100 is the 1950 standard

Measurement uncertainty± 0.5 % of the reading

this moves the range, never the age

Half-life used

Load a sample

custom sample

Tip: load the ice-age bone, then drag the uncertainty from 1.0 % to 5.0 %. The age never moves — only the range does. Then press 5568 y: the age changes, but the measurement does not.