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    Half-Life Calculator

    GCSE PhysicsAQAEdexcelOCRCalculations: Higher tier

    Find the activity remaining, the starting activity, the time passed or the half-life. The working counts the half-lives and shows the fraction left, the way GCSE mark schemes expect.

    Quick answer

    After n half-lives, the activity is the starting activity × (½)n, where n = time ÷ half-life. For example, 800 Bq with a half-life of 6 hours, after 24 hours: n = 24 ÷ 6 = 4, so the activity is 800 × 1/16 = 50 Bq.

    By Engr. Mehmood Kakar · Updated

    A = A0 × (½)n,   n = t ÷ T½
    Find:

    Counts or numbers of nuclei work the same way. Use the same kind of value for both activities.

    Simulation

    Watch the activity halve

    Set the starting activity, the half-life and how many half-lives pass. The decay graph and the grid of nuclei both show the halving.

    800 Bq
    10 min
    3

    After each half-life, the activity (and the number of undecayed nuclei) halves. Radioactive decay is random: you can’t say which nucleus decays next, only how many on average.

    Put these numbers in the calculator above

    How to do half-life calculations

    The half-life of a radioactive isotope is the time it takes for the number of unstable nuclei in a sample to halve. It is also the time for the activity (or count rate) to fall to half its starting value.

    activity left = starting activity × (½)n,   where n = time ÷ half-life

    • A and A0 are activities in becquerels (Bq): decays per second
    • n is the number of half-lives that have passed
    • t and T½ must be in the same unit of time

    A sample with an activity of 800 Bq and a half-life of 6 hours, left for 24 hours, goes through 24 ÷ 6 = 4 half-lives. Its activity halves four times: 800 → 400 → 200 → 100 → 50 Bq. That is the same as 800 × (½)⁴ = 800 × 1/16 = 50 Bq.

    At GCSE, the numbers almost always give a whole number of half-lives, so you can halve step by step. The fraction left after n half-lives is called the net decline: 1/2, 1/4, 1/8, 1/16 and so on.

    Radioactive decay is random. You can't predict when one nucleus will decay, but with a very large number of nuclei the half-life lets you predict how the activity changes.

    Common mistakes that cost marks

    1. Using different time units. If the half-life is in minutes and the time is in hours, convert one so they match.
    2. Subtracting instead of halving. Each half-life halves what is left; it doesn’t remove a fixed amount.
    3. Miscounting half-lives. 800 → 400 is one half-life, 400 → 200 is two. Count the arrows, not the numbers.
    4. Thinking activity reaches zero. It keeps halving and gets very small, but in theory never reaches zero.

    Practice questions

    Try each one on paper first, then reveal the worked answer.

    Q1A sample has an activity of 800 Bq. Its half-life is 6 hours. Calculate its activity after 24 hours.[3 marks]
    1. n = 24 ÷ 6 = 4 half-lives
    2. 800 → 400 → 200 → 100 → 50
    3. or 800 × (½)⁴ = 800 × 1/16
    4. A = 50 Bq
    Q2The activity of a sample falls from 1200 Bq to 150 Bq in 36 minutes. Calculate its half-life.[3 marks]
    1. 1200 → 600 → 300 → 150: 3 half-lives
    2. Half-life = 36 ÷ 3
    3. T½ = 12 minutes
    Q3Carbon-14 has a half-life of 5700 years. A bone has 1/8 of the carbon-14 activity of living material. Calculate the age of the bone.[3 marks]
    1. 1 → 1/2 → 1/4 → 1/8: 3 half-lives
    2. Age = 3 × 5700
    3. Age = 17,100 years

    Endless practice

    A new question every time, marked instantly. Work it out on paper, then type your answer.

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    Frequently asked questions

    What is half-life?

    The time it takes for the number of unstable nuclei in a sample of a radioactive isotope to halve, or for the activity or count rate to fall to half its starting value.

    How do I calculate the activity after several half-lives?

    Find the number of half-lives, n = time ÷ half-life, then halve the starting activity n times. That is the same as multiplying by (½)ⁿ.

    What is net decline?

    The fraction of the original activity (or nuclei) left after a number of half-lives. After 3 half-lives the net decline gives 1/8 of the original; in AQA GCSE Physics this calculation is Higher tier.

    How do I find half-life from a graph?

    Read off the starting activity, find half of it on the y-axis, go across to the curve and down to the time axis. That time is the half-life.