Use this half life calculator to solve remaining quantity, elapsed time, half-life, initial quantity, decay constant.
Last updated
Half-life calculator Use this half life calculator to solve remaining quantity, elapsed time, half-life, or starting quantity for radioactive decay and other first-order decay problems. The same model works for isotope dating, tracer loss, and any process that repeatedly halves over a fixed interval.
Solve for
Example scenarios
What this model assumes
Single-step exponential decay: the same fraction disappears in every half-life.
Activity falls with quantity: for radioactive samples, activity and undecayed nuclei drop by the same fraction.
No decay chain modelling: daughter products, branching pathways, shielding, or biological clearance need more specific tools.
Remaining
25 MBq
After 16 d, about 25% remains and 75% has decayed.
Remaining
25%
Decayed
75%
Half-lives elapsed
2
Decay constant
0.09 /d
Mean lifetime
11.54 d
1% remaining at
53.15 d
Formula used
N(t) = N₀ × (1/2)^(t/t½)
Interpretation
About 2 half-lives have elapsed. Every additional 8 d cuts the current amount in half again.
Practical checkpoint
Five half-lives leaves about 3.125% remaining. This page also shows the stricter 1% threshold so users can distinguish “mostly decayed” from “almost gone.”
Working and solved steps
Step
Expression
Value
Initial quantity
N₀
100 MBq
Half-lives elapsed
t ÷ t½ = 16 ÷ 8
2
Remaining quantity
N(t) = 100 × (1/2)^(2)
25 MBq
Half-life schedule
Checkpoint
Elapsed time
Remaining
% remaining
Start
0 d
100 MBq
100%
1 half-life
8 d
50 MBq
50%
2 half-lives
16 d
25 MBq
25%
3 half-lives
24 d
12.5 MBq
12.5%
5 half-lives
40 d
3.13 MBq
3.13%
10 half-lives
80 d
0.1 MBq
0.1%
Use isotope-specific half-life data A half life calculator is only as good as the half-life you enter. Use published isotope data for carbon-14, iodine-131, technetium-99m, or any other radionuclide, and treat this page as a simple first-order decay model rather than a full chain-decay or shielding simulation.
Half-life calculator: remaining amount, elapsed time, decay constant, and isotope examples
This half life calculator is built for the common questions people actually ask: how much of a radioactive sample remains after a given time, how long it takes to reach a known remainder, how to calculate half-life from measurements, and how half-life relates to decay constant and mean lifetime.
What half-life means
Half-life is the time required for a decaying quantity to fall to half of its current amount. In radioactive decay, that means half of the undecayed nuclei remain after one half-life, one quarter remain after two half-lives, and one eighth remain after three half-lives.
That is why a good half life calculator must do more than return one number. Users usually need to see the remaining fraction, the number of half-lives elapsed, and the practical checkpoints that explain whether the result means half the sample is left, only a few percent remain, or the sample is still in an early decay stage.
The same mathematical pattern appears in carbon dating, medical isotope planning, tracer loss, and many other first-order decay processes. The page stays focused on the generic science intent, while more specific medical elimination questions belong on dedicated drug half-life pages.
N(t) = N₀ × (1/2)^(t ÷ t½)
Remaining quantity after elapsed time t This is the specific relationship the calculator applies when building the result.
t = t½ × ln(N₀/N(t)) ÷ ln(2)
Elapsed time from a known starting and remaining quantity
t½ = t × ln(2) ÷ ln(N₀/N(t))
Half-life from measured decay over a known interval
Half-life, decay constant, and mean lifetime
Competitor pages frequently mention the decay constant and mean lifetime because users searching for a decay constant calculator or mean lifetime calculator are often solving the same physical model from a different starting point. The decay constant λ describes the probability per unit time that an undecayed nucleus will decay, while the mean lifetime τ is the average lifetime before decay in an exponential model.
These quantities are linked directly to half-life. A shorter half-life means a larger decay constant and a shorter mean lifetime. A longer half-life means a smaller decay constant and a longer mean lifetime. Keeping all three relationships visible helps users compare isotope data tables, classroom equations, and laboratory references without switching calculators.
This page therefore reports the decay constant and mean lifetime automatically after every solve, which makes it more useful than a bare half-life formula calculator that stops at a single output.
λ = ln(2) ÷ t½
Decay constant from half-life This is the specific relationship the calculator applies when building the result.
τ = 1 ÷ λ = t½ ÷ ln(2)
Mean lifetime from half-life This is the specific relationship the calculator applies when building the result.
A(t) ∝ N(t)
For radioactive decay, activity falls in the same proportion as undecayed nuclei
How many half-lives until almost nothing remains?
A common user question is not just how to calculate half-life, but how many half-lives it takes to get close to zero. After one half-life, 50% remains. After two half-lives, 25% remains. After three half-lives, 12.5% remains. After five half-lives, 3.125% remains. After about 6.64 half-lives, only about 1% remains.
That distinction matters because many SERP pages mention five half-lives as a rule of thumb but do not help users compare that checkpoint with a stricter 1% threshold. This page shows both. Five half-lives is useful for 'mostly decayed'; 6.64 half-lives is more useful when the user means 'almost gone.'
A practical radioactive decay calculator should expose those checkpoints directly because users often need planning context, not just a rearranged algebraic result.
1 half-life: 50% remaining
2 half-lives: 25% remaining
3 half-lives: 12.5% remaining
5 half-lives: 3.125% remaining
6.64 half-lives: about 1% remaining
Worked example: carbon-14 dating
Carbon-14 is the classic half-life example because its half-life is about 5,730 years and the isotope is useful for radiocarbon dating over archaeological timescales. If a sample has 25% of its original carbon-14 remaining, then two half-lives have passed because 25% equals one quarter, or (1/2)^2.
Two carbon-14 half-lives correspond to about 11,460 years. That is exactly the kind of elapsed-time solve people look for when they search terms like carbon-14 half life calculator, radioactive dating calculator, or how old is a sample from the remaining fraction.
The calculator handles this directly by solving elapsed time from the initial quantity, remaining quantity, and half-life. It then gives the same decay relationships in a clearer way than competitor pages that leave users to infer the checkpoint table on their own.
Worked example: iodine-131 and technetium-99m
Shorter-lived isotopes are common in imaging and therapy planning. Iodine-131 has a half-life of about 8 days, while technetium-99m has a half-life of about 6 hours. Those examples are useful because they show how the same half-life formula applies across very different time scales.
If an iodine-131 sample starts at 100 MBq and 16 days pass, two half-lives have elapsed, so 25 MBq remain. If a technetium-99m tracer starts at 12 mCi and 18 hours pass, three half-lives have elapsed, so 1.5 mCi remain. The decay constant and mean lifetime differ greatly, but the fraction-remaining logic is the same.
This generic page uses isotope examples to explain the physics, not to provide medical advice. For patient-specific timing, biological clearance, or drug-elimination questions, use a dedicated calculator built for that context.
When a simple half-life model is appropriate
The standard half-life formula assumes one-step exponential decay. That works well for a single radionuclide, classroom kinetics problems, and many first-pass planning questions where the task is to compare quantity over time or estimate a remaining fraction.
The model is weaker when daughter products also decay, when decay branches are important, when the quantity being tracked is not a simple single-component exponential process, or when the relevant real-world outcome depends on shielding, detector geometry, biological elimination, or multiple compartments.
That is why the calculator keeps the assumptions visible instead of hiding them. A result can be mathematically correct for the simple model and still be the wrong decision aid for a more complex physical system.
Common mistakes with a half life formula calculator
One frequent mistake is mixing units. If elapsed time is entered in days but the half-life is in hours, the answer will be wrong unless the units are converted consistently. This page uses one displayed time unit at a time so the relationship is explicit.
Another mistake is treating the decay as linear instead of exponential. After each half-life, you remove half of what remains, not half of the original amount. That is why the curve flattens over time and why a sample can keep tiny residual amounts for many half-lives.
A third mistake is assuming 'five half-lives' means literal zero. It does not. A sample still has about 3.125% left at that point, which may or may not matter depending on the context.
Why this page is stronger than a bare radioactive decay calculator
Many competing pages stop after solving one unknown. This page goes further by surfacing the decay constant, mean lifetime, number of half-lives elapsed, a worked-step table, and a checkpoint schedule through ten half-lives. That makes the result easier to interpret for both quick answers and deeper study.
The scenario presets also cover common search intents: generic radioactive decay, carbon dating, and short-lived isotope questions. Instead of forcing the user to start from blank fields, the page demonstrates realistic solves immediately and lets the user pivot from them.
That combination of calculator utility, interpretation, and source-backed article depth is what gives the page a meaningful advantage over thinner half life calculator results in the SERP.
Frequently asked questions
What is the formula for a half life calculator?
The standard formula is N(t) = N₀ × (1/2)^(t ÷ t½), where N₀ is the starting quantity, N(t) is the remaining quantity after time t, and t½ is the half-life. Rearranging that equation lets you solve elapsed time, half-life, or initial quantity from the other known values.
How do I calculate elapsed time from half-life and the remaining amount?
Use t = t½ × ln(N₀/N(t)) ÷ ln(2). In practice, you enter the initial quantity, the remaining quantity, and the half-life, and the calculator returns how much time must have passed for that decay to occur.
How do I calculate half-life from measurements?
If you know the initial quantity, the remaining quantity, and the elapsed time, solve t½ = t × ln(2) ÷ ln(N₀/N(t)). This is useful for classroom decay experiments where you observe how a count rate or sample amount changes over a known interval.
What is the difference between half-life and decay constant?
Half-life is the time needed for the amount to fall by 50%. The decay constant λ is the per-unit-time decay probability in the exponential model. They are linked by λ = ln(2) ÷ t½, so they describe the same process from different angles.
What is mean lifetime?
Mean lifetime τ is the average lifetime before decay in an exponential model. It is equal to 1 ÷ λ and also equal to t½ ÷ ln(2). Mean lifetime is longer than half-life because it describes the average survival time rather than the 50% checkpoint.
How many half-lives until 1% remains?
It takes about 6.64 half-lives for only 1% to remain. That is stricter than the common five-half-life rule of thumb, which still leaves about 3.125% of the original amount.
How many half-lives until 25% remains?
Two half-lives. The remaining fraction after n half-lives is (1/2)^n, so (1/2)^2 = 1/4 = 25%.
Is radioactive activity reduced by the same fraction as the remaining quantity?
Yes, for a single radionuclide under a simple radioactive decay model. Activity is proportional to the number of undecayed nuclei, so if 25% of the nuclei remain, the activity is also 25% of its original value.
Can this page be used as a radioactive decay calculator?
Yes. A half life calculator and a simple radioactive decay calculator are solving the same exponential relationship when the problem is to find remaining quantity, elapsed time, half-life, or starting quantity for one radionuclide.
Can I use this for carbon-14 dating?
Yes. Carbon-14 dating is one of the most common half-life applications. If you know the expected original carbon-14 level, the measured remaining amount, and the carbon-14 half-life, the calculator can estimate elapsed time.
Does five half-lives mean the sample is gone?
No. After five half-lives, about 3.125% remains. That is often small enough to be described as mostly decayed, but it is not literally zero and it may still matter depending on the context.
When does the simple half-life model break down?
It becomes less adequate when you need to model branching decay chains, daughter-product buildup, biological elimination, detector effects, or any system that is not a single-step exponential process. In those cases, a more specific model is needed.
