Radioactive Decay Energy Calculator

Calculator

Enter half-life, elapsed time, and energy per decay. Choose atoms or activity for the starting amount. Results appear above this form after submission.

Input mode *

Pick the starting measurement you trust most.

Half-life T½ *

Time for half the nuclei to decay.

Elapsed time t *

Set 0 to evaluate initial conditions.

Energy per decay *

Use Q-value, gamma energy, or released energy.

Branching ratio (0–1] *

Set 1 if the energy applies to every decay.

Initial quantity *

Moles are converted using Avogadro’s constant.

Initial activity A0 *

Activity mode converts A0 to nuclei using λ.

Tip: Scientific notation like 3e20 is supported.

Formula used

Decay constant: λ = ln(2) / T½, where T½ is the half-life in seconds.

Exponential decay: N(t) = N0 · e^−λt.

Number of decays: ΔN = N0 − N(t).

Total energy released: E = ΔN · E_decay · BR.

Activity: A(t) = λ · N(t). Instantaneous power is P(t) = A(t) · E_decay · BR.

How to use this calculator

Select Input mode: nuclei count or activity.
Enter the half-life and choose its time unit.
Enter elapsed time and choose its unit.
Provide energy per decay in MeV, keV, or joules.
Set branching ratio if energy applies sometimes.
Press Calculate to show results above the form.
Use Download CSV or Download PDF to export.

Example data table

These sample values demonstrate typical outputs. Results vary by isotope and energy channel.

Mode	Half-life	Elapsed time	Start amount	Energy per decay	Total energy (approx.)	Avg power (approx.)
Atoms	30 day	10 day	2.00e20 atoms	0.66 MeV	~1.24 MJ	~1.44 W
Activity	8 day	24 h	5.0 MBq	1.00 MeV	~0.48 kJ	~5.6 mW
Atoms	1.0 h	30 min	1.00e18 atoms	2.00 MeV	~2.2 kJ	~1.2 W

Example power is energy divided by elapsed time.

Radioactive decay energy: practical guide

1) Why decay energy matters

Radioactive sources release energy as particles and photons. Estimating this energy supports shielding design, detector planning, thermal loading checks, and safe storage decisions. For many sealed sources, heating is small, but high-activity inventories can create measurable power.

2) Half-life connects time to change

Half-life describes how quickly the number of unstable nuclei decreases. The calculator converts your half-life into seconds, then uses the decay constant λ = ln(2)/T½. This keeps unit handling consistent across seconds, minutes, hours, days, and years.

3) From nuclei to activity

Activity is the decay rate, measured in becquerels (Bq), where 1 Bq equals 1 decay per second. If you start from activity, the tool computes N0 using N0 = A0/λ. For reference, 1 curie equals 3.7×10¹⁰ Bq.

4) Energy per decay and unit conversion

Nuclear energies are often provided in eV, keV, or MeV. The calculator converts to joules using 1 eV = 1.602176634×10⁻¹⁹ J. Enter a Q-value, dominant gamma energy, or another channel energy that matches your study goal.

5) Branching ratio improves realism

Some nuclides decay through multiple pathways. If the energy you entered applies only to a fraction of decays, set the branching ratio (BR) between 0 and 1. Total energy becomes E = ΔN·E_decay·BR, which can prevent large overestimates.

6) Total energy vs. power

Total energy sums all decays from time 0 to time t. Average power divides that energy by elapsed time. The instantaneous power uses activity at time t: P(t) = A(t)·E_decay·BR. This is useful when heat output changes significantly during the interval.

7) Interpreting magnitudes

A few watts can warm a small capsule, while milliwatts are typically negligible. Compare results to the thermal capacity of the package and ambient cooling conditions. If you export CSV, you can trend energy and power across multiple time points.

8) Data quality and safety notes

Use consistent energy definitions and verify whether neutrino energy is included. Measured dose rates do not directly equal released energy without transport modeling. Always follow local radiation safety rules and approved handling procedures when working with real sources.

FAQs

1) What does this calculator output?

It reports remaining nuclei, activity at time t, decays in the interval, total released energy, average power over the interval, and power at time t. You can export results as CSV or PDF.

2) Should I start from atoms or activity?

Use atoms when you know the inventory from chemistry or production data. Use activity when you have a measured source value. Both paths use the same decay constant and time conversion.

3) What energy per decay should I enter?

Enter the energy channel you want to track, such as a gamma line or total Q-value. If your dataset lists several lines, use the branching ratio to weight the chosen line appropriately.

4) Why is my power different from dose-rate readings?

Dose rate depends on radiation type, geometry, shielding, distance, and energy absorption. Power here is the released nuclear energy rate, not the absorbed dose in a person or detector.

5) How do I model multiple time points?

Run the calculator with different elapsed times and export CSV each time, or copy values into a spreadsheet for time-series plots. Keep half-life, energy per decay, and branching ratio consistent.

6) What if elapsed time is zero?

The tool returns initial conditions. Total energy becomes zero over the interval, average power is zero, and instantaneous power reflects the initial activity and chosen energy per decay.

7) Does this include daughter decays?

No. It models a single radionuclide with exponential decay. For chains or ingrowth, you need Bateman equations or a dedicated decay-chain tool, especially when daughter half-lives are comparable.