Quick start
- Choose Remaining amount, Elapsed time, or Half-life.
- Enter the values the selected mode asks for.
- Use the same time unit for elapsed time and half-life.
- Press Calculate half-life.
- Review the answer, percent remaining, half-lives passed, and formula steps.
The half-life formula
The remaining amount formula is remaining amount = initial amount x (1/2)^(elapsed time / half-life). The exponent is the important part: elapsed time divided by half-life tells how many half-lives passed.
For example, if 18 hours pass and the half-life is 6 hours, then 18 / 6 = 3 half-lives. After 3 half-lives, 100 mg becomes 12.5 mg.
What half-life means
Half-life does not mean the whole thing disappears after two half-lives. It means the current amount gets cut in half every time that interval passes. Starting with 100, one half-life leaves 50, two half-lives leave 25, three leave 12.5, and it keeps shrinking.
That is why half-life is exponential decay, not straight-line subtraction. The first drop from 100 to 50 removes 50 units, but the next drop from 50 to 25 removes 25 units. Same time interval, smaller absolute drop.
Know what kind of half-life you mean
The calculator only does the math you enter. A radioactive half-life, a medicine half-life, and a body-clearing half-life are not the same safety question. Use the page for homework-style decay, labels, and rough planning notes.
If the answer affects dosing, exposure, storage, lab safety, or medical care, use a proper source for that exact substance and ask a qualified person. The calculator cannot know the material, route, dose, or safety rule behind your numbers.
Caffeine and medicine examples are math practice here. Real sleep, dosing, or safety choices need a reliable source for the exact substance, not a generic calculator.
Choose the right mode
Unit tips
Keep time units consistent. If the half-life is in hours, enter elapsed time in hours. If the half-life is in years, enter elapsed time in years.
The amount unit is a label for readability. You can use mg, g, kg, %, atoms, or another unit as long as the initial and final amounts use the same unit.
How to read the answer
Start with the big answer, then read the supporting lines. Half-lives passed tells how many halving intervals fit into the time. Percent remaining tells what share of the starting amount is still there. Percent decayed is the rest.
If the calculator says 3 half-lives passed and 12.5% remains, that is just the halving chain in percent form: 100% to 50% to 25% to 12.5%.
Physical, biological, and effective half-life
The math tool uses one half-life value at a time. In real science, people may use more specific words. Physical or radiological half-life is radioactive decay. Biological half-life is how fast a body removes a substance. Effective half-life combines both.
That matters because a homework-style decay problem and a medical or radiation safety decision are not the same thing. This page explains the calculator math; it does not set a dose, safety rule, storage rule, or treatment plan.
Examples from the half-life calculator
12.5 mg remaining after 3 half-lives
36 hours because 80 to 10 is 3 halving steps
5 days because two half-lives passed
Common mistakes
Do not mix time units, such as entering half-life in hours and elapsed time in days. Convert one value first so the calculator compares the same kind of time.
For elapsed-time and half-life modes, the final amount must be greater than zero. To solve the half-life itself, the final amount must also be less than the initial amount.
Also check whether your final amount is the amount remaining or the amount decayed. If a question says 75% has decayed, then 25% remains. The calculator wants the remaining amount when you are solving for elapsed time or half-life.
FAQ in plain language
What formula does the Half-Life Calculator use?
For remaining amount, it uses remaining amount = initial amount x (1/2)^(elapsed time / half-life). The elapsed time divided by the half-life tells how many times the amount gets cut in half. The calculator also rearranges that same formula to solve for elapsed time or the half-life itself.
What is a half-life?
A half-life is the time it takes for a quantity to drop to half of whatever amount is currently there. If 100 mg has a 6-hour half-life, about 50 mg remains after 6 hours, 25 mg after 12 hours, and 12.5 mg after 18 hours. It halves again and again instead of subtracting the same amount every time.
What do the main Half-Life Calculator inputs mean?
Initial amount is what you start with before decay. Final amount is what is left after decay when you are solving for elapsed time or half-life. Half-life is the time needed for the current amount to halve. Elapsed time is how long the decay has been happening. Amount unit and time unit are labels, so the calculator does not convert mg to g or hours to days for you.
How should I read the Half-Life Calculator answer?
Read the headline answer, then check the supporting lines and examples to understand how the calculator got there. If one input changes, rerun the tool and compare the new answer instead of guessing.
What does half-lives passed mean?
Half-lives passed is elapsed time divided by half-life. If the elapsed time is 18 hours and the half-life is 6 hours, then 3 half-lives passed. That means the amount was halved three times: 100 to 50, 50 to 25, then 25 to 12.5.
Can I solve for elapsed time?
Yes. Choose Elapsed time, enter the initial amount, final amount, and known half-life, then calculate. The final amount must be greater than zero and not greater than the initial amount.
Can I solve for the half-life itself?
Yes. Choose Half-life, enter the initial amount, final amount, and elapsed time. The final amount must be less than the initial amount so the decay rate can be calculated.
Why does the final amount have to be greater than zero?
The log formula needs a positive final-to-initial ratio. Zero would mean the amount is completely gone, but an ideal exponential decay curve keeps getting smaller and closer to zero instead of hitting exact zero in a normal finite time calculation.
Do the units matter?
Yes. Keep elapsed time and half-life in the same time unit, such as hours with hours or years with years. The amount unit is only a label and should match between initial and final amounts.
What should I double-check before trusting the answer?
Check that you picked the right mode, used the same time unit for elapsed time and half-life, entered the final amount as the amount remaining, and kept the final amount positive. If a question says 75% decayed, enter 25% remaining.
What is the difference between physical, biological, and effective half-life?
Physical or radiological half-life is about radioactive decay itself. Biological half-life is about how fast the body removes a substance. Effective half-life combines both ideas. This calculator only handles the basic exponential decay math you enter; it does not decide medical, biological, or radiation safety rules.
Can I use this for medicine dosing or radiation safety decisions?
No. This tool is for general math, study, and planning examples. Do not use it as medical advice, dosing advice, or radiation safety guidance.
Is my half-life calculation history private?
Yes. Recent half-life answers stay only in the current browser tab while you use the page. They are not sent to a server.
Research and references
These sources are here for checking the definition and formula ideas, not for replacing a lab, medical, or radiation-safety rule.
Safety and privacy
This calculator is for general math, science study, and planning examples. It is not medical advice, dosing advice, or radiation safety guidance.
Recent half-life answers stay only in the current browser tab while you work. They are not sent to a server.