Centuries to Millenniums

A Half-Life Printed in Years, a Sample Age Quoted in Millennia

Open a decay table and every half-life is a plain number of years: 5 730 for carbon-14, 1 600 for radium-226, 75 400 for thorium-230. Open the site report that used them and nobody speaks that way. The occupation layer is "roughly six millennia old" and the phase above it is "three centuries later". The measurement and the interpretation sit two orders of magnitude apart, and somebody has to move between them before a date means anything at all.

Centuries are the resolution excavation argues at. Millennia are the resolution the isotope works at. Getting from one to the other is arithmetic rather than judgement, and doing it early tends to settle the question of whether the chosen nuclide can reach the age in front of you.

Conversion factor: 1 c = 100 yr and 1 mil = 1 000 yr, so 1 c = 0.1 mil — divide centuries by ten. The carbon-14 half-life of 5 730 yr is 57.3 c, which comes back as 5.73 mil.

Where the Two Scales Meet in a Dating Report

Decay constants are tabulated in years

Nuclear data tables publish a half-life in years with an uncertainty attached: 5 730 ± 40 yr for carbon-14. Nothing in the physics prefers that unit; it is what the measuring community settled on.

Stratigraphy is argued in centuries

Floors, hearths and rebuilds are separated by decades or a century or two. That is the grain at which a site narrative is written, and it is finer than any single measurement on a sample can deliver.

Decay curves are read in millennia

Plot surviving activity against elapsed time and the usable stretch of a carbon-14 curve runs out somewhere near 50 mil. Millennia keep that axis to two digits instead of five.

The error bar converts with the value

A quoted ± 40 yr becomes ± 0.4 c and ± 0.04 mil. Rescaling never sharpens a figure, and a converted number should carry no more digits than its uncertainty can support.

Rescaling a Half-Life Before You Compare It

Half-lives arrive in whatever unit the source happened to use. Putting them all on one scale is the step that decides whether a nuclide can even reach the age you are trying to pin down.

Key in the half-life you are working with

Put 57.3 in the century box for carbon-14, or 754 for thorium-230, and the millennium figure appears as the digits land. A comma serves as the decimal mark, so 57,3 lifted from a European data sheet needs no editing first.

Hold it against the age you are chasing

Set the converted half-life beside the span you want dated. A layer around 30 mil old is a little over five carbon-14 half-lives, which is workable; one at 300 mil is far outside anything that nuclide can say something useful about.

Turn it round when the paper counts in millennia

The swap control (↔) runs the pair as mil → c, so a half-life stated as 32.76 mil comes back as 327.6 c for a comparison table built in century columns.

Take the bare digits into the decay sheet

Copying either field yields the number with no unit and no space grouping, which is what a cell computing a fraction of one half raised to a power needs. Selecting the value and pressing Ctrl + C behaves the same way.

Mind which year is meant: half-lives are normally published in Julian years of 365.25 d, while this tool works from the Gregorian mean of 365.2425 d. The gap is about 0.002 %, invisible beside a ± 40 yr counting error — and a reminder that no conversion adds precision the experiment never had.

Isotope Half-Lives on Both Scales

A selection of the nuclides used to put numbers on the past, each half-life given as centuries and as millennia together with the material it is normally applied to. The list runs from the short end, where a half-life is a matter of a few centuries, out to nuclides that outlast the whole of human prehistory.

Isotope	Half-life (centuries)	Half-life (millennia)	Typically used to date
Argon-39	2.69 c	0.269 mil	Groundwater and glacier ice a few centuries old
Radium-226	16 c	1.6 mil	Uranium-series work on young carbonate deposits
Carbon-14	57.3 c	5.73 mil	Charcoal, wood, bone and other once-living material
Protactinium-231	327.6 c	32.76 mil	Deep-sea sediment and coral, paired with thorium-230
Thorium-230	754 c	75.4 mil	Cave formations, reef corals, raised beaches
Uranium-234	2 455 c	245.5 mil	The parent side of uranium-series carbonate dating
Chlorine-36	3 010 c	301 mil	Rock surfaces exposed by retreating ice, and old groundwater
Beryllium-10	13 870 c	1 387 mil	Erosion rates and surface exposure ages

What the two middle columns really encode is reach. A method stays usable for roughly eight to ten halvings before the surviving signal disappears into the laboratory background, which is why carbon-14 at 5.73 mil gives out near 50 mil while thorium-230 at 75.4 mil keeps working across several hundred. Picking a nuclide is mostly picking a half-life the target age fits comfortably inside.

What the Converter Handles in Dating Work

Both boxes stay live

Nothing needs submitting: edit one side and the other settles at once, which suits running down a column of nuclides while a data table is open next to it.

Direction follows the source

One press flips the pair, so a value taken from a paper that counts in millennia does not have to be retyped in the opposite orientation.

Fifteen units behind a search box

The dropdowns cover everything from nanoseconds to millennia and filter as you type — handy when a short-lived tracer belongs in days rather than on this page's scale.

Numbers leave undecorated

Copying hands over digits alone, unspaced and unlabelled, ready for the exponent arithmetic that turns an age into a surviving fraction.

Questions From the Dating Lab

How many millennia is one carbon-14 half-life?

5.73 mil. The accepted value is 5 730 yr, which is 57.3 c and, divided by ten, 5.73 mil. A second figure is still in circulation: Libby's original 5 568 yr, or 5.568 mil, which laboratories deliberately keep using when they publish a conventional radiocarbon age so that decades of older results stay comparable. The two differ by around 3 %, and that discrepancy is absorbed during calibration rather than at the counting stage. Use 5 730 yr for your own arithmetic; expect a lab's uncalibrated number to be built on 5 568.

Why does radiocarbon run out of usable signal near 50 000 years?

50 000 yr is 500 c, or 50 mil, and against a half-life of 5.73 mil that works out at about 8.7 halvings. Each one removes half of what remains, so 8.7 of them leave roughly 0.2 % of the starting activity. At that level the count coming off the sample is barely distinguishable from the laboratory background and from any modern carbon introduced during collection or preparation — a fraction of a per cent of fresh contamination mimics a genuine signal exactly. Careful pretreatment pushes the ceiling towards 55 mil, but nothing recovers what has already decayed.

How do I work out how many half-lives fit inside a span quoted in millennia?

Divide the span by the half-life once both sit on the same scale, then raise one half to that power. A deposit thought to be 30 mil old, tested with carbon-14 at 5.73 mil, gives 30 ÷ 5.73 = 5.24 halvings, and one half to the power 5.24 is about 0.027 — just under 3 % of the original activity surviving. Run the same sum with thorium-230 at 75.4 mil and you get 0.4 halvings and around 76 % remaining, which is why that nuclide is wasted on a sample so young: the change is barely bigger than the measurement error.

Does a date given in BP line up with centuries counted from today?

Not exactly. BP means before present, and "present" was fixed at 1950 CE, the year chosen because atmospheric weapons testing after it wrecked the natural carbon-14 baseline. So 3 000 BP is 30 c before 1950, landing around 1050 BCE — not 30 c before whatever year you happen to be reading in. Moving a BP figure into a calendar era means subtracting 1950 and then allowing for the fact that no year zero exists between 1 BCE and 1 CE. Beyond a few tens of millennia the offset stops mattering, but for the last few thousand years it is already three-quarters of a century.

Why does each isotope only cover a limited window of the past?

A method needs enough decay to measure and enough parent left to detect. Below roughly a tenth of a half-life the change in activity is smaller than the counting error; above eight to ten half-lives there is effectively nothing left to count. Those two limits turn a half-life into a working window. Argon-39 at 0.269 mil is applied to groundwater and ice a few centuries old, carbon-14 at 5.73 mil reaches back around fifty millennia, and thorium-230 at 75.4 mil serves the last few hundred. Choosing a nuclide really means choosing a window, and converting the half-life is how you check your sample falls inside one.