Half-Life Calculator
How much of a substance is left after a time, how long it takes to fall to a level, or its half-life, from N = N₀ × (1/2)^(t / t½).
Result…
How it's calculated
N = N₀ × (1/2)^(t / t½) t = t½ × log₂(N₀ ÷ N) · t½ = t ÷ log₂(N₀ ÷ N) λ = ln 2 ÷ t½ · mean lifetime τ = t½ ÷ ln 2
A half-life is the time it takes for half of something to be gone. It describes radioactive decay exactly on average (carbon-14 has a half-life of about 5,730 years), and it is a common simple model for how a drug leaves the body. After one half-life 50% remains, after two 25%, after three 12.5%, and so on; it never quite reaches zero. Enter the time and the half-life in the same unit. Many drugs follow more than one rate, so for them the result is a rough guide only.
Your numbers, step by step
About the Half-Life calculator
This half-life calculator uses the decay formula N = N₀ × (1/2)^(t / t½) in three directions: how much of a substance remains after a time, how long it takes to fall to a given amount, or what its half-life is from two measurements. Alongside the answer it shows the fraction and percentage left, the number of half-lives that have passed, the decay constant and the mean lifetime. Amounts can be in any unit, such as milligrams, grams, becquerels or atoms, and the times in seconds, minutes, hours, days or years, as long as both times use the same unit. Students use it for radioactive decay and carbon dating questions, and it is a simple model of how a medicine level falls in the body. Drug levels found this way are an estimate, not medical advice. The steps show the powers and logarithms with your numbers; the logarithm calculator explains log₂.
How to use it
- Under “Solve for”, choose “Amount left”, “Time elapsed” or “Half-life”.
- Enter the “Starting amount” in any unit you like.
- Fill in the other two of “Amount remaining”, “Time elapsed” and “Half-life”.
- Pick the “Time unit (for both times)”, such as hours or years.
- Read the answer with the fraction and percent remaining and the number of half-lives.
Worked example
With a half-life of 6 hours, 400 mg falls to 400 × (1/2)^(18 ÷ 6) = 400 × (1/2)³ = 50 mg after 18 hours: 12.5% remains after 3 half-lives. Iodine-131 has a half-life of about 8.02 days, so falling to 10% takes 8.02 × log₂(100 ÷ 10) ≈ 26.64 days. With carbon-14's half-life of 5730 years, a quarter (25%) is left after 11,460 years, 2 half-lives.
Updated
Questions people ask
How do I calculate how much is left after a half-life?
Divide the time by the half-life to get the number of half-lives, then multiply the starting amount by (1/2) to that power. 100 g after 10 hours with a 5-hour half-life is 100 × (1/2)² = 25 g.
What is the formula for half-life?
N = N₀ × (1/2)^(t / t½). Rearranged, the time is t = t½ × log₂(N₀ ÷ N) and the half-life is t½ = t ÷ log₂(N₀ ÷ N). The exponent calculator works out powers like (1/2)^1.5.
How many half-lives until a substance is gone?
In theory it never reaches zero, because each half-life only halves what is left. After 5 half-lives about 3.1% remains, after 10 about 0.1%.
What is the difference between half-life and the decay constant?
They describe the same rate. The decay constant λ = ln 2 ÷ t½ is the fraction lost per unit of time in the continuous form N = N₀ × e^(−λt), and the mean lifetime is t½ ÷ ln 2.
Can I use this to work out a drug level in my body?
Only as a rough estimate. Real levels depend on the person, the dose and its timing, and how a drug is absorbed and cleared, and many drugs do not follow a single half-life. Ask a doctor or pharmacist before acting on it.