Radiocarbon (C-14) Age Estimator | Archaeology · Geology · Physics
Result
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📝 Step-by-step solution
Select what to calculate and enter values
💡 C-14 half-life T½ = 5730 years | λ = ln(2)/T½ ≈ 0.00012097 per year | 1 year ≈ 365.25 days
📖 What is Carbon Dating?
Carbon dating (also called radiocarbon dating) is a scientific method for estimating the age of organic materials up to about 50,000 years old.
It works by measuring the amount of radioactive carbon-14 (C-14) remaining in a sample.
Living organisms continuously exchange carbon with the atmosphere. When they die, that exchange stops, and the C-14 inside them begins to decay at a known rate.
By measuring how much C-14 remains, scientists can estimate how long ago the organism died.
This method was developed by Willard Libby in 1949, who received the Nobel Prize in Chemistry in 1960 for this work.
🧮 Carbon Dating Formula
t = [ ln(N₀ / N) ] / λ
Where:
• t = Age of the sample (years)
• N₀ = Initial C-14 amount (100% at death)
• N = Remaining C-14 amount
• λ = Decay constant = ln(2) / T½
• T½ = Half-life of C-14 = 5,730 years
Example: A fossil has 25% of its original C-14. How old is it?
Given: N/N₀ = 25% = 0.25 | T½ = 5730 years
Step 1: λ = ln(2) / 5730 = 0.6931 / 5730 = 0.00012097 / year Step 2: t = [ ln(1 / 0.25) ] / λ = [ ln(4) ] / 0.00012097 Step 3: t = 1.3863 / 0.00012097 Step 4: t ≈ 11,460 years
💡 Notice this is exactly 2 half-lives (5730 × 2 = 11,460), because 25% = (1/2)².
📊 Carbon-14 Half-Life Reference
0 half-lives: 100% remaining → 0 years
1 half-life: 50% remaining → 5,730 years
2 half-lives: 25% remaining → 11,460 years
3 half-lives: 12.5% remaining → 17,190 years
4 half-lives: 6.25% remaining → 22,920 years
5 half-lives: 3.125% remaining → 28,650 years
~9 half-lives: 0.2% remaining → ~50,000 years (limit)
⚠️ Limitations & Assumptions
📌 Important Notes
Assumes the initial C-14 concentration was the same as today's atmosphere. This can vary slightly over time.
Reliable only for samples up to about 50,000 years old — beyond that, C-14 levels are too low to measure.
Only works on organic materials (wood, bone, charcoal, shell, cloth, etc.).
Contamination (by modern carbon or older carbon) can seriously skew results.
Requires calibration with tree-ring data, coral, and ice cores for accurate dating.
This calculator provides a simplified estimate — real archaeological dating requires professional lab work.
📚 Sources & References
Authoritative Sources
Libby, W. F. (1960) — Nobel Prize Lecture on Radiocarbon Dating
Radiocarbon Journal — International calibration curves (IntCal)
USGS — Radiocarbon Dating Principles
Cambridge University — Radiocarbon Dating Laboratory
NIST — Carbon-14 Half-Life Measurements
❓ Frequently Asked Questions
What is the half-life of carbon-14?
The half-life of carbon-14 is approximately 5,730 years. This means half of the C-14 atoms in a sample decay every 5,730 years.
What is the maximum age carbon dating can measure?
Carbon dating is reliable up to about 50,000 years. Beyond that, C-14 levels are too low to measure accurately.
Can carbon dating be used on rocks?
No — carbon dating works only on organic materials like wood, bone, charcoal, shell, and cloth.
Rocks don't contain carbon in the same way. For rocks, other methods like potassium-argon dating are used.
Why does carbon dating need calibration?
Atmospheric C-14 levels have varied slightly over time (due to solar activity, volcanic events, and fossil fuel emissions).
Calibration curves (like IntCal20) correct for these variations to give accurate calendar dates.
Is this calculator accurate enough for real archaeology?
It uses the same fundamental formula that archaeologists use, but real dating requires calibration, lab precision, and multiple sample testing.
Use this tool for educational purposes only.
This Carbon Dating Calculator is provided for informational and educational purposes only.
It uses a simplified version of the radiocarbon decay formula and does not account for calibration curves,
environmental variations, sample contamination, or laboratory measurement uncertainty.
Real archaeological dating requires professional laboratory analysis. Do not use this tool for academic, legal, or scientific publication without verification.