Calculate Half-Life

Solve exponential decay for starting amount, remaining amount, elapsed time, or half-life.

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ToolHalf-Life Calculator
Input
Output
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Preview

How it works

Decay follows N(t) = N₀(1/2)^(t/T½). Logarithms rearrange that identity to solve the one missing quantity from the other three.

  • The rate is constant and first-order.
  • Exactly one unknown is required.

Worked example

Carbon-14 dating
A sample has decayed from 100g to 25g, elapsed time left blank
Input
											Initial quantity: 100
Remaining quantity: 25
Half life: 5730
Output
												Initial quantity: 100
Remaining quantity: 25
Elapsed time: 11460
Half life: 5730

When to use this

Nuclear physics estimates activity, pharmacokinetics models elimination, and radiometric dating relates time to isotope half-life.

Edge cases

  • Equal remaining and initial quantities provide no decay-time information.
  • Negative quantities are invalid amounts.
  • Changing rates or decay chains do not follow one constant half-life.