Carbon 14 Half Life Calculator

Calculator

Calculation mode

Half life preset

Custom half life, years

Initial carbon 14 amount

Initial amount unit

Elapsed time, years

Remaining carbon 14 amount

Remaining amount unit

Fraction, percent modern, or ratio

Fraction input type

Initial activity

Measured activity

Sample count rate, cpm

Modern standard count rate, cpm

Background count rate, cpm

Relative uncertainty, percent

Reset

Example Data Table

Case	Input	Half life	Expected result
Remaining after one half life	100 ng, 5730 years	5730 years	50 ng remains
Age from 25 percent modern	25 percent modern	5730 years	About 11,460 years
Counting data	Sample 18 cpm, standard 34 cpm, background 2 cpm	5730 years	About 5,730 years

Formula Used

Decay constant: λ = ln(2) / T_1/2

Remaining amount: N = N₀e^-λt = N₀(1/2)^t/T_1/2

Age from ratio: t = -ln(N / N₀) / λ

Activity: A = λN

Corrected count fraction: f = (sample cpm - background cpm) / (standard cpm - background cpm)

Atom count: atoms = (mass in grams / 14.003242) × 6.02214076 × 10²³

How to Use This Calculator

Select the calculation mode that matches your data.
Choose a half life preset or enter a custom value.
Enter mass, time, activity, fraction, or count data.
Add measurement uncertainty when you want a rough range.
Press Calculate to show the result above the form.
Use CSV or PDF download for saving the output.

Understanding Carbon 14 Half Life

Carbon 14 is a radioactive isotope of carbon. It forms in the upper atmosphere. Living plants and animals take it in. They keep exchanging carbon while alive. After death, exchange stops. The carbon 14 atoms then decay at a steady rate.

Why Half Life Matters

A half life is the time needed for half of a radioactive sample to decay. Carbon 14 is commonly modeled with a half life of 5,730 years. This makes it useful for dating once living material. It is best for archaeological, geological, and forensic samples within useful age ranges.

What This Calculator Does

This tool handles several common chemistry cases. It can find remaining carbon 14 after a known time. It can estimate age from fraction modern, percent modern, activity ratio, or counting data. It also reports decay constant values, remaining percent, decay percent, atom estimates, and activity estimates when mass is supplied.

Using Measured Activity

Activity measures decays per second. A fresh standard has higher activity than an old sample. The ratio between measured activity and original activity gives the remaining fraction. The calculator can also subtract background counts from both sample and standard. That step helps remove detector noise and natural background radiation.

Interpreting Results

Radiocarbon results are estimates. Contamination can add new carbon or old carbon. Reservoir effects can shift apparent age. Instrument calibration can also change calendar age. This page gives the mathematical radiocarbon age. It does not replace laboratory calibration curves or expert sample preparation.

Good Practice

Use clean data. Enter units carefully. Keep half life values consistent. Use the physical half life for basic decay work. Use the Libby value when matching conventional radiocarbon age rules. Always record assumptions beside the result. The CSV and PDF options help keep a clear record.

Useful Output Notes

The decay constant shows the yearly decay rate. The mean life shows the average lifetime of one atom. Remaining mass helps when the initial carbon 14 mass is known. Remaining percent is easier for quick checks. Age output is shown in years before present. In radiocarbon work, present means 1950. Use the uncertainty range as a rough mathematical spread only. It is not a full calibration or contamination model.

FAQs

What is the half life of carbon 14?

The common physical half life is about 5,730 years. Some conventional radiocarbon calculations use the older Libby value of 5,568 years. This calculator supports both values and also allows custom input.

What does percent modern mean?

Percent modern compares sample carbon 14 activity with a modern reference. A value of 50 percent means the sample has half the modern reference level, before other corrections.

Can this calculator date any object?

No. It is meant for once living carbon materials. It cannot directly date metal, stone, or pottery unless connected organic material is tested.

Why can carbon 14 age be negative?

A negative age can appear when the remaining fraction is above one. This may suggest modern carbon, contamination, enriched carbon, or data entered in the wrong units.

What is activity in this calculator?

Activity is the number of radioactive decays per second. The unit becquerel means one decay per second. Activity decreases as carbon 14 atoms decay.

Why subtract background counts?

Detectors record some counts even without the sample. Background subtraction removes that extra signal. It gives a cleaner sample to standard ratio.

Is this the same as calibrated radiocarbon dating?

No. This gives a mathematical radiocarbon age. Calendar calibration needs laboratory methods, calibration curves, sample pretreatment, and expert review.

Which half life should I choose?

Use 5,730 years for general chemistry decay work. Use 5,568 years when matching conventional radiocarbon age calculations that require the Libby value.