About the Half-Life Calculator
Half-Life Calculator solves the exponential decay formula N = N₀ × (½)^(t ÷ T) for whichever value you are missing. Choose whether to find the amount remaining, the time elapsed, the half-life or the starting amount, fill in the other three values, and read the answer. The amounts can be in any unit, such as grams, atoms or percent, and the times can be entered in seconds, minutes, hours, days or years, with the half-life and the elapsed time allowed to use different units. The tool also shows the decay constant, the mean lifetime and a table of how much is left after each half-life. It is useful for radioactive isotopes, carbon dating, medicine that leaves the body and any quantity that halves at a steady rate. Everything is worked out in your browser.
Updated September 2026
How to use the Half-Life Calculator
- 1Choose what you want to find: amount left, time, half-life or starting amount.
- 2Fill in the other boxes. The amounts can use any unit as long as both use the same one.
- 3Pick the time unit for the elapsed time and for the half-life.
- 4Read the answer in the big box, with the number of half-lives that passed.
- 5Look at the table to see how the amount falls after each half-life.
What a half-life is
A half-life is the time it takes for half of something to disappear. It was first used for radioactive atoms, where each atom has the same chance of decaying in any moment, so a large group falls in a steady, predictable way even though nobody can say when one atom will decay. The half-life is a property of the isotope: uranium-238 has about 4.5 billion years, carbon-14 about 5,730 years and iodine-131 about 8 days.
The same maths describes any exponential decay, such as a medicine in the blood, caffeine in the body, light passing through a material or a charged capacitor draining through a resistor.
The four questions this tool answers
- Amount left: you know the start, the half-life and the time.
- Time: you know how much started and how much is left, and the half-life.
- Half-life: you have measured the start, the end and the time between.
- Starting amount: you know how much is left now and want to go back in time.
Worked examples
A hospital has 40 mg of iodine-131 with a half-life of 8 days. After 24 days, three half-lives have passed and 5 mg remain. A sample of wood retains 12.5 percent of its carbon-14: three half-lives, so it is about 17,190 years old. If the caffeine in your body has a half-life of 5 hours and you drank a cup with 100 mg, about 25 mg is left after 10 hours.
Times do not have to match units: you can enter the half-life in years and the elapsed time in days, and the tool converts the time for you. A year is taken as 365.25 days.
Tips and limits
Amounts must be positive, and the remaining amount must be smaller than the starting amount, except when you solve for the starting amount from a smaller amount. Use the same unit for both amounts. For very large or small results, the tool switches to scientific notation, which Scientific Notation Converter can convert back to a plain decimal.
For the powers and logarithms behind the formula, Exponent, Root and Log Calculator helps, and Percentage Calculator turns the fraction left into a percentage. Unit Converter changes units of mass or time for your answers, and Compound Interest Calculator uses the same idea in reverse, for growth instead of decay.
Features
- Solves for remaining amount, time, half-life or initial amount
- Time units from seconds to years, mixable
- Decay constant and mean lifetime
- Table of the amount after each half-life
- Works for any unit of amount
- Clear messages for impossible inputs
- Runs in your browser
Frequently asked questions
What is the half-life formula?
N = N₀ × (1/2)^(t ÷ T), where N₀ is the starting amount, N the amount left, t the time that has passed and T the half-life. After one half-life half remains, after two a quarter, after three an eighth, and so on.
How do I calculate the amount remaining?
Divide the elapsed time by the half-life to get the number of half-lives, raise one half to that power and multiply by the starting amount. With 80 g of a substance that has a half-life of 5 years, after 15 years there are 3 half-lives, so 80 × 1/8 = 10 g remain.
How do I find the half-life from measurements?
Use the starting amount, the amount left and the time between them: T = t × ln 2 ÷ ln(N₀ ÷ N). If 100 g fall to 25 g in 10 days, the ratio is 4, which means two half-lives, so the half-life is 5 days. Choose Half-life in the tool to do this.
What are the decay constant and the mean lifetime?
The decay constant λ is the fraction that decays per unit of time, λ = ln 2 ÷ T. The mean lifetime τ is the average time a single atom survives, τ = T ÷ ln 2, which is about 1.44 times the half-life. Both are shown below the result.
Can I use it for carbon dating?
Yes, as a calculation. Carbon-14 has a half-life of about 5,730 years, so a sample with 25 percent of its original carbon-14 is about 11,460 years old. Real dating also needs calibration for changes in atmospheric carbon-14, which this tool does not do.
Does it work for things other than radioactivity?
Yes, for anything that falls by the same fraction in equal times. Examples are the amount of caffeine or medicine in the body, a drug's elimination half-life, and the voltage across a discharging capacitor. It will not fit processes that do not decay exponentially.