Home › Math Calculators › Half-Life Calculator

Half-Life Calculator

Enter any three of the four values (initial amount, remaining amount, elapsed time, half-life) and leave one empty — the calculator solves it.

Quick Presets:

Exponential Decay & Half-Life Solver

Fill any 3 fields and leave 1 empty to solve for the missing parameter.

Decay Analysis Result

—
Advertisement
Formula: H = t · ln(2) / ln(I / R)
Decay law: R = I × 0.5^(t / H)
Inputs: Any 3 of 4 values
Use case: Radioactivity, medicine, chemistry

What is half-life?

Half-life is the time needed for half of a decaying quantity to disappear. After one half-life, 50% remains; after two, 25%; after three, 12.5%. It is a constant property of the material, independent of how much you start with.

Exponential decay follows the rule R = I × 0.5^(t/H), where I is the initial amount, R the remaining amount, t the elapsed time and H the half-life. Taking logarithms lets you solve for any one of these values.

Where half-life is used

Physicists use it for radioactive isotopes, doctors for drug clearance and imaging tracers, and archaeologists for carbon-14 dating.

The decay constant k = ln(2) / H describes how quickly decay happens per unit time. Its reciprocal, the mean lifetime, is the average time a single particle survives. The calculator reports all three.

How to use this calculator

  1. Fill in three of the four fields with positive numbers.
  2. Leave exactly one field empty — that is the value to solve for.
  3. Press Solve to find the missing value.
  4. Read the decay constant, mean lifetime and remaining percentage table.

Pro tips

  • The remaining amount must be less than the initial amount when solving for half-life or time.
  • Use the same time unit for elapsed time and half-life (hours, days, years).
  • After 10 half-lives, only about 0.1% remains.

Advantages & considerations

✅ Advantages

  • Solves any of the four unknowns
  • Shows decay constant and mean lifetime
  • Includes a remaining-percentage table

⚠️ Considerations

  • All filled values must be positive
  • Requires exactly one empty field

Frequently asked questions

What is the half-life formula?▶
Half-life is found with H = t × ln(2) / ln(I / R), where I is the initial amount, R the remaining amount and t the elapsed time.
How much remains after 3 half-lives?▶
Each half-life halves the amount, so after 3 half-lives 0.5 × 0.5 × 0.5 = 12.5% remains.
What is the decay constant?▶
The decay constant k = ln(2) / half-life measures how quickly a substance decays per unit time. A larger k means faster decay.
Can half-life be used for non-radioactive things?▶
Yes. The same math models drug elimination from the body, chemical reaction rates and even depreciation of assets over time.
What is mean lifetime?▶
Mean lifetime is the average time a single atom or particle survives before decaying. It equals 1/k, about 1.44 times the half-life.