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Radioactive decay and half-life calculator

GCSEA-level Nuclear and particles

The amount of a radioactive isotope left after a given time. The same equation works for count rate and activity.

N = N₀ (½)^{t / T_½}

This free calculator is for GCSE and A-level physics. Choose the quantity you want to find, enter the other values with their units, and it shows the working in the layout used in exams, with the answer to the number of significant figures you choose. The values shown are an example. Change them to your own.

Quantity to find

NAmount remaining to find 100

N₀Starting amount

tTime elapsed

T_½Half-life

Significant figures

Working

Write the equation
N = N₀ (½)^{t / T_½}
Substitute the values
N = 800 × (½)^{30 ÷ 10}
Calculate
N = 100
Give the answer to 3 significant figures
N = 100

Worked example

Find N, the amount remaining. Given: starting amount N0 = 800; time elapsed t = 30.0 s; half-life T½ = 10.0 s.

Write the equation
N = N₀ (½)^{t / T_½}
Substitute the values
N = 800 × (½)^{30 ÷ 10}
Calculate
N = 100
Give the answer to 3 significant figures
N = 100

Symbols and units

Symbol	Quantity	SI unit
N	Amount remaining	no unit
N₀	Starting amount	no unit
t	Time elapsed	s
T_½	Half-life	s

Radioactive decay and half-life: rearranged

To find amount remaining: N = N₀ (½)^{t / T_½}
To find starting amount: N₀ = N / (½)^{t / T_½}
To find time elapsed: t = T_½ log₂(N₀ / N)
To find half-life: T_½ = t / log₂(N₀ / N)

Exam tip

Use the same unit for t and for the half-life. The number of half-lives is t divided by T½.

Common questions

What is the formula for radioactive decay and half-life?

The equation is N = N0 (½)t / T½, where N is the amount remaining; N0 is the starting amount; t is the time elapsed (s); T½ is the half-life (s).

What units should I use for radioactive decay and half-life?

In SI units: amount remaining in no unit (a ratio), starting amount in no unit (a ratio), time elapsed in s, half-life in s. The calculator also accepts common alternatives such as kilometres, grams or minutes, and converts them for you.

How do I rearrange N = N0 (½)t / T½?

Rearranging gives these forms: to find amount remaining: N = N0 (½)t / T½. to find starting amount: N0 = N / (½)t / T½. to find time elapsed: t = T½ log2(N0 / N). to find half-life: T½ = t / log2(N0 / N).

Practise radioactive decay and half-life questions

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Read the full explanation on the Radioactive decay and half-life formula page. More nuclear and particles equations: Photon energy, Photon energy from wavelength, Photoelectric equation, de Broglie wavelength, Activity and decay constant, Half-life and decay constant, Mass–energy equivalence. See the full list on the physics equation calculator page.