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Carbon Dating Calculator

Estimate the age of organic material from the percent of carbon-14 it still contains, in both physical years and conventional radiocarbon years.

Level: Grades 11–12

  • Common Core standard HSF.LE.A.4For exponential models, express as a logarithm the solution to ab^(ct) = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.
Printable worksheet

Carbon Dating Calculator

Know the answer you need? Pick an input to work backward.

Inputs

The sample's carbon-14 level as a percent of the level in living material (percent modern carbon).

Result

Age (5,730-year half-life)

7,575 years

With 40% of its carbon-14 left, the sample is about 7,575 years old using the 5,730-year half-life, or 7,360 radiocarbon years using the conventional 5,568-year half-life.

Conventional radiocarbon age (5,568-year half-life)
7,360 years BPThe figure labs report, before calibration.
Difference between the two
214 years
Half-lives elapsed
1.322
Carbon-14 decayed
60%

See the step-by-step solution ↓

Step-by-step solution

  1. Turn the percent left into a fraction, F, so it can go into the decay formula

    F=40%100=0.4

  2. Find the mean-life τ, the average time one atom lasts: the 5,730-year half-life ÷ ln 2

    τ=5,730 yearsln2=8,266.64 years

  3. Work back to the time since death: multiply the mean-life by ln(1 ÷ F) to undo the decay

    t=8,266.64×ln(10.4)=7,575 years

  4. Repeat with the older 5,568-year half-life, because labs report radiocarbon ages that way

    t₁₄C=5,568ln2×ln(10.4)=7,360 years

  5. The two answers differ only because of the half-life used

    7,575−7,360=214 years

Test yourself

20 quick questions built from this calculator's formula: work out results, predict what happens when an input changes, and work backward from an answer. Every answer comes with the working.

What this calculator does

Find out roughly how old a piece of wood, bone or other once-living material is from the carbon-14 it still holds. Living plants and animals keep taking in carbon. So the share of radioactive carbon-14 in their tissue stays close to the level in the air. When a plant or animal dies, that intake stops. The carbon-14 it holds then slowly decays, with a half-life (the time for half of it to break down) of about 5,730 years. Measuring how much is left tells you roughly how long ago it died.

Enter the carbon-14 level as a percent of the modern level, and this calculator gives two ages. The first uses the best measured half-life of 5,730 years. The second is the conventional radiocarbon age. Labs work it out with the older 5,568-year figure, so results stay comparable across decades of published work.

Where it's used

Why this math matters outside the classroom:

  • Archaeology. Archaeologists dating charcoal that keeps 50% of its carbon-14 put its age at one half-life, about 5,730 years.
  • Two half-lives. A bone that keeps 25% of its original carbon-14 has passed two half-lives, roughly 11,460 years.
  • Museum records. Museum conservators use radiocarbon results to check whether a wooden artifact or textile is as old as its catalog says.
  • Method limits. Students learn why the method stops working after about 50,000 years, when too little carbon-14 remains to measure.
  • Past climates. Geologists date peat, shells and buried wood in sediment layers to build timelines of past climate and sea level.

Grade level and standards: Grades 11–12; Common Core State Standards for Mathematics HSF.LE.A.4. © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

How to use it

  1. Find the sample's carbon-14 level as a percent of the modern reference level, often written as percent modern carbon (pMC).
  2. Enter that percent. 50% means one half-life has passed; 25% means two.
  3. Read the age from the 5,730-year half-life and the conventional radiocarbon age beside it.
  4. Treat both as uncalibrated estimates. Calendar dates need a calibration curve, which this tool doesn't apply.

What the inputs mean

Carbon-14 remaining
The ratio of carbon-14 in the sample to carbon-14 in a modern reference, times 100. A value of 100% means the sample is effectively modern, so its age is 0.

Formula and method

F = percent remaining ÷ 100
t = (T½ ÷ ln 2) × ln(1 ÷ F)
Age: T½ = 5,730 years, so T½ ÷ ln 2 = 8,266.64 years
Conventional radiocarbon age: T½ = 5,568 years, so T½ ÷ ln 2 ≈ 8,033 years

F is the fraction of the original carbon-14 still left, and t is the time since death in years. T½ is the half-life. ln is the natural logarithm, a button on most calculators that undoes exponential growth or decay. This is the half-life law N = N₀(1/2)^(t/T½) rearranged to solve for time. Here N is the carbon-14 left now and N₀ is what the sample started with.

Dividing the half-life by ln 2 gives the mean-life (the average time one carbon-14 atom lasts). Multiplying the mean-life by ln(1/F) then gives the time needed for the carbon-14 to fall to the fraction F.

Willard Libby's early measurement put the half-life at 5,568 years. Later work in the 1960s refined it to 5,730 ± 40 years, often called the Cambridge half-life. By then many ages had already been published, so the radiocarbon community kept 5,568 years as a fixed convention. A conventional radiocarbon age is stated in years before present (BP), where 'present' is fixed at 1950.

Because both ages use the same logarithm, they always differ by the same proportion. The Libby figure is about 2.8% (5,568 ÷ 5,730) lower. That gap is small next to the corrections that calibration makes.

Worked example

A wood sample holds 40% of the carbon-14 found in modern wood. How old is it?

  1. F = 40 ÷ 100 = 0.4, and ln(1 ÷ 0.4) = 0.916291.
  2. Age: 8,266.64 × 0.916291 = 7,575 years.
  3. Conventional radiocarbon age: 8,032.93 × 0.916291 = 7,360 years BP.
  4. Difference: 7,575 − 7,360 = 214 years (from the unrounded ages).

Result: The sample is about 7,575 years old by the 5,730-year half-life, and its conventional radiocarbon age is 7,360 years BP.

Understanding the result

The radiocarbon age is the number a lab would report, but it isn't a calendar date. The amount of carbon-14 in the air has varied over time. So a radiocarbon age has to be calibrated (matched against records of known age, such as tree rings) to give a calendar range. Calibrated ranges can sit hundreds of years away from the raw figure.

Small percentages mean old samples, and the method loses precision quickly. Below roughly 0.2% remaining (about 50,000 years), too little carbon-14 is left to measure reliably. The calculator warns you when that happens.

Assumptions and limitations

  • The sample started with the modern reference level of carbon-14 and has neither gained nor lost carbon since death.
  • Decay follows a single exponential with a constant half-life.
  • The percent you enter has already been corrected for isotope fractionation (small natural differences in how living things take up heavier and lighter carbon). Lab-reported pMC values usually are.
  • No calibration is applied. Real dating converts radiocarbon ages to calendar years with internationally agreed calibration curves, which this tool doesn't do.
  • No measurement uncertainty is carried through; real results come with an error range.
  • Some samples need specialist corrections. These include contaminated samples and reservoir effects (older carbon taken in from sources like seawater, as in marine samples). Samples from after the 1950s do too, because nuclear tests raised the carbon-14 in the air.

Frequently asked questions

Why are there two half-lives for carbon-14?

5,568 years was the first measured value; 5,730 years is the more accurate later value. Labs keep 5,568 years for the reported radiocarbon age, so every published result uses the same rule. Calibration then takes care of the difference.

Which age should I use?

For a homework-style 'how old is this' question, use the 5,730-year age. If you're comparing with a published radiocarbon date, use the conventional radiocarbon age. That's how those dates are reported. Neither is a calibrated calendar date.

How far back does carbon dating work?

Up to about 50,000 years. After roughly nine half-lives less than 0.2% of the original carbon-14 remains, and background radiation and contamination swamp the signal.

Can carbon dating be used on rocks or dinosaur bones?

No. It only works on material that once took in carbon from the atmosphere within the last 50,000 years or so. Older material is dated with isotopes that have much longer half-lives.

How this calculator is checked

Method: Exponential decay t = (T½/ln 2)·ln(N₀/N); carbon-14 half-life 5,730 years (Cambridge value); conventional radiocarbon age uses the Libby half-life of 5,568 years by convention. The calculation is covered by automated tests with known reference values and edge cases. Last updated 2026-10-18. Found a problem? Tell us.

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