Half-Life Calculator

Enter a starting amount, half-life, and elapsed time to see what remains, or switch modes to solve elapsed time or half-life. Results show half-lives passed, percent remaining, and formula steps.

All tools

Smoke mascot beside a glowing half-life decay curve and calculator buttons for the Half-Life Calculator. — The Half-Life Calculator artwork shows an amount shrinking by half while the tool works through decay steps. View in the smoke-kawaii gallery

Remaining amount Elapsed time Solve half-life Decay steps

Initial amountThe starting amount before decay begins. Use the same amount unit as the final amount.Half-lifeHow long it takes for the current amount to be cut in half. Match this time unit with elapsed time.Elapsed timeHow much time has passed. Use the same kind of time as the half-life, such as hours with hours.Amount unitOptional label only, such as mg, g, atoms, %, or grams. It does not change the math.Time unitOptional label only, such as hours, days, or years. The calculator will not convert units for you.

100 mg for 18 hours12.5 mg remaining

12.5% remains and 87.5% has decayed.

Half-lives passed: 3
Decayed amount: 87.5 mg
Percent remaining: 12.5%

Steps

Use the decay formula: remaining amount = initial amount x (1/2)^(elapsed time / half-life).
18 hours / 6 hours = 3 half-lives.
100 mg x (1/2)^3 = 12.5 mg.

How to use the Half-Life Calculator

Choose whether you want remaining amount, elapsed time, or half-life.
Enter the known initial amount and the other values requested for that mode.
Use matching time units for elapsed time and half-life, such as hours with hours.
Press Calculate half-life to see the answer, percentages, formula steps, and recent history.

What people use it for

Estimate how much of a substance remains after a number of half-lives.

Find elapsed time when you know the initial amount, final amount, and half-life.

Solve for half-life when you know initial amount, final amount, and elapsed time.

Check chemistry, physics, biology, environmental science, and study decay examples.

Quick examples

Remaining amount

100 mg, half-life 6 hours, time 18 hours

12.5 mg remaining after 3 half-lives

Find elapsed time

80 g to 10 g, half-life 12 hours

36 hours because 80 to 10 is 3 halving steps

Find half-life

100 g to 25 g in 10 days

5 days because two half-lives passed

Need the guide or a nearby tool?

Need a slower walkthrough, a related calculator, or the full library? These links keep you close to the task you started.

How to use the Half-Life Calculator See slower examples, input meanings, formula notes, result limits, and mistakes to avoid.
Calculators Browse related calculators and utilities in the same category.
Calculator and utility guides Find more guides that use real tool inputs and example numbers.
All free tools Search every live tool, converter, calculator, AI helper, and browser utility.

Frequently asked questions

Quick answers about decay formulas, units, elapsed time, solving half-life, safety limits, and privacy.

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.