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Carbon Dating Calculator

Computes the age of a sample from the percentage of carbon-14 remaining by first-order decay with the Cambridge half-life of 5730 years, or the remaining percentage from a known age, and also reports the conventional radiocarbon age based on the Libby half-life of 5568 years.

When to use

You know the fraction of ¹⁴C left relative to modern carbon and want an uncalibrated age, or want the ¹⁴C remaining after a given number of years.

Do not use when: You need calibrated calendar dates (that requires a calibration curve such as IntCal20), the sample is older than about 50,000 years, or you are working with another isotope or drug (use half-life).

Formula

t = −(t½ / ln 2) × ln(fraction_remaining); fraction_remaining = 2^(−t / t½); λ = ln 2 / t½; τ = t½ / ln 2; Libby age = −(5568 / ln 2) × ln(fraction_remaining)

First-order decay with the Cambridge half-life 5730 ± 40 years. Laboratories report conventional radiocarbon ages with the Libby half-life (5568 years, mean life 8033 years) per Stuiver & Polach (1977); both are uncalibrated and must be converted to calendar years with a calibration curve. Practical limit about 50,000 years (≈ 0.2 % remaining).

Inputs

ParameterTypeUnitRequiredDescription
percent_c14_remainingnumber%noCarbon-14 activity of the sample as a percentage of the modern reference (100 = modern). Give this or age_years. Range: > 0, ≤ 100
age_yearsnumberyearsnoKnown age; when given, the remaining percentage is computed instead. Give this or percent_c14_remaining. Range: ≥ 0, ≤ 1000000
half_life_yearsnumberyearsdefault 5730Half-life used for the age: default is the Cambridge value 5730 ± 40 years for ¹⁴C; the Libby value 5568 is reported separately. Range: > 0, ≤ 1000000000

Outputs

OutputTypeUnitDescription
age_yearsnumberyearst = −(t½ / ln 2) × ln(fraction remaining), uncalibrated.
radiocarbon_age_libby_yearsnumberyears BPSame fraction with the Libby half-life 5568 years, as used for conventional radiocarbon ages (before calibration).
percent_remainingnumber%100 × 2^(−t / t½).
fraction_remainingnumberN / N0.
half_lives_elapsednumbert / t½ = log2(N0 / N).
decay_constant_per_yearnumber1/yearln 2 / t½.
mean_lifetime_yearsnumberyearst½ / ln 2 (8267 years for 5730).
solved_forstringage_years or percent_remaining.

Example

10 % of ¹⁴C remaining: {"percent_c14_remaining":10} → {"age_years":19035,"radiocarbon_age_libby_years":18496,"half_lives_elapsed":3.3219,"decay_constant_per_year":0.00012097,"mean_lifetime_years":8266.6,"solved_for":"age_years"}

Sample 2,000 years old: {"age_years":2000} → {"percent_remaining":78.5106,"fraction_remaining":0.785106,"half_lives_elapsed":0.349,"radiocarbon_age_libby_years":1943,"solved_for":"percent_remaining"}

GET https://tttkmbb.com/api/v1/calculate/carbon-dating?percent_c14_remaining=10

Machine access

Sources

FAQ

Why two half-lives?

Libby's original 5568 years is kept by convention for reported radiocarbon ages (years BP) so that all dates stay comparable; the more accurate Cambridge value 5730 gives the physically better age. Calibration curves correct the Libby-based age anyway.

Is the age a calendar date?

No. Atmospheric ¹⁴C varied over time, so an uncalibrated age must be calibrated (IntCal20, SHCal20, Marine20) to get a calendar range; differences reach several thousand years for old samples.

How is percent_c14_remaining measured?

As the sample's ¹⁴C/¹²C ratio (or activity) divided by that of the 1950 modern standard, after correcting for isotopic fractionation (δ¹³C); 100 % means modern carbon.

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