Dating with Carbon — Radiocarbon Dates, Read with an Hourglass and Tree Rings

A Piece of Charcoal from a Hearth

When you put out a campfire at a campsite, pitch-black pieces of charcoal are left behind. A fire someone lit in a cave thousands of years ago leaves charcoal behind in the exact same way. If an excavator picked up a piece of charcoal like that, how could they tell how many years ago that fire burned?

Charcoal does not have a date written on it. A hearth from before writing existed has no records left beside it either. There is a tool most widely used for this kind of situation. Radiocarbon dating is a method that measures the radioactive carbon remaining in something that was once alive, and counts backward to find how much time has passed since it stopped taking in new carbon. It is the method most frequently used when measuring things from the past several tens of thousands of years (PMID 42720026).

This article carries a single piece of charcoal all the way through. This charcoal and the numbers attached to it are examples made for explanation. Beside it, we place an hourglass. If it is an hourglass whose speed of falling sand is known, you can look at the remaining sand and count backward to when it was flipped. Measuring age with carbon is this exact kind of calculation, and where this calculation goes astray can also be seen through the same hourglass.

Sand That Fills While Alive

Charcoal used to be wood. While alive, trees breathe in carbon dioxide from the air to build their bodies, and animals and humans that eat those trees take that same carbon into their bodies too. The carbon in the air contains a very small amount of a special kind of carbon.

Carbon-14 is carbon that is created when particles pouring down from space high in the sky collide with nitrogen in the air, and over time, turns back into nitrogen on its own and disappears. Carbon-14 created in the sky spreads into the air, the ocean, and living organisms along the cycle of carbon (PMID 34735228).

Because animal and human bodies continuously receive new carbon by eating and breathing, the carbon-14 inside the body stays filled at almost the same proportion as the air. When they die, the process of receiving new carbon stops, and from that moment on, the carbon-14 inside the body only decreases.

Trees are a bit different. Trees add a new layer of tree rings year by year, and once a layer captures that year's carbon, that layer no longer receives new carbon (DOI: 10.1017/s0033822200013898). Even while the tree is alive, the carbon-14 in each individual tree ring starts decreasing from the year that layer was formed.

Translated into an hourglass, it works like this. Even while alive, the sand drops bit by bit, but as much as drops is immediately refilled from the air, so the top chamber is always full. The moment the filling hand stops — when an animal dies, or for a tree ring, the year that layer was formed — from that point on, the sand only drops. This hourglass is somewhat unusual because the dropping speed is determined by the remaining amount. The half-life is the time it takes for half of the initial amount to disappear. Once the half-life passes once, half remains in the top chamber, twice leaves one-quarter, and three times leaves one-eighth. The length of the half-life is a fixed value for carbon-14, so it is the same whether it is charcoal, bone, or a seed.

Therefore, if the carbon-14 in charcoal is half of the original amount, we can count that as much time as one half-life has passed since that tree took in that carbon.

Because the carbon-14 that was being filled decreases by half every half-life after the filling stops, the remaining amount points to the time that has passed.

The Machine That Counts the Remaining Sand

The device used to measure the remaining amount has changed. The one primarily used now is accelerator mass spectrometry. Accelerator mass spectrometry is a device that separates carbon atoms in a sample by weight, measuring as a ratio how much carbon-14 is mixed in compared to other carbon (DOI: 10.1017/s0033822200040121). The calculation that turns this measured ratio into an age also includes a calculation to subtract contamination mixed into the sample.

After this device was introduced, the amount of sample needed decreased and measurements became more precise (DOI: 10.1002/2017rg000588). This means measurements can now be made with even a small crumb of charcoal.

An hourglass has an end. After the half-life passes several times, the sand remaining in the upper chamber becomes too little to count anymore. The limit this method reaches is about 55,000 years ago (PMID 34735228). Things older than that, such as fossils or dinosaur bones hundreds of thousands of years old, cannot be measured with this hourglass.

At First, the Amount of Sand Differed Each Year

The counting done so far hides an assumption. It assumes that in the year a piece of charred wood grew its tree ring, carbon-14 in the air was always the same as a set standard value. Laboratories measure the age of a sample by comparing its ratio to this standard value (DOI: 10.1017/s0033822200040121). In terms of an hourglass, it is the assumption that the upper chamber always contained the same amount of sand when flipped.

This assumption is incorrect. Measurements of trees from the past 2,000 years, whose exact years are known through tree rings, show that carbon-14 in the air fluctuated by several percent. The fluctuations on a century scale were caused by changes in the intensity of particles pouring in from space, which changed the amount of carbon-14 being produced (DOI: 10.1029/jz070i023p05937). In the distant past, there are also sections where this wavering appears much larger. Between 48,000 and 40,000 years ago, a large shift in Earth's magnetic field caused more carbon-14 to be produced, making the radiocarbon clock in this section appear to run nearly twice as fast as the actual time (PMID 32817536). While 1 year passes on the calendar, the age measured by carbon advances by nearly 2 years.

Therefore, the number calculated by comparing against the standard value is not yet a year. Radiocarbon age calibration is the task of converting the value obtained by measuring carbon-14 left in charcoal or seeds into an actual year, and because the share of carbon-14 among atmospheric carbon differed across eras, a year does not come out simply by calculating. All radiocarbon ages must go through this calibration (PMID 42720026).

A ruler is needed for this conversion. The first ruler is tree rings. As seen earlier, each layer of a tree ring captures that year's carbon, so measuring tree rings of known years layer by layer reveals the carbon-14 in the air for those years. Tree trunks buried in river gravel or swamp beds and submerged in water survive well even after thousands of years, and by stringing such trees together, an oak and pine tree ring chronology spanning 11,000 years was built in Germany (DOI: 10.1017/s0033822200013898).

In places where trees do not reach, the bottom of a lake serves as the ruler. At the bottom of Lake Suigetsu in Japan, stripes stack up one layer each year, so counting the layers yields the year. Measuring the carbon-14 of terrestrial plant fragments recovered from between the layers and pairing it with that year creates a ruler identical to the tree rings (DOI: 10.1017/s0033822200034627).

A calibration curve is a reference table that connects how much carbon-14 was in the air each year, obtained by measuring the carbon-14 of samples whose ages are already known. The international standard is created by a research consortium called IntCal, and it is periodically revised as new data accumulates (PMID 42720026). The 2020 edition extended the curve used for Northern Hemisphere land samples back to 55,000 years ago. Compared to the previous edition, recent times remained nearly identical, but on the older side, the calibrated ages shifted by up to several centuries (DOI: 10.1017/qua.2020.42).

Returning to our charcoal, the first number the laboratory produces is "the age calculated assuming the air was always equal to the standard value." This number must be checked against the calibration curve to find which year's tree ring has the same value, and only then does the calendar year emerge.

The laboratory's first number is not yet a year; it must be checked against a ruler made of tree rings and lake layers of known age to become a year.

Not a Single Year, But a Range

Even when you apply a ruler, a single year cannot be pinned down. Measurements always come with errors, and even the ruler is not straight. Because the calibration curve does not run straight in one direction but rises, falls, and meanders, there is a limit to how much a single piece of charcoal can narrow down a year (DOI: 10.1017/s0033822200035967). When it gets caught in a meandering section of the curve, the same value matches two different time periods, so the calibrated year sometimes comes out as a range split into multiple pieces (DOI: 10.1017/qua.2020.42).

That is why radiocarbon dates come out as a range, not a single year. The answer is not "some specific BC year" but "somewhere within this section."

There is a way to narrow down the range. Let us imagine we dug up a cave floor and found that three layers of hearths are stacked on top of one another. The bottom hearth would have been lit before the middle one, and the middle one before the top one. A Bayesian chronological model is a calculation that narrows down the range of each date by feeding in sequence information such as "this layer accumulated before that layer" alongside multiple measurement values. This calculation, which weaves together multiple measurements into sequences and bundles, is becoming a core tool in radiocarbon research (DOI: 10.1017/s0033822200033865). It has been confirmed through simulation data that adding sequence information where we know who came first, like parents and children, often narrows the range compared to calibrating dates one by one separately, and also partly resolves ranges split into two pieces. Just how much it narrows down depends on the precision of the measurements and the shape of the curve (PMID 35771856, family tree simulation data).

This calculation can only be trusted as much as the assumptions put into it. Commonly used models assume that all measurement values came from their proper places and were measured correctly, but in reality, a few are usually discarded as outliers. While there are calculation methods that screen out outliers more objectively, they are not widely used (DOI: 10.1017/s0033822200034093). A paper reviewing Bayesian models published in archaeology notes that only about half disclosed enough information to critically evaluate the models (DOI: 10.1080/00438243.2015.1067640).

Things That Trick the Hourglass

The assumption that the hourglass fills with sand from the air is not always correct. The ocean has less carbon-14 than the air (DOI: 10.1002/2017rg000588). The reservoir effect is a phenomenon where living things that got carbon from places with less carbon-14 than the air, like the ocean or a river, turn out older than they actually are. Spoken in terms of the hourglass, they filled from an old bucket of sand instead of the air, so there was less sand inside from the start.

Things that grew in the surface ocean come out older by a global average of about 400 years in uncorrected numbers, and in polar oceans that discrepancy is larger (DOI: 10.1191/0309133305pp461ra). This discrepancy is hard to measure accurately, so many researchers avoid samples from the ocean if other options exist (DOI: 10.1002/2017rg000588).

Rivers and lakes are like this too. Hard water with dissolved ancient limestone is a common cause, and even within a single river, values mismatched by up to 2,000 years have appeared. The bones of people who mainly ate freshwater fish, and the residue baked onto pottery used to boil fish, can also turn out older than they actually are (DOI: 10.1186/2050-7445-1-24).

If different carbon gets mixed into a sample, the numbers also go off. Organic matter that is younger or older, having seeped in from underground, is a typical example, and the reason tree trunks buried while submerged in water are precious for calibration is because they are well protected from this kind of contamination (DOI: 10.1017/s0033822200013898). Contamination in bone has been an age-old problem, but as pretreatment technologies for washing and selecting samples have improved, our understanding has deepened and chronologies have also improved (DOI: 10.3285/eg.57.1-2.1).

Our charcoal also has traps. Because the hourglass of a single tree-ring stops filling in the year that ring formed, charcoal burned from the inner rings of a long-lived tree can point to a year earlier than the year the fire was lit. Charcoal and wood fragments are known as samples prone to this mismatch, so when precise dating is needed, they are often not used at all. There are experimental results showing that this mismatch could be corrected within a Bayesian model that binds multiple dates together (DOI: 10.2458/56.16685).

Even with the same hourglass, the year it points to changes depending on what was measured.

Sand Poured by Nuclear Tests

In the 20th century, humans dumped sand into a sand bucket all at once. During the Cold War, atmospheric nuclear tests conducted mostly between 1955 and 1963 significantly increased carbon-14 in the air (PMID 21208756). Bomb carbon is the trace left by that significant increase in atmospheric carbon-14 caused by those nuclear tests.

This trace serves as a scale for measuring recent things. Because atmospheric carbon-14 has been recorded year by year, comparing the carbon-14 contained in tooth enamel to those records makes it possible to pinpoint when a person was born with high precision (PMID 21208756). When peat layers from Greenland and Denmark are sliced into 1-centimeter sections and matched against records from the northern part of the Northern Hemisphere, layers from the mid-1950s onward can be pinpointed with an error of 1 to 2 years (DOI: 10.1017/s0033822200041163).

Bones are a different story. Because bones are gradually replaced with new material throughout life, estimating the time of death using bomb carbon in bone can diverge from reality by several years depending on the skeletal site and age (PMID 39824038, systematic review).

A Ruler Where Each Mark Is a Year

The tree-ring ruler is becoming increasingly dense. Studies measuring tree rings year by year independently are on the rise, and since the 2020 edition, such data has grown substantially (PMID 42720026). With this ruler where each interval is a year, new clues have emerged for two long-standing questions.

The first is the volcanic eruption on the Aegean island of Thera, present-day Santorini. This eruption serves as a benchmark for aligning the chronologies of the Aegean, Egypt, and the Near East on a single line. However, radiocarbon has pointed to the late 17th to early 16th century BCE, while the archaeological chronology has pointed to the later mid-16th to early 15th century BCE, leading to a long-running dispute.

A year-by-year ruler has added a clue to this dispute. When a research team measured carbon-14 year by year for a 200-year span around that period using tree rings of known dates, there were spots that disagreed with the international calibration curve. Reflecting that discrepancy shifted the date range of Thera toward the 16th century BCE. Since this is the century the archaeological chronology has pointed to, the radiocarbon date has effectively moved closer to the archaeological side. However, the expression used by the authors goes only as far as saying this result "sheds new light" on the long debate, and they do not claim the debate is over (PMID 30116779).

Even when the ruler becomes denser, not all discrepancies vanish. This is because a single international curve is applied collectively to multiple regions. Trees from the Mediterranean and Anatolia can differ from the international curve and carbon-14 age by up to some 20 years. One reason cited for this is that the growing seasons of trees vary by region, capturing the seasonally fluctuating carbon values in the air at different times. Therefore, to assess the impact of the Thera eruption on society and the environment, precise dates are still required (PMID 32807792).

The second is the beginning of the Viking Age. With the discovery of years when carbon-14 in the air suddenly changed due to particles pouring in from the sun, the creation of year-by-year calibration data caught fire. When dates were pinned to the strata of a trading town in the Viking Age using this ruler, a trend of increasing goods from Arctic Norway and the Middle East was revealed. The authors linked this trade expansion to the beginning of the Viking Age, placing that point at 790 CE ± 10 years (PMID 34937937). Even though the densest ruler was used, a margin of 10 years either way remains, and these are dates derived from the strata of a single town.

As the ruler becomes denser, the range narrows, but a range remains to the end.

When Reading a News Headline

Now let us imagine you have encountered a headline like this: "Charcoal in Cave Revealed to Be 3,000 Years Old." This headline is also a manufactured example. Based on what we have seen so far, there are four things to ask.

First, is this 3,000 years a calibrated year or the initial number from the laboratory? If it is the initial number, it is not yet a calendar year. Second, how wide is the range? Radiocarbon dates come out as a range, and where the calibration curve bends, the range might be split into several pieces.

Third, what was measured? If it was charcoal, it might have been the inner part of a long-lived tree, and if it was the bone of a person who mainly ate freshwater fish, it could have come out as old as the reservoir effect. Finally, was the sequence checked against other layers in the same spot? If it is a date that incorporates sequence, the range might have been narrowed down further.

If answers are attached to these four things, you can gauge for yourself how far to trust that number. And carbon-14 only answers "when"; it does not tell who lit that fire or why. That is why historians place records, bones, and genes side by side next to carbon.

When you encounter a radiocarbon date, you ask whether it was calibrated, how wide the range is, what was measured, and whether the sequence was matched.

Where to Look Next

The next version of the calibration curve, containing a vastly expanded dataset of single-year tree-ring data, is scheduled for release soon, and reliably weaving together that massive amount of data remains a work in progress (PMID 42720026).

How this tool is used in actual debates can be seen in "Did the Bronze Age World Collapse All at Once? — What Ended and What Carried On". One of the central axes of that article is how far we can distinguish the chronological order between sites using dates that fall on flat segments of the calibration curve where multiple years share the same value.

The other articles in "How Do We Know the Past?" cover different types of evidence. "Reading Historical Records — Grandmother's Diary and That Day's Newspaper" looks at how we trust and doubt old documents, "What Bones Tell — One Person's Diary, Split Between Teeth and Bone" examines the traces of life left in ancient teeth and bones, and "What Genes Can Tell Us — An Old Book Copied Down the Generations" explores the questions that ancient DNA can answer.

Source Papers

• "Challenges and opportunities for the construction of the next IntCal and SHCal radiocarbon calibration curves." (2026) — PMID 42720026 — Radiocarbon is the most common method for measuring the past 55,000 years, and past 14C levels have changed, requiring the calibration of curves made with reference samples of known age. Since 2020, single-year tree-ring data have increased significantly, the next edition is scheduled to come out within 1 year, and securing reliability is a challenge.
• "Radiocarbon: A key tracer for studying Earth's dynamo, climate system, carbon cycle, and Sun." (2021) — PMID 34735228 — 14C is produced in the atmosphere and spread through the carbon cycle, and the calibration curve extends back to about 55,000 years ago, which is the limit of this technique.
• "Secular variations of the cosmic-ray-produced carbon 14 in the atmosphere and their interpretations" (1965) — DOI: 10.1029/jz070i023p05937 — In about 150 trees whose ages are known from tree rings, atmospheric 14C varied by several %, and 100-year-scale fluctuations are caused by changes in cosmic ray intensity.
• "Extended dilation of the radiocarbon time scale between 40,000 and 48,000 y BP and the overlap between Neanderthals and Homo sapiens." (2020) — PMID 32817536 — In IntCal20, between 48,000 and 40,000 years ago, the radiocarbon clock runs nearly twice as fast, which is due to increased 14C production caused by the Laschamp geomagnetic excursion.
• "Isotope-Ratio and Background Corrections for Accelerator Mass Spectrometry Radiocarbon Measurements" (1990) — DOI: 10.1017/s0033822200040121 — The procedure for converting the 14C/13C ratio measured by accelerator mass spectrometry into a radiocarbon age, and correction for sample contamination.
• "The Worldwide Marine Radiocarbon Reservoir Effect: Definitions, Mechanisms, and Prospects" (2018) — DOI: 10.1002/2017rg000588 — Defines the chronological discrepancy that occurs when 14C in a reservoir is lower than that in the atmosphere, and notes that researchers shy away from marine samples because quantification is difficult. AMS has reduced sample amounts and increased precision.
• "An 11,000-Year German Oak and Pine Dendrochronology for Radiocarbon Calibration" (1993) — DOI: 10.1017/s0033822200013898 — Carbon in tree rings accumulated each year can be measured to calibrate to calendar years, and waterlogged buried trees survive well even after thousands of years and are protected from contamination.
• "New 14C Determinations from Lake Suigetsu, Japan: 12,000 to 0 Cal BP" (2011) — DOI: 10.1017/s0033822200034627 — Couples the counted layers of varved sediments with 14C of terrestrial plant fragments to create an atmospheric 14C record.
• "Composition and consequences of the IntCal20 radiocarbon calibration curve" (2020) — DOI: 10.1017/qua.2020.42 — IntCal20 spans 0 to 55,000 years for Northern Hemisphere terrestrial samples. In the recent Holocene, the effect is small, while on the older side, calibrated ages shift by up to several hundred years, and multiple ranges can emerge.
• "Wiggle-Match Dating of Tree-Ring Sequences" (2004) — DOI: 10.1017/s0033822200035967 — Because the calibration curve is not monotonic, the calendar precision of a single date is always limited.
• "Bayesian Analysis of Radiocarbon Dates" (2009) — DOI: 10.1017/s0033822200033865 — Bayesian analysis, which weaves multiple measured values into constraints and bundles, is becoming a core component of radiocarbon dating research.
• "Pedigree-based Bayesian modelling of radiocarbon dates." (2022) — PMID 35771856 — Adding relative order information in pedigree simulation data often narrows the range compared to calibrating separately, and some ranges split by curve inversions are also resolved. Precision depends on measurement precision and curve shape.
• "Dealing with Outliers and Offsets in Radiocarbon Dating" (2009) — DOI: 10.1017/s0033822200034093 — Common models assume that all measurements turned out correctly in place, but in reality, some are usually discarded as outlier values.
• "Quality in Bayesian chronological models in archaeology" (2015) — DOI: 10.1080/00438243.2015.1067640 — Among published models, only about half disclose the information needed for critical evaluation.
• "Methodological approaches to determining the marine radiocarbon reservoir effect" (2005) — DOI: 10.1191/0309133305pp461ra — The global average reservoir age of the ocean surface is about 400 radiocarbon years, and polar oceans are even older.
• "The freshwater reservoir effect in radiocarbon dating" (2013) — DOI: 10.1186/2050-7445-1-24 — Due to the freshwater reservoir effect, mainly caused by hard water, there is a difference of up to 2,000 14C years within a single river. Bones of people who ate freshwater fish and pottery used to cook the fish are affected.
• "Radiocarbon dating and its applications in Quaternary studies" (2008) — DOI: 10.3285/eg.57.1-2.1 — Outlines the origin of 14C and the background of the method, and notes that advances in pretreatment technology help understand old problems like bone contamination and improve chronologies.
• "High-Precision Bayesian Modeling of Samples Susceptible to Inbuilt Age" (2014) — DOI: 10.2458/56.16685 — Charcoal and wood fragments are vulnerable to inbuilt age, and Bayesian models (especially outlier analysis methods) could correct for this discrepancy.
• "Analysis of 14C and 13C in teeth provides precise birth dating and clues to geographical origin." (2011) — PMID 21208756 — Atmospheric nuclear tests from 1955 to 1963 significantly increased atmospheric 14C, and comparing the 14C in tooth enamel with atmospheric records allows one to pinpoint the time of birth precisely.
• "High-Resolution AMS 14C Dating of Post-Bomb Peat Archives of Atmospheric Pollutants" (2001) — DOI: 10.1017/s0033822200041163 — When peat layers are sliced into 1cm sections and measured with bomb carbon, the period after the mid-1950s can be pinned down within 1 to 2 years.
• "Radiocarbon and bomb pulse dating in the forensic context: A systematic review." (2025) — PMID 39824038 — Bomb carbon results from bone can differ from the actual time since death by multiple years due to bone turnover according to body part and age.
• "Annual radiocarbon record indicates 16th century BCE date for the Thera eruption." (2018) — PMID 30116779 — Single-year 14C from tree rings between 1700 and 1500 BCE deviates from the international curve, shifting the Thera date range toward the 16th century BCE. This sheds new light on the long-standing debate between radiocarbon and archaeological dating.
• "Radiocarbon offsets and old world chronology as relevant to Mesopotamia, Egypt, Anatolia and Thera (Santorini)." (2020) — PMID 32807792 — Mediterranean and Anatolian wood can differ from IntCal20 by about 0 to 22 14C years, with differences in the growing season being one reason. Accurate dates are needed to evaluate the impact of the Thera eruption.
• "Single-year radiocarbon dating anchors Viking Age trade cycles in time." (2022) — PMID 34937937 — Rapid changes caused by a solar particle event produced single-year calibration data, which are used to anchor the strata of a trading town, linking the expansion of long-distance trade to the start of the Viking Age (790 ± 10 CE).