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DIY Cost Tools

DIY Cost Tools

Radioactive Decay Calculator

Model exponential radioactive decay from an initial amount, half-life and elapsed time expressed in matching units.

Enter every field, including explicit zeros when permitted. Decimal and scientific notation are accepted; commas, fractions and blanks are rejected. Each input must be finite and no larger than 1 billion in absolute value. Observe the stated units and domain limits.

Remaining amount189.4645708
Remaining (%)18.94645708
Decayed amount810.5354292

How to use this calculator

  1. Enter every quantity in the unit printed beside its field.
  2. Select Calculate or press Enter.
  3. Read the labeled results and compare them with the assumptions below.

Formula and method

N(t) = N₀(1/2)^(t/t½).

The calculation runs locally in your browser. If any entry is invalid or a mathematical condition is undefined, the prior result is hidden so it cannot be mistaken for a new answer.

Worked example

Using Initial amount = 1000, Half-life (time units) = 5, Elapsed time (same units) = 12, the formula returns Remaining amount = 189.4645708, Remaining (%) = 18.94645708, Decayed amount = 810.5354292. The displayed default result is generated from these same inputs.

Limitations and safety

Returns the statistical expectation for a large population. Small samples fluctuate, daughter products are not tracked and biological or environmental transport is excluded. It is not radiation-safety advice. Results use floating-point arithmetic and are displayed to about 10 significant digits; measurement uncertainty usually supports fewer. Verify units before relying on a result.

Frequently asked questions

Can amount mean mass or number of atoms?

Yes, if initial and remaining amounts use the same unit and the isotope follows the stated half-life model.

Why might a measured result differ?

The formula isolates the stated model. Real systems can add uncertainty, losses, changing properties, geometry or forces that are not among the inputs.

How should I handle units?

Convert every value to the unit shown beside its field before calculating. A numerically valid value in the wrong unit will still produce a wrong result.

Review notes and reference

Reviewed October 3, 2026. The default example and an independent edge or scaling case were checked against expected values. The live script was also checked for blank, text, comma-formatted, non-finite and out-of-range entries. Method reference. Constants use the values stated in the formula. This page’s explanation and example are original.

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