Half-Life Calculator
Use this calculator to estimate how much of a substance remains after a given time, or how long it takes to reach a target amount.
Tip: For reverse calculations, enter a target amount and click “Calculate Time to Target”.
What Is Half-Life?
Half-life is the amount of time it takes for a quantity to decrease to half of its original value. You’ll see this concept in chemistry, nuclear physics, pharmacology, and even business modeling. If something has a half-life of 10 hours, then after 10 hours only 50% remains, after 20 hours 25% remains, and so on.
A half-life calculator helps you avoid doing repeated manual steps and gives fast, accurate results for decay problems.
The Half-Life Formula
The most common formula for decay using half-life is:
N(t) = N₀ × (1/2)t / T½
- N(t) = amount remaining after time t
- N₀ = initial amount
- T½ = half-life
- t = elapsed time
Related Exponential Form
You may also see decay written as N(t)=N₀e-λt, where λ is the decay constant. The relationship between the two forms is:
- λ = ln(2) / T½
- T½ = ln(2) / λ
How to Use This Half-Life Calculator
- Enter the initial amount.
- Enter the half-life value in your chosen time unit.
- Enter elapsed time and click Calculate Remaining Amount.
- Or enter a target amount and click Calculate Time to Target.
Keep your units consistent. If half-life is in days, elapsed time should also be in days.
Worked Examples
Example 1: Radioactive Decay
Suppose you start with 80 grams of a radioactive sample and its half-life is 6 years. After 18 years (which is 3 half-lives), the remaining amount is:
80 × (1/2)18/6 = 80 × (1/2)3 = 10 grams
Example 2: Medication in the Body
A medication has a half-life of 8 hours. If a 200 mg dose is taken, how much remains after 24 hours? Since 24/8 = 3 half-lives:
200 × (1/2)3 = 25 mg
Example 3: Caffeine Reduction
If caffeine has an average half-life of about 5 hours, a 160 mg cup of coffee leaves:
- After 5 hours: ~80 mg
- After 10 hours: ~40 mg
- After 15 hours: ~20 mg
Common Mistakes to Avoid
- Mixing units: using half-life in hours but time in days.
- Using linear thinking: half-life decay is exponential, not subtracting the same amount each period.
- Invalid target values: for time-to-target, target must be positive and usually less than the initial amount.
- Rounding too early: keep precision during intermediate steps.
Where Half-Life Calculations Are Useful
- Nuclear science and radiometric dating
- Drug dosing intervals and therapeutic planning
- Environmental pollutant breakdown estimates
- Biological elimination processes
- General exponential decay modeling
Quick FAQ
Can half-life ever change?
Yes, depending on the system. For many radioactive isotopes, half-life is fixed. In biological systems, apparent half-life can vary by person, condition, and context.
Can this calculator handle decimals?
Yes. You can enter decimal values for initial amount, half-life, elapsed time, and target amount.
What if I only know the decay constant?
Convert it first using T½ = ln(2)/λ, then use the calculator as normal.
Bottom Line
A half-life calculator is a fast way to solve real-world exponential decay problems. Whether you’re modeling isotopes, medication levels, or caffeine metabolism, the same core math applies: each half-life cuts the remaining amount in half.