Free · Physical chemistry calculators 🥼

Exponential Half-Life and Lifetime

Relate first-order half-life, decay constant and mean lifetime to a remaining quantity.

  • Formula & worked example
  • Private in your browser
  • No signup
Go to tool

Calculator inputs

Loading calculator…

How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

Private by default

Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

An initial quantity of 100 with half-life 10 seconds leaves 25 after 20 seconds.

N = N0 × 2^(−t/T½); T½=ln(2)/lambda; T½=tau ln(2)

Worked example

Enter these known values and leave the other values blank.

Initial quantity (N(0))
100
Half-life time (T)
10 sec
Total time (t)
20 sec
Remaining quantity (N(t))
25
Decay constant (λ)
0.0693147 / sec
Mean lifetime (τ)
14.42695 sec

Assumptions and limitations

  • A constant first-order decay rate is assumed. Quantity units are arbitrary but must match between initial and remaining values; elapsed time and half-life must have compatible units.
  • This mathematical decay model does not establish medication clearance, chemical stability, treatment timing or exposure safety.

Common questions

What does this model assume?

A constant first-order decay rate is assumed. Quantity units are arbitrary but must match between initial and remaining values; elapsed time and half-life must have compatible units.

Can I solve backward?

Clear the unknown value and enter compatible known values. Choices, one-way outputs and singular boundary cases cannot always be inverted.

References

Replace the captured explanatory image with a complete original text account of its formula, axes or contact geometry, preserving every identity and variant condition. No source arithmetic or data changes.

Explore physical chemistry calculators 🥼 or browse all chemistry calculators.