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DIY Cost Tools

DIY Cost Tools

Half-Life Calculator

Infer exponential half-life and decay constant from a measured initial amount, a smaller remaining amount and elapsed time.

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.

Half-life (time units)5
Decay constant (per time unit)0.1386294361

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

Decay constant λ = ln(N₀/N)/t; half-life t½ = ln(2)/λ.

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, Remaining amount = 250, Elapsed time (time units) = 10, the formula returns Half-life (time units) = 5, Decay constant (per time unit) = 0.1386294361. The displayed default result is generated from these same inputs.

Limitations and safety

Assumes one exponential process with no replenishment, background offset or mixed components. Measurement uncertainty can strongly affect the inferred result. 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

Why must the remaining amount be smaller?

A positive decay constant over positive time requires a decrease. Equal values imply no measurable decay and an infinite half-life.

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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