Chimney Top Calculators

Radioactive decay & half-life calculator

Remaining activity, elapsed time, original activity or half-life, with presets for common isotopes.

Calculator

Calculated — choose the unit for the result.

Calculated — choose the unit for the result.

Calculated — choose the unit for the result.

Results

Remaining activity
8.768 mCi
Fraction remaining (A/A₀)
87.68 %
Half-lives elapsed
0.1897
Half-life used
5.271 years
Decay constant λ
4.167 × 10⁻⁹ s⁻¹
Mean life τ = 1/λ
7.605 years
  • Co-60 half-life 5.271 years (ENSDF via NuDat 3). Daughter in-growth is not included.

How to use it

Radioactive sources lose activity on a strict exponential schedule. Source certificates give the activity on a reference date; survey calculations, shipping papers and leak-test paperwork need it today. Pick an isotope preset (or enter a custom half-life), choose what you want to solve for, and enter the other two values. The calculator also reports the fraction remaining, the number of half-lives elapsed, the decay constant and the mean life.

A year here is 365.25 days, the convention used for evaluated half-lives. For short-lived medical isotopes (Tc-99m, F-18) use hours or minutes; for calibration and gauge sources (Cs-137, Co-60, Am-241) years are natural.

Half-life presets

IsotopeHalf-lifeTypical use
Cs-13730.08 yearsPortable moisture/density gauges, level and thickness gauges, calibration sources, blood irradiators.
Co-605.2711 yearsIndustrial radiography, sterilization irradiators, teletherapy, level gauges, calibration.
Ir-19273.829 daysIndustrial gamma radiography of welds and castings; high-dose-rate brachytherapy.
Am-241432.6 yearsSmoke detectors, Am-241/Be neutron sources in moisture/density gauges and well logging, thickness gauges.
I-1318.0252 daysThyroid therapy and imaging; environmental tracer after reactor releases.
Tc-99m6.0067 hoursThe most widely used diagnostic nuclear-medicine isotope (bone, cardiac and thyroid scans).
Ra-2261,600 yearsHistorical luminous paint and brachytherapy sources; legacy check sources; NORM contamination.
F-18109.77 minutesPET imaging (FDG).
Na-222.6018 yearsPET scanner calibration and instrument check sources.
H-312.32 yearsSelf-luminous exit signs and watch dials; fusion research.
C-145,700 yearsRadiocarbon dating; biochemical tracer.
P-3214.268 daysMolecular biology labeling; some therapies.
Sr-9028.79 yearsBeta check sources, thickness gauges, radioisotope thermoelectric generators.
Rn-2223.8235 daysIndoor radon (the gamma dose comes mainly from its daughters).
Po-210138.38 daysStatic eliminators; alpha sources.
Pu-23924,110 yearsNuclear fuel and weapons material; alpha reference sources.
U-2384.468 × 10⁹ yearsNatural uranium; geochronology.

The formula

A = A₀ · e^(−λt)        λ = ln 2 / T½

t  = ln(A₀ / A) / λ
A₀ = A · e^(λt)
T½ = ln 2 · t / ln(A₀ / A)

A is activity (any unit, as long as A and A₀ are converted consistently — the calculator does this), t the elapsed time, T½ the half-life and λ the decay constant.

Worked example

Co-60 after three years. A 10 mCi Co-60 source (T½ = 5.2711 y) three years after its certificate date holds 10 × e^(−ln2 × 3 / 5.2711) = 6.74 mCi, or 67.4 % of the original.

When will an Ir-192 source drop to 30 Ci? Starting from 100 Ci with T½ = 73.829 days: t = ln(100/30) / λ = 128.2 days (1.74 half-lives) — a common point at which radiographers swap sources.

Frequently asked questions

What does half-life mean?
The time for half of the radioactive atoms in a sample to decay. After one half-life the activity is 50 %, after two it is 25 %, after ten it is about 0.1 %. Half-life is a fixed property of each nuclide and does not depend on temperature, pressure or chemistry.
Can I mix units for original and remaining activity?
Yes. Each activity input has its own unit, so you can enter the original activity in mCi from a source certificate and the remaining activity in MBq from a dose calibrator.
How do I find the half-life from two measurements?
Choose "Half-life" under Solve for, then enter the two activities and the time between the measurements. The calculator uses T½ = ln 2 · t / ln(A₀/A). Counting statistics matter: measurements far apart in time give a more reliable result.
Does this include daughter products?
No. It models the decay of one nuclide. Where a daughter is itself radioactive (for example Ba-137m from Cs-137, or radon daughters) the total activity or dose rate can differ from this single-nuclide result.
What is the decay constant λ?
The probability per unit time that a given atom decays: λ = ln 2 / T½. Its inverse, 1/λ, is the mean life — about 1.44 half-lives.

Sources

  1. National Nuclear Data Center, Brookhaven National Laboratory. NuDat 3 (ENSDF evaluated half-lives and photon emission data). www.nndc.bnl.gov
  2. Cember, H. & Johnson, T. E. (2009). Introduction to Health Physics, 4th edition. McGraw-Hill. (Chapters on external radiation safety and shielding.)
  3. Thompson, A. & Taylor, B. N. (2008). Guide for the Use of the International System of Units (SI). NIST Special Publication 811. www.nist.gov