Last updated: July 3, 2026
Radiocarbon Dating Calculator
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Quick Answer
The radiocarbon dating calculator converts percent Carbon-14 remaining into an uncalibrated age before present using t = −(t½/ln2) × ln(N/N0). With the default 5730-year half-life, 50% remaining is 5730 years, 25% is 11460 years, and 12.5% is 17190 years. It also reports half-lives elapsed and the decay constant λ.
Radiocarbon age equals negative half-life divided by natural log of two, times the natural log of the fraction of carbon fourteen remaining. With a 5730 year half-life, 50 percent remaining is 5730 years before present.
Key Takeaways
- Radiocarbon age follows t = −(t½/ln2) × ln(N/N0), where N/N0 is the remaining C-14 fraction.
- The default Cambridge C-14 half-life is 5730 years; changing it scales the age linearly.
- 50%, 25%, and 12.5% remaining correspond exactly to 1, 2, and 3 half-lives: 5730, 11460, and 17190 years.
- The calculator returns an uncalibrated radiocarbon age, not a calibrated calendar-date range.
- Accurate dating also depends on sample selection, contamination removal, standards, and calibration curves.
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Formula
t = (ln(N0/N) / ln(2)) × t½ = −(t½/ln2) × ln(N/N0); λ = ln2/t½
Where:
- t=Radiocarbon age before present(years BP)
- N/N0=Fraction of Carbon-14 remaining(dimensionless)
- t½=Carbon-14 half-life(years)
- λ=Decay constant(yr⁻¹)
Worked Examples
50% remaining — one half-life
A sample with half of its original Carbon-14 activity has passed through exactly one half-life.
- 1Convert percent to fraction: N/N0 = 50/100 = 0.5.
- 2Compute half-lives: ln(1/0.5)/ln2 = 1.
- 3Age = 1 × 5730 years = 5730 years BP.
25% remaining — two half-lives
One quarter of the original activity corresponds to two successive halvings.
- 1N/N0 = 25/100 = 0.25.
- 2Half-lives = ln(1/0.25)/ln2 = 2.
- 3Age = 2 × 5730 = 11460 years BP.
12.5% remaining — three half-lives
An eighth of modern activity marks three half-lives of C-14 decay.
- 1N/N0 = 0.125.
- 2Half-lives = ln(1/0.125)/ln2 = 3.
- 3Age = 3 × 5730 = 17190 years BP.
100% remaining — modern carbon
A sample with modern C-14 activity has no radiocarbon age offset in this ideal calculation.
- 1N/N0 = 1.0.
- 2ln(1/1) = 0, so no half-lives have elapsed.
- 3Age = 0 × 5730 = 0 years BP.
About 5.5% remaining — roughly four half-lives
Very low activity near 5.5% is close to four half-lives and near the practical limits of conventional radiocarbon dating.
- 1N/N0 = 5.5/100 = 0.055.
- 2Half-lives = ln(1/0.055)/ln2 ≈ 4.184.
- 3Age ≈ 4.184 × 5730 ≈ 23977 years BP.
Introduction
Radiocarbon dating estimates the age of once-living material by measuring how much radioactive Carbon-14 remains compared with a modern standard. While living, plants and animals exchange carbon with the atmosphere; after death, exchange stops and C-14 decays with a known half-life. This calculator uses the Cambridge half-life, 5730 years, to convert percent C-14 remaining into an ideal radiocarbon age before present. For related chemical mass work, see the atomic mass calculator and molar mass calculator.
Radiocarbon dating formula
The decay law is N = N0 e^(−λt), where N is the measured C-14 activity, N0 is the initial or modern reference activity, λ is the decay constant, and t is age. Solving for age gives t = −(t½/ln2) × ln(N/N0). If you enter a percentage, the calculator first converts it to a fraction: 25% becomes 0.25. The same formula can also be written as t = (ln(N0/N)/ln2) × t½, which counts how many half-lives have elapsed.
Why the half-life is 5730 years
The default half-life is the Cambridge value, 5730 years, widely used for decay calculations and teaching. The older Libby half-life of 5568 years appears in historical conventions, but modern reporting usually normalizes and calibrates results separately. The NIST radionuclide data page and national standards laboratories document why half-life, activity measurement, and calibration are treated carefully in radiometric dating.
Changing the half-life scales the age linearly: a 1% increase in half-life produces a 1% larger calculated age for the same percent remaining.
Percent remaining and half-lives
A useful mental model is that every half-life cuts the C-14 activity in half. After one half-life 50% remains; after two, 25%; after three, 12.5%; after four, 6.25%. This calculator reports the exact half-lives elapsed as log2(100/percent remaining).
| C-14 remaining | Half-lives | Age with 5730 yr t½ |
|---|---|---|
| 100% | 0 | 0 yr |
| 50% | 1 | 5730 yr |
| 25% | 2 | 11460 yr |
| 12.5% | 3 | 17190 yr |
| 6.25% | 4 | 22920 yr |
What materials can radiocarbon date?
Radiocarbon dating works best for organic remains such as wood, charcoal, bone collagen, shell, textile fibers, seeds, and peat. It does not directly date igneous rocks, metals, or minerals that never exchanged atmospheric carbon while alive. For organic chemistry context, unsaturation and formula interpretation are handled by the degree of unsaturation calculator, while isotopic masses are explained in the atomic mass calculator.
Best samples are clean, once-living materials with preserved original carbon.
Contamination with modern carbon makes samples appear too young.
Contamination with old carbonate or fossil carbon makes samples appear too old.
Pretreatment and lab reporting standards matter as much as the decay equation.
Radiocarbon age versus calendar age
The simple decay equation returns an uncalibrated radiocarbon age. Atmospheric C-14 has varied over time because of solar activity, geomagnetic shielding, ocean circulation, and fossil-fuel dilution. Laboratories therefore calibrate radiocarbon ages with tree-ring and other archives, especially using the internationally maintained IntCal curves. See the IntCal20 publication and Radiocarbon journal for calibration details.
Use this calculator for decay-law checks and teaching; use calibrated laboratory software for archaeological calendar-date ranges.
Decay constant λ
The decay constant λ is the probability per year that a C-14 atom decays. It is calculated from the half-life as λ = ln2/t½. With t½ = 5730 years, λ ≈ 0.00012097 yr⁻¹. The Nernst equation calculator uses a different exponential/logarithmic relationship in electrochemistry, but the mathematical idea of logarithms turning ratios into linear quantities is similar.
Quick Reference Card
Radiocarbon Dating — Quick Reference
Quick reference • Radiocarbon Dating Calculator
t = −(t½/ln2) × ln(percentRemaining/100); λ = ln2/t½Valid range: 0 < C-14 remaining ≤ 100%; practical dating often requires measurable activity above laboratory background
Common Values
⚠ Watch Out
- •The output is an uncalibrated radiocarbon age, not a calendar-year range.
- •Modern or fossil-carbon contamination can strongly bias low-activity samples.
- •Do not use C-14 dating for materials that were never part of the carbon cycle.
- •Percent remaining must be greater than 0 and no more than 100 for a physical age.
Pro Tips
- →Remember the benchmark: each half-life halves the remaining C-14 activity.
- →Use 5730 years unless you specifically need to compare a historical convention.
- →Carry several decimals for percent activity, then round the final age.
- →For publication-quality ages, pair the decay calculation with lab pretreatment and calibration curves.
FAQs
How do I calculate radiocarbon age from percent C-14 remaining?
Convert the percentage to a fraction, then use t = −(t½/ln2) × ln(N/N0). For 25% remaining, N/N0 = 0.25, so the half-lives elapsed are log2(1/0.25) = 2 and the age is 2 × 5730 = 11460 years BP.
What does years BP mean?
Years BP means years before present. In radiocarbon dating, 'present' is conventionally defined as AD 1950, the reference year used before widespread nuclear-weapons testing changed atmospheric C-14 levels.
Is this the same as a calibrated calendar age?
No. The calculator gives the ideal decay-law radiocarbon age. Calendar ages require calibration curves such as IntCal because atmospheric C-14 production and carbon-cycle reservoirs have changed through time.
Why can I change the half-life?
The default 5730-year Cambridge half-life is appropriate for modern calculations. The input is editable so you can compare textbook conventions or sensitivity-test how a different half-life linearly changes the computed age.
Can radiocarbon dating be used on dinosaur fossils?
No for original Mesozoic material. C-14 dating is useful only while enough C-14 remains to measure reliably, typically up to roughly 50,000 years under favorable conditions. Dinosaur fossils are millions of years old.
What happens at 100% C-14 remaining?
The formula gives zero age because N/N0 = 1 and ln(1) = 0. In real samples, modern standards, contamination corrections, and reporting conventions still require laboratory interpretation.