Radiocarbon Dating Calculator
Determine the age of organic materials using Carbon-14 decay and radiocarbon dating principles
Calculate Radiocarbon Age
Percentage of original C-14 remaining in sample
Standard C-14 half-life is 5,730 years
λ = ln(2) / T₁/₂
Radiocarbon Dating Results
Formula: t = -ln(N/N₀) / λ = -ln(0.0000) / 1.210e-4 = 0 years
Analysis: Very recent sample, within measurement uncertainty
Accuracy: ±50-100 years
Applications:
- •Modern archaeology
- •Recent historical events
Famous Archaeological Examples
Shroud of Turin
1,260 years old (Medieval)
84.3% C-14 remaining
Cloth dated to 13th-14th centuries
King Tutankhamun
3,300 years old (Ancient Egypt)
64.8% C-14 remaining
New Kingdom pharaoh (18th Dynasty)
Ötzi the Iceman
5,300 years old (Copper Age)
51.8% C-14 remaining
Naturally mummified human
Lascaux Cave Paintings
17,000 years old (Paleolithic)
20.4% C-14 remaining
Upper Paleolithic cave art
Chauvet Cave Art
32,000 years old (Paleolithic)
6.25% C-14 remaining
Oldest known cave paintings
Neanderthal Remains
45,000 years old (Paleolithic)
1.56% C-14 remaining
Near limit of C-14 dating
C-14 Dating Ranges
0-1,000 years
Recent history
±20-50 years accuracy
1,000-10,000 years
Neolithic period
±50-100 years accuracy
10,000-30,000 years
Paleolithic period
±100-300 years accuracy
30,000-50,000 years
Near detection limit
±500-1000 years accuracy
Key Formulas
Where: N = current amount, N₀ = initial amount, λ = decay constant, t = time, T₁/₂ = half-life
Carbon Isotopes
ppt = parts per trillion. ¹⁴C is continuously produced in the atmosphere by cosmic rays.
Understanding Radiocarbon Dating
What is Radiocarbon Dating?
Radiocarbon dating, also known as Carbon-14 dating, is a method for determining the age of organic materials by measuring the decay of the radioactive isotope ¹⁴C. This technique revolutionized archaeology and provided a reliable way to date artifacts up to 50,000 years old.
Key Principles
- •¹⁴C is continuously produced in the atmosphere by cosmic rays
- •Living organisms maintain constant ¹⁴C levels through metabolism
- •After death, ¹⁴C decays with a half-life of 5,730 years
- •Measuring remaining ¹⁴C reveals time since death
Historical Impact
Developed by Willard Libby in the 1940s (Nobel Prize 1960), radiocarbon dating transformed archaeology, anthropology, and earth sciences by providing absolute dating capabilities for organic materials.
Mathematical Framework
N = N₀e^(-λt)
t = -ln(N/N₀) / λ
λ = ln(2) / 5730 years
Variables
- N: Current amount of ¹⁴C
- N₀: Initial amount of ¹⁴C (at death)
- λ: Decay constant (1.21 × 10⁻⁴ year⁻¹)
- t: Time elapsed since death
- T₁/₂: Half-life (5,730 years)
Note: Modern calibration curves account for atmospheric ¹⁴C variations over time.
Applications and Limitations
Archaeological Dating
Dating artifacts, settlements, and human remains to establish chronological sequences and cultural timelines.
Climate Studies
Dating organic materials in ice cores, sediments, and fossils to reconstruct past climate conditions.
Art Authentication
Detecting art forgeries by dating organic materials in paintings, sculptures, and manuscripts.