Half-Life Calculator

Enter initial amount, half-life and elapsed time to get the remaining quantity.

Inputs
Results
Remaining amount
12.5
Fraction remaining
12.5%
Half-lives elapsed
3
Formula
N(t) = N₀ × (½)^(t/τ).
Example

100 units, half-life 5 → after 15 units of time: 12.5 remain.

About the Half-Life Calculator

The Half-Life Calculator applies the standard physics, chemistry, or engineering formula for half life and returns a numeric answer with the correct units. It's aimed at students, teachers, and working engineers who need a quick, dependable calculation without opening a full CAS.

Constants are taken from CODATA / NIST reference values and rounded to the precision most useful for classroom and applied work. If you need higher precision, the formula shown below the Half-Life Calculator lets you verify by hand.

  • SI-first inputs with imperial options where they apply
  • Answers labeled with units and, where useful, scientific notation
  • Published formula visible on the page for verification
  • No hidden assumptions — every input is exposed

How to use the Half-Life Calculator

Enter every value in the units listed next to each field. The Half-Life Calculator does not silently convert between systems mid-calculation, so mixed units produce a warning rather than a wrong answer.

For teaching, work through the formula shown under the results by hand, then confirm your answer against the Half-Life Calculator. This is a fast way to catch algebra mistakes without waiting on a marker.

Precision and limitations

The Half-Life Calculator uses double-precision floating-point math, which is accurate to about 15 significant figures — more than enough for undergraduate coursework and most engineering calculations involving half life.

Edge cases (division by zero, negative logarithms, out-of-range temperatures) are guarded, so the Half-Life Calculator surfaces a clear message rather than silently returning ±Infinity or NaN.

Frequently asked questions