1. Radiocarbon Dating

1.1 Fundamental principles

Radiocarbon (¹⁴C) is a naturally occurring radioactive isotope of carbon that is formed in the upper atmosphere when neutrons produced by cosmic rays interact with nitrogen atoms (Fig. 1). It is unstable, with a physical half-life of 5730±40 years.

Once produced, radiocarbon atoms rapidly oxidise to form carbon dioxide (CO₂) that disperses quickly within the atmosphere and enters the terrestrial food chain through photosynthesis. This means that the ¹⁴C content of plants that live on land, and the animals that eat the plants, is in equilibrium with the contemporary atmosphere.

When an organism dies it ceases to take up radiocarbon, and so over time, due to natural isotopic decay, the proportion of ¹⁴C in the dead organism decreases. By measuring the proportion that remains, the elapsed time since death can be estimated. The age can be calculated from the ratio of ¹⁴C in the material of unknown age to that in a modern standard, using the exponential formula for radiocarbon decay (Bowman 1990, 11).

Radiocarbon enters other reservoirs more slowly or, once there, is diluted by a component of ¹⁴C-free carbon. For example, the ocean surface is on average 400 radiocarbon years older than the contemporary atmosphere, although regional up-welling of deep water can make offsets in some areas much larger than this. Freshwater offsets in rivers and lakes are extremely variable and need to be measured locally.

Any organic material that was once alive can be dated using radiocarbon (e.g. bones, seeds, wood, shell), as can some materials that absorb carbon during their manufacture (e.g. lime mortar, steel).

Further information on the principles of radiocarbon dating and the carbon cycle can be found in Bowman (1990) or Walker (2012).

1.2 Measuring radiocarbon

The procedures used for the preparation and dating of samples in the laboratory are critical for accurate radiocarbon dating.

Radiocarbon is very difficult to measure, in large part because the ¹⁴C concentration in living material is extremely low (about 1 in every 1 million million carbon atoms). This makes detecting a radiocarbon atom in a sample at the limit of detection (c 50,000 years old) equivalent to identifying a single specific human hair that might occur on the head of any of the human beings alive on earth today!

During the past 60 years, techniques for purification of samples and measurement of radiocarbon have developed. There are, however, steps common to all methods of radiocarbon dating (Fig. 2).

To date an archaeological sample accurately, it is essential that only the ¹⁴C that was part of the organism when it died is measured. Therefore, the first task is to pretreat the sample effectively to remove any exogenous carbon that has entered the sample since death. This contamination usually comes from the burial environment, but can also come from such things as inappropriate packaging or the conservation procedures that an object may have undergone.

Pretreatment includes a mixture of physical and chemical processes, and varies both according to the type of material being processed and the laboratory undertaking the analysis. The outcome is a contaminant-free chemical fraction of a sample that can be dated.

There are fundamentally two ways of measuring the amount of radiocarbon in a sample.

Until the mid-1980s all radiocarbon dating was undertaken using conventional techniques, which count the decay of ¹⁴C atoms using either gas proportional counting or liquid scintillation spectrometry. Respectively, these techniques involve converting the purified sample into either a gas (e.g. carbon dioxide) or a carbon-rich aromatic liquid (e.g. benzene), and then measuring β-particles emitted by the radioactive decay of ¹⁴C.

While conventional dating methods can be extremely precise and accurate, they require large samples (e.g. 200g of bone) and usually require long processing and counting times taking several months.

Nowadays, Accelerator Mass Spectrometry (AMS) is almost always used for measuring the amount of radiocarbon in samples. This enables much smaller samples to be dated (e.g. 1g of bone).

Typically, a sample is combusted to carbon dioxide and then converted to graphite (Fig. 3). This is pressed into a target that is loaded into the accelerator. In the AMS carbon atoms are given a specific electric charge and accelerated to very high speeds, which allows the three carbon isotopes (¹²C, ¹³C and ¹⁴C) to be separated by mass using one or more powerful magnets.

The methods used for combustion, graphitisation and dating vary according to both the equipment available and the laboratory undertaking the analysis.

Further information on the methods used for radiocarbon dating can be found in Bayliss et al. (2004) or Taylor and Bar-Yosef (2014, chapter 4).

1.3 Radiocarbon results

Most radiocarbon results obtained for archaeological projects are reported as conventional radiocarbon ages measured on the radiocarbon timescale in units ‘BP’. This reflects the concentration of radiocarbon in a sample (with 0 BP defined as the radiocarbon concentration in AD 1950).

Such ages have been calculated using standards that have been internationally agreed (Stuiver and Polach 1977), and have been calculated in a way that allows for improvements in our understanding of the half-life of radiocarbon and for fractionation (see section 1.4). They provide a common standard for users of radiocarbon dating and should be published in preference to other forms of radiocarbon result that may be reported (e.g. measured radiocarbon ages, which are not corrected for fractionation).

There are three essential components to each measurement: the unique laboratory identifier, the conventional radiocarbon age and the error estimate (e.g. Beta-194560, 3630±30 BP).

By convention, error estimates are reported at 1σ. Samples that date to beyond the limit of radiocarbon dating will be reported as beyond the background detection limit of the facility concerned (e.g. GrA-32659, > 45,000 BP).

Some samples may date to after AD 1950. The radiocarbon content of these samples is expressed as a fraction of modern carbon (Mook and van der Plicht 1999). Again, there are three essential components to the measurement: the unique laboratory identifier, the fraction modern value and the error estimate (e.g. SUERC-6782, 1.0300±0.0047 F¹⁴C). The fraction modern value should be reported in preference to other forms of result that may be reported (e.g. percent modern carbon, PMC).

Sometimes replicate ages may be obtained by dating a sample more than once. In these cases, the statistical consistency of the results can be assessed using the method of Ward and Wilson (1978), and consistent groups of ages combined before calibration by taking a weighted mean.

For example, carbonised residue on the interior of an Iron Age vessel from Beckford, Worcestershire, provided two radiocarbon ages from different laboratories (OxA-16776, 2296±28 BP and GrA-33519, 2235±35 BP), which are statistically consistent (T'=1.8; T'(5%)=3.8; df=1), and so a weighted mean can be calculated (2272±22 BP). This approach is only valid for groups of radiocarbon determinations that are true replicates — that is repeat measurements on the same sample or organism.

Alternative statistical approaches are available for other situations where we have groups of measurements that are related in other ways (see section 2.2).

1.4 Fractionation and δ¹³C values

Fractionation occurs when the heavier carbon isotopes, ¹³C and ¹⁴C, are processed in a different way to the lighter ¹²C isotope during certain physical, chemical or biological processes.

It occurs both in nature and during the laboratory processing of a radiocarbon sample. For example, during photosynthesis the lighter isotopes are kinetically favoured and so are taken up preferentially. This means that the parts of a growing plant that are still exchanging CO₂ with the atmosphere will have a lower ¹⁴C concentration than the air, and will produce a date that is too old unless a correction is applied for fractionation.

Physical processes can discriminate against either heavier or lighter isotopes. Such fractionation in the laboratory is most common in the combustion stage of conventional dating, and in the graphitisation and measurement stages of AMS.

Fortunately, ¹³C and ¹²C are stable isotopes and so the ¹³C /¹²C ratio in a sample remains constant over time and can be measured. This is the δ¹³C value, which is the difference, in parts per thousand (per mille, ‰), between the ratio of ¹³C to ¹²C in the sample and the ratio of ¹³C to ¹²C in an internationally agreed standard.

The δ¹³C can be used to estimate the original ¹⁴C :¹²C ratio in a sample, because the effect of fractionation on the ¹⁴C:¹²C ratio is approximately double that for the ¹³C:¹²C ratio, reflecting the mass difference between the heavier isotopes and ¹²C.

The δ¹³C values provided by radiocarbon laboratories are of interest to users of radiocarbon dating for three reasons:

First, they can be used to correct fractionation in the measured ¹⁴C concentration and to calculate a conventional radiocarbon age. The conventional radiocarbon age of an enriched sample (with a less negative δ¹³C value than the −25.0‰ to which all conventional radiocarbon ages are normalised) is greater (older) than its measured radiocarbon age.

Correction for isotopic fractionation in a depleted sample (with a more negative δ¹³C value) gives a lower (younger) conventional radiocarbon age. A difference of 1‰ in δ¹³C corresponds to a ¹⁴C age difference of c. 16 BP.

Ideally, all conventional radiocarbon ages should be calculated using a measured δ¹³C value. Occasionally, samples are too small to enable a measurement of δ¹³C as well as the radiocarbon content, and in the past not all radiocarbon facilities had access to the equipment needed to measure δ¹³C. In these cases, an assumed value based on typical values for different types of material can be used for age calculation (Table 1). This is, however, not ideal, particularly as the precision of measurements improves, and so for archaeological samples, measured δ¹³C values should be obtained whenever possible.

The second use of δ¹³C values for archaeologists is to check for samples whose carbon is not derived fully from atmospheric or terrestrial sources, and so could have reservoir effects that have to be considered during the calibration process (see section 1.6).

Again, δ¹³C values measured by conventional mass spectrometry that are more than a few per mille away from the typical values listed in Table 1 should invoke caution. For example, a bulk sediment sample from the base of Askham Bog, Yorkshire, produced a measurement of 9150±55BP (OxA-8262) with a δ¹³C value of −15.0‰, which suggests that this sample may have a significant hard-water error.

Potentially, such enriched carbon isotopic values in human bone or food residues from pottery can indicate samples with a strong input of marine resources. Examples such as these from England, however, are rare.

More common are samples from humans who have ingested a modest component of marine or freshwater fish in their diets (< 20%). This can be indicated by only slightly elevated δ¹³C values (> −19.0‰), and further isotopic studies would be required to estimate the proportion of such resources consumed (see section 5.2).

The significance of diet-induced reservoir offsets of this scale depends on the precision and accuracy required from the specific application.

The third use of δ¹³C values for archaeologists is as a quality check on the radiocarbon age. For this purpose, it is essential to determine how the quoted δ¹³C value has been obtained.

Basically, there are two ways of measuring δ¹³C. In many accelerators, it can be measured on-line during the dating process. In this case, the measurement includes the natural isotopic composition of the sample, but also all the fractionation that may have occurred during laboratory processing and AMS measurement. Values of this kind are normally reported as ‘δ¹³C_AMS’.

It is also possible to measure δ¹³C by conventional Isotopic Ratio Mass Spectrometry (IRMS), as is done for stable isotopic studies. Values of this kind are normally reported as ‘δ¹³C_IRMS’. In this case, either the collagen extracted for dating or the carbon dioxide produced by the combustion process is sub-sampled.

For AMS measurements, where closed-system combustion is employed, the resultant value largely relates to the natural isotopic composition of the sample; but for conventional dating, where open-tube combustion is used, the reported δ¹³C value will include both the natural isotopic composition of the sample and any fractionation that has occurred during combustion (and so again these measurements do not necessarily reflect the natural isotopic composition of the sample).

Unfortunately, at present there is no consensus among radiocarbon laboratories about how δ¹³C is measured and about which values are reported to users. Some laboratories use δ¹³C values measured on the AMS to calculate ages, and report those values (e.g. ETH-, KIA-) or do not report these values (Poz-); some laboratories use δ¹³C values measured by conventional mass spectrometry to calculate ages, and report those values (e.g. SUERC-); some laboratories use δ¹³C values measured on the AMS to calculate ages, but report a second δ¹³C value on the same sample measured by conventional mass spectrometry (e.g. OxA-, GrM-).

Consequently, it is necessary to ask your chosen facility:

1. how the δ¹³C value that has been used to calculate the reported conventional radiocarbon age has been measured, and
2. how the δ¹³C value that has been reported to you has been measured.

This is important because the utility of a δ¹³C value for quality assurance of radiocarbon dates for users of radiocarbon dating depends on how it has been measured. Values measured by AMS are of great worth for the calculation of accurate conventional radiocarbon ages, but can vary appreciably from the typical values listed in Table 1 without affecting the quality of the resultant age.

Values measured by conventional mass spectrometry usually lie within a few per mille of the typical values listed in Table 1. Where they do not, there is possibly either a contamination issue with the sample or a problem with the measurement process, either of which merits further consideration.

For example, a crouched burial at Mile Oak, Sussex produced a radiocarbon age of 2240±70 BP (GU-5269), with a δ¹³C value measured by conventional mass spectrometry of −26.4‰. This is notably depleted for a sample of bone collagen (Table 1) and so the skeleton was re-dated, producing two statistically consistent ages, both of which are significantly earlier than GU-5269 (GU-5675, 2810 ±70 BP and GU-5691, 2960±100 BP) and have δ¹³C values within the expected range (−20.5‰ and −22.9‰). It seems probable that the original measurement was in error.

1.5 Calibration

Calibration is an essential step in using radiocarbon measurements to estimate the calendar date of samples. It is necessary because the production rate of radiocarbon in the atmosphere is not constant, but varies through time. This means that we need to convert the radiocarbon measurement of a sample to the calendar scale using a calibration curve made up of radiocarbon ages measured on samples of known calendar date.

Calibrated dates must be accompanied by a statement of the calibration curve and method used for their calculation and, if appropriate, details of any reservoir correction applied.

Calibrated radiocarbon dates are usually cited at 95% probability, but the 68% probability is also often provided. In some circumstances, 99% probability is more appropriate. In English archaeology, calibrated dates are usually given on the historical cal BC/cal AD scale, although the cal BP scale (measured from AD 1950) is common in the palaeoenvironmental literature.

Fortunately, there is now a set of internationally agreed consensus calibration curves for the whole timescale covered by the radiocarbon method. These should be used for all applications. Those relevant to England are:

• the terrestrial calibration curve for the mid-latitude northern hemisphere (IntCal20; Reimer et al. 2020)
• the atmospheric calibration curve for samples from the northern hemisphere zone 1 dating to after AD 1950 (bomb21NH1; Hua et al. 2021)
• the hypothetical ‘global’ marine reservoir (Marine20; Heaton et al. 2020), which has to be modified to reflect local surface water using location-specific corrections (see section 1.6).

Radiocarbon calibration is an active area of research, and these curves are refined and updated periodically. It is thus certain that radiocarbon measurements will need to be re-calibrated in due course, and so it is essential that both the unique laboratory identifier and the uncalibrated radiocarbon age and error are cited in publication in addition to the calibrated radiocarbon date (see section 3.6.1).

Bayesian Chronological Modelling provides date estimates that include the calibration process, and so single-sample calibration is not required for applications where modelling is employed.

Calibration is usually undertaken using the probability method (Stuiver and Reimer 1993) illustrated in Figure 4. This is where the probability distribution of the radiocarbon age (in red; Fig. 4a) is converted to the calendar scale through the calibration curve to produce a probability distribution of the calibrated radiocarbon date (in black).

This distribution is the most accurate reflection of the full complexity of the calendar date of a sample and is used when further statistical modelling is undertaken (see section 2). In discussion, however, this distribution needs to be summarised. As illustrated in Figure 4b, the probability method usually produces several date ranges, all of which, however, are needed to summarise the probability distribution of the calibrated date adequately. This can be awkward.

For this reason, quantile ranges can be quoted (Fig. 4c). These always provide a single, continuous date range that is easy to cite in publication and has a known probability (again 95% probability or 68% probability is usually employed). The disadvantage of this summary is that it does not reflect the full complexities of the calibrated radiocarbon date. This possibly does not matter if, for example, the measurement is providing a range-finder date for a deposit or structure (see section 2.1).

As in any scientific process, at the last stage of analysis, results should be rounded to avoid false precision. Calibrated radiocarbon date ranges should be rounded outwards, to a resolution that is dependent on that of the calibration curve used and the radiocarbon age that is being calibrated (Fig. 5).

Using IntCal20, results that calibrate after cal AD 1950, should be rounded outwards to one year (Fig. 5a); results with error terms less than ±25 BP that calibrate between cal AD 1950 and cal AD 1000 should also be calibrated outwards to one year (Fig. 5b); and results with error terms greater than this should be rounded outwards to five years; those that calibrate between cal AD 1000 and 12,277 cal BC (14,226 cal BP) should be rounded outwards to 10 years (or five years when error terms are less than ±25 BP) (Fig. 5c); those that calibrate between this date and 20,050 cal BC (25,000 cal BP) should be rounded outwards to 10 years (Fig. 5d); and those that calibrate between this date and the limit of calibration should be rounded outwards to 20 years (Fig. 5e).

Ages that calibrate across these boundaries should be rounded to the larger value. Determinations that are calibrated using mixed-source or marine calibration should be round outwards to 10 years, or to 20 years for Pleistocene samples (Fig. 5f).

So, for example, using this protocol the date ranges of GrA-24663 calculated using the probability method (Fig. 4a–b) become: 750–680 cal BC (11% probability) or 670–630 cal BC (5% probability) or 570–380 cal BC (79% probability). Sometimes ranges can merge on rounding.

Single-point summary statistics, such as the mean, the median, or an intercept point estimate, are poor approximations of the calibrated date and should not be used (Telford et al. 2004).

1.6 Reservoir effects

Reservoir effects occur when the carbon that is incorporated into a sample during life is not in equilibrium with the contemporary atmosphere. This gives the sample an apparent radiocarbon age older than that of a contemporary terrestrial sample.

In order to obtain an accurate calibrated date for such a sample, it is necessary to correct the apparent age during the calibration process using the relevant reservoir offset.

Most samples requiring reservoir correction derive from the marine environment. On average, the apparent age of a marine sample is about 400 radiocarbon years older than the contemporary atmosphere. This offset is caused by the time it takes atmospheric radiocarbon to exchange into ocean bicarbonate, and by the dilution effect caused by the mixing of surface waters with upwelling ¹⁴C-depleted deep water. Consequently, the marine reservoir correction deviates locally from the global average.

Marine samples should be calibrated using the internationally agreed marine calibration curve (Marine20; Heaton et al. 2020) and an appropriate local ΔR (‘Delta R’) correction. These values have been measured either on marine samples that were collected at a known date before AD 1950 in a known location, or on perfect pairs of contemporary terrestrial and marine samples.

A database of such values is available at http://calib.org/marine/, although data from around the English coast are sparse. It should be noted that ΔR values need to be recalculated for use with Marine20, as methodological advances mean that those calculated for use with IntCal13 are no longer appropriate.

Marine reservoir effects can vary, not only spatially, but also temporally, and this is an area of active research. Calibration of samples from marine mammals, which can range widely and incorporate carbon from a wide variety of reservoirs, is complex.

Hard-water error, or the freshwater-reservoir effect, is local and extremely variable. It can be of considerable magnitude. This arises from the dilution of dissolved atmospheric carbon in the water with ¹⁴C-free geological carbonate from the surrounding bedrock.

If it is necessary to date samples that come from organisms that live fully submerged in freshwater (such as certain species of ostracod or pondweed), then a local correction must be available or measured — either on local freshwater material collected at a known date before AD 1950 or on perfect pairs of contemporary terrestrial and fully freshwater samples.

There is presently no central repository of freshwater offset values for England, and so existing data must be sought in the literature on a case-by-case basis.

Estuarine conditions are produced by the mixing of freshwater and marine waters. Reservoir effects within estuaries are thus again extremely variable and, if it is necessary to date samples that obtained their carbon from the waters of the estuary, then, again, a local correction must be applied. If this is not already available, it must be measured as part of the study.

It should be noted that in many cases it is possible to avoid offsets deriving from hard-water or estuarine conditions by dating emergent plants (such as Cladium mariscus), which fix their carbon by photosynthesis from the atmosphere and thus, in calibration terms, count as fully terrestrial.

In cases where the origin of the dated material is unclear (for example, organic sediments), the presence of a reservoir offset is potentially indicated by a δ¹³C value that is enriched in comparison to equivalent material of a terrestrial origin (see section 1.4).

Dietary offsets can occur in samples of bone, as the food consumed by an organism can derive from a variety of sources that potentially can have marine and freshwater, as well as terrestrial, reservoirs.

Bone collagen derives mainly from the protein component of the diet, and bone apatite mainly from the whole diet. For accurate calibration, the proportion of the diet of a sampled individual deriving from each source must be estimated and the radiocarbon reservoir of each dietary source determined. Appropriate calibration data can then be mixed proportionately.

So, for example, a radiocarbon age on bone collagen from a human whose protein intake consisted of 80±10% terrestrial herbivore and 20±5% marine fish would be calibrated using 80±10% IntCa20 and 20±15% Marine20 (with an appropriate local ΔR correction). As marine, freshwater and estuarine reservoirs are always depleted in radiocarbon in comparison to the contemporary atmosphere, a mixed-source sample that is calibrated erroneously using a fully atmospheric calibration curve will always be too old (see section 5.2).

In England dietary offsets in human bone are generally modest in scale, although these can be significant for producing accurate, high-precision chronologies.

Larger offsets do sometime occur in Viking and later individuals, but are by no means universal.

A component of marine or freshwater foods in the diet can generally be inferred from stable isotopic evidence. Marine foods lead to enriched δ¹³C and δ¹⁵N values, whereas freshwater foods generally lead to enriched δ¹⁵N values only. Stable isotopic measurements relevant to dietary reconstruction should therefore be undertaken routinely when dating human bone.

Estimating the absolute contributions of different dietary sources in an individual is extremely complex, and specialist advice should be sought in cases where it is required.

Comparing dates on human skeletons and contemporary terrestrial material is a way to check directly for the presence of a dietary offset (Fig. 6).

A male human skeleton from Eriswell, Suffolk provided a radiocarbon age of 1640±20 BP (UB-6347), and the horse skeleton in the same grave provided a statistically consistent radiocarbon age of 1611±20 BP (UB-6348; T'=1.1; T'(5%)=3.8; df=1). This indicates that there was no significant offset in the radiocarbon age of the human bone in this individual.

Dating of such perfect pairs should be undertaken where the opportunity arises, especially where a wider programme of radiocarbon dating of human bone is being undertaken on a site.

In English archaeology, there are generally suitable samples of terrestrial material available, which should be preferred for dating, as they avoid the complexities and additional uncertainties outlined in this section. Occasionally, however, the best material for dating could derive from a non-terrestrial source, in which case specialist advice should be sought.

1.7 Citation of radiocarbon dates

Protocols for reporting newly commissioned radiocarbon dates and chronological models are described below (section 3.6).

It is often necessary, however, to cite radiocarbon dates obtained by previous workers in discussion. These results should be re-calibrated using the same method and calibration curve as used in the rest of the study, and the laboratory number, radiocarbon age and uncertainty estimate provided.

For example, in the form: ‘…the transition from marine to freshwater peat accumulation had certainly occurred by 4680–4340 cal BC (HAR-1831; 5650±70 BP; Jordan et al. 1994, 165) at nearby Ashcott Heath’.

If not provided elsewhere in the publication, references should also be given to the curve and method used for calibration and, if appropriate, details of any reservoir correction applied.

Back to contents | Introduction | 2. Bayesian Chronological Modelling