Radiocarbon dating method has been developed from the study of influence of cosmic irradiation to the Earth and its atmosphere. Radioactive isotope of carbon (radiocarbon,  ¹⁴C) is created in upper layers of the atmosphere by the capture of a cosmic-ray produced neutron on nitrogen in the reaction:

¹⁴N + n  →  p + ¹⁴C

The ¹⁴C is then oxidized to ¹⁴CO₂ and distributed evenly throughout the global atmosphere.  The concentration ratio of carbon isotopes ¹²C : ¹³C : ¹⁴C is almost the same in the whole atmosphere and it is 10¹² : 10¹⁰ : 1. Only the isotope ¹⁴C is radioactive, so the nuclei decay according to the reaction: 

 ¹⁴C  → ¹⁴N + β^- + ν

The reaction energy is 156 keV.

Since the desintegrated ¹⁴C atoms are replaced by those formed in the atmosphere, where the production is constant for millenia, the specific activity of ¹⁴C in the nature and living organisms remains constant. Natural specific activity in atmospheric CO₂ , in ocean carbon and in living organisims (plants, animals, humans) is:

A₀=(13.56±0.70) dpm/g carbon

or 

A₀=(0.226±0.012) Bq/g carbon,

and in air 0.037 Bq/m³ =1.0810^-12 Ci/m³, because 1 m³ of air contains 0.177 g carbon at normal conditions.

The total activity of ¹⁴C at the Earth is estimated to be 140·10¹⁵ Bq.

Plants assimilate ¹⁴C during photosynthesis, and animal eat plants. Thus, all living terrestrial creatures maintain their ¹⁴C input during the life. ¹⁴CO₂, like normal CO₂, dissolves in the oceans and is available to plankton, corals, molluscs and fish, so all creatures during their life continuously replenish their ¹⁴C content. At death of organisms ¹⁴C input ceases  and the amount of ¹⁴C  in organic matter decreases according to the exponential law of radioactive decay: 

A  = A₀ · e^-λt

where  A₀  is the concentration of ¹⁴C activity in the organism in the moment of death and  A   in the moment of measurement, i.e. after the time  t  elapsed from the moment when the sample was removed from the dynamic reservoir of carbon. The letter λ denotes the radioactive constant for ¹⁴C: 

λ = ln2 / T_1/2

 where T_1/2 is the half life of ¹⁴C (T_1/2 = 5730 years). The age of sample is then expressed by relation:

t  =  1/λ · ln( A₀/A)  =  8033 · ln( A₀/A)

By convention, the ¹⁴C age is expressed in years BP (Before P resent), where for the start year 1950 is taken. Also by convention, the "old", so-called Libby radiocarbon half-life of 5560 years is taken for ¹⁴C age calculation.

Fig. 1: Decay of ¹⁴C during the time  t   elapsed from the death of organism 

The result can be expressed as the percentage of the natural specific activity in the atmosphere (A₀) as: 

a¹⁴C = A/A₀  · 100   pMC 

(pMC= percent of modern carbon).  Deviations of the measured activity from the natural activity are expressed by so called δ-values:

δ¹⁴C = (A-A₀)/A₀ · 1000 ‰

Samples suitable for ¹⁴C dating are primarily those containing organic carbon:  wood, charcoal, peat, organic mud, bones, leather, hair, horns, organic soil, wheat etc.  Carbonates containing carbon that is a part of the natural cycle can be dated too:  shells, carbonate sediments, as speleothems (stalactites, stalagmites), tufa, lake sediments, as well as dissolved carbon (bicarbonates) in water.

There are several factors that influence the accuracy of ¹⁴C dating: (a) the isotope exchange process, i.e. fractionation of carbon atoms, (b) past variation of ¹⁴C concentration activity in the atmosphere, as well as (c) contamination of samples with recent or old ¹⁴C. 

Measurement of ¹⁴C activity requires very sensitive techniques: gas proportional counters (GPC), liquid scintillation counters  (LSC) or accelerator  mass spectroscopy (AMS). The maximal age which can be measured by GPC is about 40,000 years, by LSC 50,000 years and by AMS more than 60,000 years. The amount of carbon measured by GPC and LSC techniques should be at least several grams, while by the AMS method miligram-sized samples can be measured.

The main international journal for research papers and data lists relevant to ¹⁴C problematic is RADIOCARBON. More information about radiocarbon dating can be found on Radiocarbon WEB info pages.

There are generally three basic techniques for measuring ¹⁴C isotope activity  in various materials: gas proportional counter, liquid scinitillation counter, and accelerator mass spectroscopy. The main characteristic of all these methods is that they are destructive, i.e. the sample whose age wants to be determined should be combusted and subsequently prepared in a form suitable for the ¹⁴ C measurement.

Radiometric methods are based on the counting of individual decays of radioactive isotope ¹⁴C. The required amount of carbon depends on the size and type of counters, but it cannot be less than 5 g, by taking into account the fact that carbon makes up about one-third the mass of organic material. For dating of bones much larger sample amount should be taken, because collagen must be extracted from bones, and its amount decreases in old bones. A particular problem is the impact of environmental and cosmic radiation, which overshadows the detection of radioactive decay of atoms ¹⁴C. This background radiation should be reduced as much as possible by applying the so-called. passive and active shields. The passive shield is composed of large amounts of lead that reduces the impact of cosmic rays, and paraffin, which reduces the impact of neutron radiation. Additionally, radiocarbon laboratories are usually placed in the basement rooms to reduce the impact of cosmic rayst. The active shield consists of additional detectors that register the passage of cosmic radiation and is working in the so-called anticoincident technique. If both detectors, one that measures the activity of ¹⁴C in the sample, and the other that represents the shield, detect a pulse at the same time, it means that this pulse is caused by background radiation, and not by decay of ¹⁴C atoms, and  therefore should be discarded.

GPC - gas proportional counter: For measurement of ¹⁴C activity by this counter, it is necessary to obtain a gas by certain chemical procedures. It should contain all of the carbon in the sample and it will be used as working gas in the counter. Depending on the lab, carbon dioxide, methane, acetylene or benzene can be used. A proportional counter consists typically of a cylindrical cathode and central anode in the form of a thin wire. Between them there is a difference of several thousand volts. β-particles, resulting from the decay of carbon as the integral part of the molecule of counting gas, ionize gas molecules on their way, leaving tracks that consist of positive ions and electrons. Electrons are accelerated towards the anode and near its vicinity, where the electric field is the strongest, form an avalanche of ion-electron pairs, which are collected at the anode, producing electrical impulses. Each β-decay creates a pulse which is then detected electronically.

LSC - liquid scintillation counter: For measurement by liquid scinitillation counter sample should be chemically converted into benzene, C₆H₆, which is very suitable material, since contents 96% of carbon. Scintillation detectors are based on the fact that ionizing radiation particles, slowing down or stopping in certain organic compounds (scintillators), form pulses of photons. Therefore, a small amount of organic scintillators should be added to benzene in order to get a scintillation solution (cocktail). Since ¹⁴C is an integral part of the sample, electrons created by β-decay excite its molecules. Excitation energy is transferred from one molecule to another, until is captured by the scintillator molecule, followed by the emmission of light (photons). Number of emitted photons is proportional to the ionization energy. The resulting photons are converted into electrons on the photocathode (photoelectric effect). The photomultiplier accelerates primary electrons from the photo-cathode, multiplying their number. At the exit we get a strong electrical pulse proportional to the amplitude of light (scintillation), thus proportional to the energy of incident particle.

AMS - accererator mass spectrometry: In contrast to radiometric techniques, accelerator mass spectrometry measures the ratio of ¹⁴C isotopes of atoms in relation to the most common isotope of carbon, ¹²C, instead of decays of individual ¹⁴C atoms. The counting is not affected by cosmic radiation, which is the main source of problems in gas and liquid counters. Accelerator technique can determine the age of much smaller sample amounts, up to milligrams or even micrograms (e.g .a grain of cereal, a piece of cloth, part of the paper), and the age limit that can be achieved by this method reaches to 60 000 years. Additional advantages of this method are the short measurement time and lower error, but it is more expensive because requires work on expensive nuclear machines.

The sample is chemically converted to graphite, which represents a target which will be exposed bombardment by particle in an accelerator. Ionised atoms are then accelerated in a strong electric field. Passing through the magnets Atoms of mass 14 are then separated by those of mass 12 and 13 in a magnet, and afterwards they are registered in a specially designed detector in order to determines the ratio of ¹⁴C/¹²C for each sample.

In Rudjer Bošković Institute Radiocarbon and Tritium Laboratory measurements of ¹⁴C activity were performed by gas proportional counter in the period 1968-2003. Since 2001 the ¹⁴C activity is measured by  liquid scintillation counter Quantulus 1220. The method of graphite preparation for AMS measurements was introduced in 2010, and AMS measurements are performed abroad.