Half-Life Calculator

Solve remaining amount, elapsed time, or half-life period for exponential decay with step-by-step solutions

Check Half-Life Calculator

Examples:

Formula result

Copy-ready result handoff

Use this after calculating remaining amount, elapsed time, or half-life.

Common searches
half-life calculatorradioactive decayhalf life formula
Input check

Confirm the time unit is consistent across elapsed time and half-life.

Assumption

The model assumes exponential decay with a constant half-life.

Half-life decay note

Copy this after replacing the bracketed result with the value shown by the calculator.

Half-life result: [paste initial amount, half-life, elapsed time, and remaining amount].
Inputs checked: Confirm the time unit is consistent across elapsed time and half-life.
Assumption: The model assumes exponential decay with a constant half-life.
Use case: Chemistry homework, lab decay, medicine context, or remaining amount check.
Next check: Use Percentage Calculator when converting remaining amount into percent remaining.

Choose whether you need remaining amount, elapsed time, or the half-life period. Keep all time inputs in the same unit and use positive amounts so the logarithm steps are valid.

How the result is built

Formula, Variables, And Worked Example

N(t) = N0 * (1/2)^(t / t_half)
t = t_half * log2(N0 / N)
t_half = t / log2(N0 / N)

N0 is the starting amount, N is the remaining amount, t is elapsed time, and t_half is the half-life period.

Worked example

If 80 units have a half-life of 4 hours, then after 8 hours two half-lives have passed. Remaining amount = 80 * (1/2)^2 = 20 units.

Assumptions and common mistakes
  • Use the same time unit for elapsed time and half-life.
  • Half-life is exponential decay, not subtracting the same amount each period.
  • Initial and remaining amounts must be positive when solving with logarithms.
  • The simple model assumes a constant half-life over the whole interval.
Mode guide
  • Remaining amount: use starting amount, half-life, and elapsed time.
  • Time elapsed: use starting amount, remaining amount, and half-life.
  • Half-life period: use starting amount, remaining amount, and elapsed time.
Related checks
ExponentsLogarithmsScientific calculatorScientific notation

Half-Life Formula, Units, And Limits

Calculator Task Context

Use this calculator for exponential decay problems where a quantity is repeatedly reduced by half over a fixed time interval.

Formula And Method Used

The calculator uses N(t) = N0*(1/2)^(t/T), where T is the half-life, and can rearrange the equation for related unknowns.

Worked Example

  1. If 80 grams has a half-life of 5 days, after 10 days there are two half-lives.
  2. Remaining amount = 80*(1/2)^2 = 20 grams.

Common Mistakes And Limits

  • Use the same time unit for elapsed time and half-life.
  • Half-life describes exponential decay, not linear subtraction.
  • A remaining amount never becomes exactly zero in the ideal model.

Related Calculators

Exponent CalculatorUse it to verify decay powers.Log CalculatorUse logs when solving for elapsed time or half-life.Scientific CalculatorUse it for compound exponential expressions.

What this calculator solves

Use remaining amount mode when the starting amount, half-life, and elapsed time are known. Use time elapsed mode when you know how much remains and need the time. Use half-life period mode when observed decay data implies the half-life.

How to interpret the decay table

The decay table shows the repeated-halving pattern from 0 to 10 half-lives. One half-life leaves 50%, two leave 25%, three leave 12.5%, and each additional half-life halves the amount again.

Unit and model limits

The formula assumes one constant decay rate. It is a good fit for math homework and simplified science examples, but not for changing rates, multiple decay paths, safety planning, medical dosing, environmental compliance, or professional engineering decisions.

Related math skills

Use the Exponent Calculator to practice the decay power, and the Log Calculator when solving for elapsed time or half-life from a remaining amount.

References & Sources

Common result checks

Questions about this tool

What does half-life mean?
Half-life is the time required for a quantity following exponential decay to fall to half of its previous amount.
Do elapsed time and half-life need the same unit?
Yes. If half-life is in hours, elapsed time must also be in hours. Convert units before calculating.
Can the remaining amount become exactly zero?
In the ideal exponential model, the amount gets smaller and smaller but never reaches exactly zero.
Can this page be used for medical or safety decisions?
No. Use it for math practice and educational exponential decay examples. Medical, safety, environmental, and engineering decisions need qualified guidance.