The time in which the activity of a radionuclide, and the number of its atoms, falls by half. After n half-lives the fraction left is 2 to the power of minus n: 50 %, 25 %, 12.5 % and so on. It is a property of the nuclide alone, independent of the amount, the temperature and the chemistry it is in.

Where do the half-lives come from?

From the isotope table on this site: ENSDF evaluations read through NuDat 3 and the IAEA Live Chart API on 2026-09-16, with the evaluation cut-off recorded per nuclide. ICRP-107 (2008) differs in the third or fourth figure for some nuclides, ¹⁷⁷Lu 6.647 d against 6.6443 d for instance; over one half-life that difference moves the activity by less than 0.05 %.

Why both MBq and mCi?

The becquerel is the SI unit of activity, one decay per second, and the unit European labels and most journals use. The curie is defined as exactly 3.7 × 10¹⁰ Bq and remains the working unit in US practice, so 1 mCi = 37 MBq and 1 GBq = 27.03 mCi. The conversion is exact; nothing about the nuclide enters it.

Does the planner account for daughters, residuals or dose?

No. It applies the single-exponential law to the parent's activity only. Decay chains with their own half-lives (²²⁵Ac, ²¹²Pb, ²²³Ra), the activity left in a syringe or tubing, and any question of absorbed dose or dosimetry are outside it and belong to your validated procedures.

Radioactive decay and activity calculator

This planner applies the exponential decay law to a single radionuclide: the activity left after any time from a calibration, or the reverse, for the 27 clinical radionuclides of the isotope table or any custom half-life. It is for people who plan radiopharmaceutical work, radiochemists, imaging scientists and students, and it prints the formula, the half-life it used and the same activity in MBq, GBq, mCi and µCi with every result.

Planner

Radionuclide6.6443 d

27 nuclides of the isotope table (ENSDF half-lives), or a custom half-life.

Direction

Activity at target timeActivity needed at calibration

Activity at calibrationA

The activity on the calibration certificate, or measured now.

Time between calibration and targett

Elapsed time; a whole number of half-lives halves the activity that many times.

Results

Activity at target: 5.411GBq
MBq: 5411
GBq: 5.411
mCi: 146.3
µCi: 146300
Elapsed half-lives: 0.4515
Fraction remaining: 73.13%
Decay constant λ: 0.004347h⁻¹
Half-life used: 6.6443 d · ¹⁷⁷Lu, ENSDF · 574,068 s

For reference and education. Nothing on this page is clinical guidance, a dose recommendation or an Epitorix performance figure; check every number against your own validated procedures.

The formulas

ln 2 = 0.693 147

One exponential

A(t): A(t) = A₀ · e^(−λt); The activity after time t from an initial activity A₀. Activity is the number of decays per second; it falls at the same rate as the number of atoms.
λ: λ = ln 2 / T½; The decay constant, the fraction of atoms that decay per unit time. ¹⁷⁷Lu: 0.004 347 h⁻¹; ¹⁸F: 0.3789 h⁻¹.
n, fraction: n = t / T½ ; fraction = 2^(−n); Elapsed half-lives and the fraction left: 1 half-life leaves 50 %, 2 leave 25 %, 3.32 leave 10 %, 10 leave 0.098 %.
Reverse: A₀ = A(t) · e^(λt) = A(t) · 2^(n); What the calibration must read to have A(t) at the target time. The same law, run backwards.
Curie: 1 Ci = 3.7 × 10¹⁰ Bq (exact) ; 1 mCi = 37 MBq ; 1 GBq = 27.03 mCi; The becquerel is the SI unit (one decay per second); the curie is defined in terms of it. The conversion is exact and independent of the nuclide.

Worked examples

ENSDF half-lives

By hand

Each row is computed from the formulas above with the isotope table's half-lives; the planner reproduces every value.

Worked examples of the decay law with the isotope table's half-lives.
Nuclide · T½	Input	Time	Half-lives	Result	Note
¹⁷⁷Lu · 6.6443 d	7.4 GBq at calibration	6.647 d	1.0004	3.699 GBq	one ICRP-107 half-life later: 200 mCi has become 100 mCi
¹⁸F · 109.77 min	370 MBq at calibration	109.77 min	1.0000	185 MBq	exactly one half-life: 10 mCi → 5 mCi
⁹⁹ᵐTc · 6.0072 h	740 MBq at calibration	6.0072 h	1.0000	370 MBq	20 mCi → 10 mCi
⁶⁸Ga · 67.71 min	1 000 MBq at calibration	30 min	0.4431	735.6 MBq	2^(−0.4431) = 0.7356
¹⁷⁷Lu · 6.6443 d	7.4 GBq wanted at target	3 d	0.4515	10.12 GBq	reverse: the calibration must read 2^0.4515 = 1.3675 times more
²²⁵Ac · 9.920 d	10 MBq wanted at target	3 d	0.3024	12.33 MBq	reverse; parent activity only, the chain is not modeled
custom · 10 h	100 MBq at calibration	30 h	3.0000	12.5 MBq	three half-lives: 1/8

Questions

What the numbers mean

What is a half-life?: The time in which the activity of a radionuclide, and the number of its atoms, falls by half. After n half-lives the fraction left is 2 to the power of minus n: 50 %, 25 %, 12.5 % and so on. It is a property of the nuclide alone, independent of the amount, the temperature and the chemistry it is in.
Where do the half-lives come from?: From the isotope table on this site: ENSDF evaluations read through NuDat 3 and the IAEA Live Chart API on 2026-09-16, with the evaluation cut-off recorded per nuclide. ICRP-107 (2008) differs in the third or fourth figure for some nuclides, ¹⁷⁷Lu 6.647 d against 6.6443 d for instance; over one half-life that difference moves the activity by less than 0.05 %.
Why both MBq and mCi?: The becquerel is the SI unit of activity, one decay per second, and the unit European labels and most journals use. The curie is defined as exactly 3.7 × 10¹⁰ Bq and remains the working unit in US practice, so 1 mCi = 37 MBq and 1 GBq = 27.03 mCi. The conversion is exact; nothing about the nuclide enters it.
Does the planner account for daughters, residuals or dose?: No. It applies the single-exponential law to the parent's activity only. Decay chains with their own half-lives (²²⁵Ac, ²¹²Pb, ²²³Ra), the activity left in a syringe or tubing, and any question of absorbed dose or dosimetry are outside it and belong to your validated procedures.

Sources

ENSDF — Evaluated Nuclear Structure Data File (NNDC, Brookhaven), via NuDat 3 (opens in a new tab) — the half-lives, per nuclide, as read for the isotope table
IAEA Nuclear Data Section — Live Chart of Nuclides and API (opens in a new tab) — cross-check of each half-life and its evaluation date
ICRP Publication 107 — Nuclear Decay Data for Dosimetric Calculations (2008) (opens in a new tab) — the dosimetry half-lives noted where they differ
BIPM — The International System of Units (SI Brochure), 9th edition, Table 8 (opens in a new tab) — the curie, 3.7 × 10¹⁰ Bq exactly
NIST Special Publication 811 — Guide for the Use of the International System of Units, §B.8 (opens in a new tab) — curie to becquerel conversion factor
IAEA, Nuclear Medicine Physics: A Handbook for Teachers and Students (2014), chapter 1 (opens in a new tab) — the decay law, activity and its units

A reference tool. It evaluates one exponential from a published half-life; it does not plan, prescribe or verify a dose, and nothing here is an Epitorix performance figure.

Planner

Results

One exponential

By hand

What the numbers mean

The other six, open in the browser.