Half-Life CalculatorFree online math calculator — instant results, no sign-up
Remaining quantity after radioactive decay.
About the Half-Life Calculator
This calculator determines the remaining amount of a substance undergoing exponential decay and computes its decay constant. It is commonly used by students, researchers, and lab technicians working with radioactive isotopes, chemical reaction kinetics, or pharmacokinetics.
- Initial quantity
- The starting amount of the substance prior to decay, expressed in any unit such as grams, moles, or counts (must be non-negative).
- Time elapsed
- The total duration of time over which decay takes place, using the same time unit as the half-life.
- Half-life
- The time required for half of the substance to decay, expressed in the same time unit as time elapsed (must be greater than zero).
Formula and method
Remaining = N0 × 0.5^(t / h) Decay constant = ln(2) / h
- N0Initial quantity of the substance
- tTime elapsed
- hHalf-life period
- ln(2)Natural logarithm of 2 (approximately 0.693147)
The tool raises 0.5 to the power of elapsed time divided by half-life and multiplies the result by the initial quantity to determine the remaining amount. It also calculates the decay constant by dividing the natural logarithm of 2 by the half-life. Both values are rounded to six decimal places.
Worked example
These are the calculator's starting values and the results it actually produces for them.
Inputs
- Initial quantity100
- Time elapsed10
- Half-life5
Results
- Remaining25
- Decay constant0.138629
How to use the Half-Life Calculator
- 1Divide the elapsed time (t) by the half-life (h) to find the number of half-life cycles that have passed.
- 2Raise 0.5 to the resulting exponent to obtain the remaining fraction.
- 3Multiply that fraction by the initial quantity (N0) to compute the remaining substance.
- 4Divide the natural log of 2 (~0.693147) by the half-life (h) to calculate the decay constant.
Reading your result
The 'Remaining' value shows the quantity of the original substance left after the specified time elapsed. The 'Decay constant' indicates the proportional decay rate per unit of time associated with the specified half-life.
Limitations
The calculation assumes ideal first-order exponential decay with a constant decay rate. It does not account for background radiation, replenishment of the substance, measurement uncertainty, or complex multi-step decay chains.
Common questions
Do the time elapsed and the half-life need to be in specific units?+
No, you can use seconds, minutes, hours, days, or years, but both time elapsed and half-life must be entered using the exact same unit of time.
What does the decay constant represent?+
The decay constant (often denoted by the Greek letter lambda, λ) represents the probability per unit time that an individual atom or molecule will decay.
What happens if elapsed time is less than one half-life?+
The formula handles any non-negative time value smoothly; if time elapsed is less than one half-life, the fraction of the substance remaining will be between 50% and 100%.
Does the calculator save my information?+
Calculations run in your browser. While signed in, inputs and results are automatically recorded in account history; saving a result creates a separate saved record.
Further reading
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Results are estimates for informational purposes and are not financial, medical or legal advice.