Radiocarbon Dating Calculator (Carbon 14 Dating)

Find the age of an organic sample from the carbon-14 it still contains.

Seconds or Julian years on both time boxes, with the reported age rounded to convention.

Updated October 19, 2026

CreatorFrank Zhao

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Introduction

A radiocarbon age is a clock that starts running at death. While a plant or animal is alive it keeps exchanging carbon with its surroundings, so the share of radioactive carbon-14 in its tissue stays level with the atmosphere. Once it dies the exchange stops and the carbon-14 already there decays away, halving about every 5,730 years. Hand this page the percentage of carbon-14 a sample still holds and it returns the time since the organism died — or hand it an age you already have and it returns the percentage that age implies.

The page reports that answer in boxes that are easy to mix up. Time elapsed is the decay age itself, unrounded. Age of the sample is that age rounded to a coarse grid — the resolution the result is reported at — and Reporting uncertainty is the ± band that belongs to the rounded age. Both of those are reporting conventions rather than measurements of laboratory error, and the section on the decay law takes them apart.

5,730 years

The half-life the page opens with, the usual value for carbon-14

Strictly between 0% and 100%

The only percentages that can be dated; both ends are refused

Past 50,000 years

The page warns that the method, not the arithmetic, has run out

Quick start

Enter the remaining percentage

This is the number a dating laboratory reports: the sample's carbon-14 measured against a modern reference of the same material. A living sample reads 100, a sample one half-life old reads 50, and a sample that has lost nine tenths of it reads 10.

Check the half-life

5,730 years is already filled in. It belongs to the isotope rather than to your sample, so change it only on purpose — for instance to match a published age that was computed from a different half-life. Both time boxes share one clock, so a half-life and an elapsed time may be written in either seconds or years and still be compared correctly.

Leave the age empty, or fill it in

With Time elapsed empty, the percentage drives the age. If you already have an age — from a report, a museum label, a paper — type it there instead and the percentage is solved backwards.

Read the age and the band together

Age of the sample is rounded to the nearest 10, 50 or 100 years depending on its size, and Reporting uncertainty is the band that belongs to that rounded age. Read them as one statement: 690 years, ± 5 means the reported age sits on a 10-year grid with a five-year band either side.

Worked example: a wooden object at 92%

A timber sample whose carbon-14 measures 92% of the modern reference, with the default half-life. The age comes straight out of the decay law:

t

=

T\,\frac{\ln\left(100/p\right)}{\ln 2}

=

5730 \times \frac{\ln\left(100/92\right)}{\ln 2}

\approx

689.29\ \text{years}

The Time elapsed box prints 689.286 — the unrounded age with a few digits showing. The two result boxes then report it the conventional way: 689.29 rounds to 690 on the 10-year grid, and an age under 1,000 years carries the ± 5 band.

That is what the page shows: 690 ± 5 years

Two different roundings are at work. The 689.286 in Time elapsed is the decay age with the digits shortened for display; 690 is the age reported on the conventional 10-year grid. Neither is more accurate than the other, and the unrounded figure in Time elapsed is the one to set beside a laboratory measurement.

The decay law and the reported age

One exponential does all of the arithmetic. The fraction of carbon-14 left falls by the same factor in every equal span of time, which is what a half-life means:

C = 2^{-t/T} = e^{-\,t\,\ln 2/T}

Read in either direction, the relation takes three forms. The age is the one most people arrive for; the half-life is the one that turns a measured percentage plus a known age into a decay rate.

t

=

T\,\frac{\ln\left(1/C\right)}{\ln 2}

=

T\,\frac{\ln\left(100/p\right)}{\ln 2}

T

=

\frac{t\,\ln 2}{\ln\left(1/C\right)}

C

The fraction of the original carbon-14 still in the sample — 0.92 for the 92% box

p

The same thing as a percentage, which is how the first box is written

t

The time since the organism died, the page's Time elapsed

T

The half-life of carbon-14, 5,730 years unless you change it

\mathrm{T}_{\mathrm{report}}

The reported age: the elapsed time rounded on the ladder below

\mathrm{band}

The ± figure quoted with that reported age

If you want the same law for another isotope, or the decay constant and mean lifetime behind a half-life, the half-life calculator works those directions against seven time scales.

The two time boxes run on one clock

A half-life and an elapsed time typed in different units would give a nonsense answer if they were compared as written, so both are normalised to seconds before the logarithm runs. The year used here is the Julian year of 31,557,600 seconds — 365.25 days — the average radiocarbon reporting has long worked on. The figure reported back is the same elapsed time divided by that number:

t_{\mathrm{s}}

=

t_{\mathrm{entered}} \times 31\,557\,600

\quad(\text{for a value in years})

t_{\mathrm{yrs}}

=

\frac{t_{\mathrm{s}}}{31\,557\,600}

How the reported age is rounded

The reported age and its band follow two different ladders, and this is the part of the page most easily misread. The rounding grid coarsens with the age itself, while the band steps up at 1,000 and at 25,000 years — so the two ladders share only one of their boundaries.

Elapsed time	Age rounded to the nearest	Band reported with it
1,000 years or less	10 years	± 5 years
Above 1,000, up to 10,000	10 years	± 10 years
Above 10,000, up to 25,000	50 years	± 10 years
Above 25,000	100 years	± 50 years

The mismatch is deliberate: it reproduces the convention this page follows, so that its numbers can be set beside a quoted date. At exactly 25,000 years the result reads 25,000 ± 10 — a band finer than the grid the age sits on — and one year later the same 25,000 comes back with a ± 50 band. Treat the pair as one statement about how finely the age is being reported, not as two independent measurements.

What the age is, and what it is not

Age of the sample is a decay age: the time carbon-14 would have had to decay, at the half-life in the box, to fall to the percentage you entered. It is neither a calendar year nor quite the "radiocarbon years" a laboratory prints, for two separate reasons.

Laboratories report radiocarbon years using the older Libby half-life of 5,568 years rather than the 5,730 used here. Even for a flawless measurement the two numbers differ slightly.
Radiocarbon years then have to be calibrated to calendar years, because the level of carbon-14 in the atmosphere has not been constant. The IntCal working group maintains those calibration curves, and its current curve, IntCal20, reaches back 55,000 calibrated years.
A laboratory's own counting error is a third number again, and it is the one to quote when a date matters. None of these three corrections happens on this page.

So a calendar date can sit centuries away from this one

The 92% sample above is a decay age of about 690 years. Its calendar date would be read off a calibration curve — a curve that is not a straight line and that has flat stretches where a whole century of calendar time collapses into a narrow band of radiocarbon years. Use this page to understand what a measurement means and to check it, and use calibration software with the laboratory's own error when a calendar date has to be published.

Worked examples

Three situations that each use a different direction of the same relation. Every result below is what the page returns for those inputs.

Checking a date you already have

A museum label puts a wooden beam at 1,000 years old and you have a carbon-14 reading to compare with it. Type 1,000 into Time elapsed instead of a percentage:

C

=

2^{-t/T}

=

2^{-1000/5730}

\approx

0.88606 \rightarrow 88.61\%

A reading near 88.6% agrees with the label. The box itself prints 88.6062, the reported age stays at 1,000 years, and the band is ± 5 because 1,000 years is still on the ± 5 rung. A reading well above 88.6% means the sample has lost less carbon-14 than a 1,000-year-old sample should — the signature of contamination with modern carbon.

The one case you can check by hand

A sample that has lost exactly half of its carbon-14 is exactly one half-life old, whatever the half-life happens to be:

t

=

T\,\frac{\ln\left(1/0.5\right)}{\ln 2}

=

T\,\frac{\ln 2}{\ln 2}

=

5730\ \text{years}

The reported age is 5,730 years, and here the band is ± 10 rather than ± 5, because 5,730 is past the 1,000-year threshold. Watching the band change while the arithmetic stays that simple is the quickest way to see the two ladders working independently.

A sample at the edge of the method

The edge of the method is a percentage so small that no counter can separate it from contamination. Enter 0.0001% anyway — the page keeps applying the decay law and flags what it finds:

t

=

T\,\frac{\ln\left(1/0.000001\right)}{\ln 2}

=

5730 \times 19.9316

\approx

114\,208\ \text{years}

The Time elapsed box prints 114,207.89 years and turns red with the warning that carbon-14 dating is not reliable past 50 thousand years. The reported age is still on screen — 114,200 years, ± 50 — because the arithmetic is sound; it is the method that has run out of signal. At a millionth of the modern level the carbon-14 left is far below what a laboratory can measure, and far below the contamination that sample preparation is trying to remove.

Reading a real measurement

Contamination pulls in both directions

A little modern carbon — from handling, packaging, conservation treatments, roots or groundwater — makes an old sample look younger. Older carbon, from fossil fuels or limestone, makes it look older. The effect grows with age: the older the sample, the smaller the contaminating fraction that will move the answer, which is why pretreatment matters more for a 30,000-year sample than for a 500-year one.

100% is an edge, not a young sample

The page refuses exactly 100%, and the arithmetic says why: at 100% nothing has decayed, so the age is zero and the reverse direction for the half-life becomes a division by zero. Real modern samples rarely land exactly there either. Samples that grew during or after the atmospheric weapons tests of the 1950s and 1960s can even carry more than the natural level — the northern-hemisphere atmosphere roughly doubled in the mid-1960s — and a percentage above 100 is outside what this page models.

The band is not the laboratory's error

± 5, ± 10 and ± 50 are the resolution of the reported age, not a statement about how well the measurement was made. When you quote a date, quote the laboratory's own uncertainty and the calibrated range it comes with. This page's band tells you how finely the age is being written down, nothing more.

Very young samples round to zero

Four years of elapsed time is 99.9516% of the original carbon-14, and the reported age comes back as 0 ± 5 — the 10-year grid, not a claim that the sample is younger than a year. Under a few decades the arithmetic stops being the limiting factor: the calibration curve and the laboratory's error dominate.

The date belongs to the tissue, not always to the event

Carbon-14 stops being exchanged when the plant or animal dies, so the age you get is the age of the material. A long-lived tree can carry heartwood centuries older than the year it was felled, and driftwood or old timber reused in a building carries the age of the tree rather than the age of the structure. When a sample is chosen to date an event, the gap between the two is part of the measurement, not an error in this calculator.

If you counted activity rather than atoms, the radioactive decay calculator turns a measured activity into the amount of the isotope behind it, which is the step between a counter reading and a percentage.

Questions

Why is the age here different from the date in a laboratory report?

A reported date has passed through three transformations this page does not make. The laboratory recomputes the age on the conventional Libby half-life of 5,568 years, then applies a calibration curve to turn radiocarbon years into calendar years, and finally attaches its own measurement uncertainty. Any of the three can move the number by decades or centuries. The value here is the raw decay age for the percentage and half-life you supplied, which is the right thing to compare with a measured percentage and the wrong thing to quote as a calendar date.

How far back can carbon-14 dating reach?

About 50,000 years in practice. The limit is not the decay law but the signal: after roughly nine half-lives the remaining carbon-14 is such a small fraction of the carbon in the sample that contamination from handling, storage or the surrounding sediment can outweigh it. The calibration curves reflect the same ceiling — the current IntCal20 curve reaches about 55,000 calibrated years. The page keeps computing past that point and warns you instead, so you can see the number and decide whether to trust it.

Which materials can be dated this way?

Anything that once was alive and still contains its original carbon: charcoal, wood, seeds, peat, plant fibres, bone collagen, antler, ivory, and shell. Stone, metal and fired pottery cannot be dated directly — only the organic material found with them, or organic temper inside a pot. Two materials need extra care: shell and other marine carbon carry a reservoir offset, because the ocean is not in step with the atmosphere, and bone only works when enough collagen survives, which is why a bone sample is usually reported with its collagen yield.

How far to trust it

This is a decay calculation, not a dating service. It takes one percentage at face value and solves the exponential. Calibration, the laboratory's measurement error and any correction for sample treatment all happen elsewhere.
Contamination and reservoir effects are not modelled. A sample that exchanged carbon with its surroundings, or one from a marine or freshwater setting, can be centuries away from what this page returns. Those offsets come from the sample and its context, not from the formula.
The ± band is a reporting convention. It says how coarsely the age is written down. It is not a confidence interval and must not be quoted in place of a laboratory's uncertainty.
Past roughly 50,000 years the method is out of range. The page keeps the number visible and turns the field red rather than blanking it, because the warning is about the technique, not about the arithmetic.
For publication, heritage or planning decisions, use the laboratory's result. A dated object deserves a calibrated range from a dating specialist, not a single number from a decay equation. Use this page to understand what a measurement means, to check one, or to teach the method.

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