Radiation Half Life Calculator

Calculator Inputs

Use one page, one form, and responsive input groups.

Calculation mode

Initial amount

Remaining amount

Half life

Elapsed time

Target remaining percent

Reference activity (optional, Bq)

Quantity unit

Time unit

Decimal places

Trend table rows

Example Data Table

Sample engineering case using an initial amount of 100 g and a half life of 8 days.

Elapsed Time	Half Lives	Remaining Amount	Decayed Amount	Remaining %
0 days	0	100.0000 g	0.0000 g	100.0000%
8 days	1	50.0000 g	50.0000 g	50.0000%
16 days	2	25.0000 g	75.0000 g	25.0000%
24 days	3	12.5000 g	87.5000 g	12.5000%

Formula Used

Remaining quantity: N = N₀ × (1/2)^{t / T_1/2}

Decay constant: λ = ln(2) / T_1/2

Mean lifetime: τ = 1 / λ

Elapsed time: t = T_1/2 × ln(N₀ / N) / ln(2)

Half life from measurements: T_1/2 = t × ln(2) / ln(N₀ / N)

These equations assume exponential decay, consistent units, and no added source material during the evaluated period.

How to Use This Calculator

Step 1: Choose the calculation mode that matches your engineering problem.

Step 2: Enter known values such as initial amount, measured amount, half life, or elapsed time.

Step 3: Select matching time and quantity units, plus your preferred decimal precision.

Step 4: Press Calculate to view results, the decay trend table, and export options above the form.

FAQs

1. What does half life mean?

Half life is the time required for a radioactive quantity or activity to fall to half of its starting value under exponential decay conditions.

2. Can I use any time unit?

Yes. The equations are unit consistent. Use the same time unit for both elapsed time and half life to keep the result correct.

3. Why does activity follow the same ratio?

Activity is proportional to the number of undecayed nuclei. When quantity falls by a fixed ratio, activity changes by that same ratio.

4. What happens after many half lives?

The remaining fraction becomes very small but never reaches exact zero in the mathematical model. Practical limits depend on measurement sensitivity.

5. Can this calculator find half life from measurements?

Yes. Use the half life mode with the starting amount, measured remaining amount, and elapsed time from your test or observation.

6. Does this tool handle shielding or transport effects?

No. It models intrinsic radioactive decay only. Shielding, attenuation, geometry, and detector efficiency must be evaluated separately.

7. Why is the remaining amount smaller than expected?

Check that the half life and elapsed time use the same unit. Mismatched units are the most common source of incorrect decay estimates.

8. When should engineers use a decay table?

A decay table is useful for planning inspections, storage intervals, calibration schedules, and reporting expected source strength over time.