🏺 Carbon-14 Dating Calculator
Estimate the age of organic samples using radiocarbon dating. Enter the remaining percentage of carbon-14, the activity ratio, or the fraction modern to calculate age in years BP (Before Present = 1950). Includes decay curve visualization and reference tables.
What Is Carbon-14 Dating?
Carbon-14 dating (also called radiocarbon dating) is a method used to determine the age of organic materials by measuring the amount of carbon-14 (14C) remaining in a sample. It was developed by Willard Libby in 1949, work that earned him the Nobel Prize in Chemistry in 1960.
Carbon-14 is a radioactive isotope of carbon that is continuously produced in the upper atmosphere by cosmic rays interacting with nitrogen. Living organisms exchange carbon with the environment through photosynthesis and respiration, maintaining a constant 14C level. When an organism dies, this exchange stops, and the 14C begins to decay.
Key facts about carbon-14 dating:
- Half-life: 5,730 years (modern value); Libby's original value was 5,568 years.
- Decay constant: λ = 1.21 × 10⁻⁴ per year.
- Reference year: 0 BP = 1950 CE (the "present" in years BP).
- Dating limit: ~50,000 years BP (about 10 half-lives).
- Applicable materials: Once-living organic matter (wood, bone, charcoal, shell, etc.).
The Carbon-14 Decay Formula
The decay of carbon-14 follows first-order kinetics:
N(t) = N₀ · e−λt
where N(t) = remaining 14C at time t, N₀ = initial 14C, λ = decay constant = ln(2)/t½, t = time elapsed
To solve for age, the formula is rearranged:
t = −ln(N/N₀) / λ = −ln(F) × t½ / ln(2)
where F = N/N₀ is the fraction of modern carbon-14 remaining
For example, if a sample has 50% of its original 14C remaining (F = 0.5):
t = −ln(0.5) × 5730 / ln(2)
t = 0.693 × 5730 / 0.693
t = 5,730 years BP
Calibration and Calendar Dates
The uncalibrated radiocarbon age (measured in years BP) is not the same as a calendar date. Atmospheric 14C production has varied over time due to:
- Solar activity cycles — changes in cosmic ray flux.
- Geomagnetic field changes — variations in Earth's magnetic shielding.
- Nuclear testing (1950s–60s) — the "bomb peak" dramatically increased atmospheric 14C.
- Fossil fuel burning — the "Suess effect" diluted atmospheric 14C.
To convert a radiocarbon age to a calendar date, calibration curves are used. The most widely used modern curve is IntCal20 (Northern Hemisphere), which covers 0–55,000 calendar years BP and is based on tree rings, corals, and other records.
Other calibration curves include:
- SHCal20 — Southern Hemisphere.
- Marine20 — marine samples (accounts for ocean reservoir effect).
Why Use This Calculator?
- Solve for age or fraction: Calculate the sample age from remaining 14C, or the expected remaining fraction from a known age.
- Multiple input formats: Enter percent modern carbon (pMC), activity ratio (A/A₀), or fraction modern (F14C).
- Modern and Libby half-lives: Choose between 5,730 years (modern) and 5,568 years (Libby original).
- Step-by-step solution: See exactly how the calculation is performed.
- Decay curve visualization: See where your sample falls on the exponential decay curve.
- Free & private: No registration, no data storage — all calculations are done in your browser.
❓ Carbon-14 Dating Calculator FAQ
What is the half-life of carbon-14?
The modern accepted half-life of carbon-14 is 5,730 years. Libby's original value from the 1940s was 5,568 years, and some older publications still use this value.
What does "years BP" mean?
BP stands for "Before Present," where "present" is defined as the year 1950 CE. This convention was established to commemorate the first publication of radiocarbon dates in 1949. So a date of 5,000 BP means 5,000 years before 1950, or approximately 3,050 BCE.
What is the dating limit of carbon-14?
The practical limit of radiocarbon dating is about 50,000 years BP (approximately 10 half-lives). Beyond this, less than 0.1% of the original 14C remains, making it indistinguishable from background contamination.
What materials can be dated with carbon-14?
Carbon-14 dating works on once-living organic materials that contain carbon, including wood, charcoal, bone, shell, peat, seeds, textiles, and paper. It cannot date rocks, minerals, or metals.
Why is calibration needed?
Atmospheric 14C levels have varied over time due to solar activity, geomagnetic changes, and human activities (nuclear testing, fossil fuel burning). Calibration curves like IntCal20 correct for these variations to provide accurate calendar dates.
What is the difference between radiocarbon age and calendar age?
Radiocarbon age (years BP) is the raw measurement based on 14C decay. Calendar age (cal BP or cal BC/AD) is the calibrated date that accounts for past variations in atmospheric 14C. Calibration can shift dates by hundreds or even thousands of years.
What is the "bomb peak"?
Atmospheric nuclear testing in the 1950s and 1960s nearly doubled atmospheric 14C levels. This "bomb peak" is actually useful for dating recent samples (post-1950) with high precision, a technique called "bomb pulse dating."
How accurate is carbon-14 dating?
Modern accelerator mass spectrometry (AMS) can measure 14C with uncertainties of ±20–40 years for well-preserved samples. However, calibration can introduce additional uncertainty, and contamination or reservoir effects can skew results.
What is the Suess effect?
The Suess effect is the decrease in atmospheric 14C concentration caused by the burning of fossil fuels, which release "old" carbon that contains no 14C. This effect has diluted atmospheric 14C since the Industrial Revolution.
Is this calculator free?
Yes, this calculator is completely free to use. No registration or personal data storage is required.