MATH · FREE
Half-Life Calculator
Find the amount left after a time, solve for the half-life, or see how long until you reach a target. Works for radioactive decay, chemistry, physics and any substance with a half-life you know.
Math only. Not medical advice. Real-world elimination varies; follow your prescriber's instructions.
AMOUNT REMAINING
Amount left
Percent left
Half-lives elapsed
| Half-lives | Time | Amount left | Percent left |
|---|
Math only. Not medical advice. Real-world elimination varies; follow your prescriber's instructions.
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The half-life formula
Each half-life cuts the amount in half. For any elapsed time t, the amount left is:
N = N0 × (1/2)t ÷ t½
- N0 is the starting amount and N is the amount left.
- t is the elapsed time and t½ is the half-life, in the same unit.
- Solve for the half-life: t½ = t × ln 2 ÷ ln(N0 ÷ N).
- Solve for the time: t = t½ × log2(N0 ÷ N).
Worked example: radioactive decay
A sample starts with 100 g of an isotope whose half-life is 5 days. How much is left after 10 days? Ten days is 10 ÷ 5 = 2 half-lives, so N = 100 × (1/2)² = 25 g. After 15 days (3 half-lives) 12.5 g remains.
Worked example: a compound with a 4-hour half-life
Take 64 units of a compound that has a 4-hour half-life. After 4 hours 32 are left, after 8 hours 16, after 12 hours 8, after 16 hours 4, after 20 hours 2 and after 24 hours 1. That is 6 half-lives, which leaves about 1.6% of the start. To find how long until 10% is left, use t = 4 × log2(100 ÷ 10) ≈ 13.3 hours.
Half-life for medications and peptides
Pharmacology uses the same idea: the half-life is the time for the amount of a substance in the body to fall by half. This page only shows the arithmetic. You type the half-life, so the calculator never supplies a value for any compound, and it does not model repeated doses, dosing intervals or build-up over time.
Real elimination varies with the person, the form taken and other factors, and it does not always follow a clean curve. Do not use this page to decide when or how much to take. Follow your prescriber's instructions.
Half-life calculators for specific substances
Each page below is this calculator already set to a published half-life, with the source cited.
- Caffeine half-life calculator · about 4 to 5 hours
- Cesium-137 half-life calculator · about 30 years
- Carbon-14 half-life calculator · 5,730 years, with a carbon dating example
- Caffeine calculator · several drinks and your bedtime
Frequently asked questions
What is half-life?
Half-life is the time it takes for an amount to fall to half of its value. After one half-life 50% is left, after two 25%, after three 12.5%. It applies to anything that decays at a rate proportional to how much is left, such as radioactive atoms or a chemical that breaks down.
What is the half-life formula?
N = N0 × (1/2)^(t ÷ t½), where N0 is the starting amount, t is the elapsed time and t½ is the half-life. To solve for the half-life, use t½ = t × ln 2 ÷ ln(N0 ÷ N). To find the time to reach an amount, use t = t½ × log2(N0 ÷ N).
How many half-lives until it is almost gone?
About 5. After 5 half-lives, 1/32 or roughly 3% of the starting amount is left. After 7 half-lives it is under 1%. In theory the amount never reaches exactly zero.
Do the time units have to match?
No. This calculator lets you pick minutes, hours, days, weeks or years for the half-life and for the elapsed time, and converts between them. A year is counted as 365.25 days.
How do I calculate half-life from two measurements?
Choose the second mode. Enter the starting amount, the amount left and the time that passed. The calculator uses t½ = t × ln 2 ÷ ln(N0 ÷ N). For example, 100 falling to 25 in 10 hours means a half-life of 5 hours.
How do I find how long until a target amount?
Choose the third mode. Enter the starting amount, the target (as an amount or a percent) and the half-life. Going from 100 to 12.5 takes 3 half-lives, so with a 5 hour half-life that is 15 hours.
Can I use this as a peptide or medication half-life calculator?
It does the same arithmetic for any substance, as long as you type in the half-life yourself. It does not know any compound's half-life, does not model how doses add up and does not suggest when to take anything. Real elimination varies from person to person.
Is my information saved?
No. The calculation runs in your browser. Nothing you type is uploaded or stored.
Math only. Not medical advice. Real-world elimination varies; follow your prescriber's instructions.