Free · Mathematics models

Uncalibrated Carbon-14 Decay Age

Estimate elapsed half-lives from remaining carbon-14 and inspect the captured rounded-year report.

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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

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Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

With half the initial carbon-14 remaining and a 5730-year half-life, the model age is 5730 years.

t=half-life×ln(100/percentage remaining)/ln(2).

Worked example

Enter these known values and leave the other values blank.

Percentage of carbon-14 left
50 %
Time elapsed
5730 yrs

Assumptions and limitations

  • This is an ideal exponential-decay age estimate, not a calibrated archaeological date. Initial isotope fraction is assumed known, and the default physical half-life is 5730 years.
  • The display report rounds to 10 years through 10000, 50 years through 25000 and 100 years above 25000; those are display conventions, not uncertainty estimates.
  • Contamination, reservoir effects, historical atmospheric variations and calibration curves are omitted.
  • Clear the unknown numerical field before using a supported inverse; selection controls retain their captured branches.

Common questions

What assumptions matter for this model?

This is an ideal exponential-decay age estimate, not a calibrated archaeological date. Initial isotope fraction is assumed known, and the default physical half-life is 5730 years.

What does this model leave out?

Contamination, reservoir effects, historical atmospheric variations and calibration curves are omitted.

References

Model requirements: Remaining fraction must be positive and no greater than its initial level. Half-life must be positive. Port the exact pinned rounded-year helper as standalone arithmetic, preserving all captured year bands and editable inverse equations. Permit the exact initial-state endpoint of 100 percent remaining and zero elapsed time, as required by exponential decay.

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