Calculators
Half-Life Calculator
Solve for remaining amount, initial amount, elapsed time, or half-life with N = N0(1/2)^(t/t1/2), plus decay constant and half-lives elapsed, locally in your browser.
Choose what to solve for, then enter the other three values using consistent units. Amounts can be mass, atom count, activity, or a percentage as long as the initial and remaining values share the same unit, and the half-life and elapsed time must use the same time unit. The decay constant is reported per one time unit. Calculations run locally in your browser; your values are not uploaded or stored.
Solve exponential decay for any single variable.
Choose what to solve for, then enter the other three values in consistent units. Amounts can be mass, atom count, activity, or a percentage, as long as the initial and remaining values share the same unit; the half-life and elapsed time must share the same time unit. For example, a sample with a 5-hour half-life keeps 100 x (1/2)^(10/5) = 25 of 100 units after 10 hours, which is two half-lives. The result also reports the decay constant as ln(2) divided by the half-life, in reciprocal time units. To find a time or half-life, the initial and remaining amounts must be positive and the remaining amount cannot exceed the initial amount; determining a half-life needs a remaining amount strictly less than the initial amount and a positive elapsed time. This is a physics and chemistry estimate; all calculations stay in your browser.
Frequently Asked Questions
Everything you need to know about this tool, how it works, and privacy.
Which formula does the half-life calculator use?
It uses the exponential decay equation N = N0 x (1/2)^(t / t1/2), where N is the remaining amount, N0 is the initial amount, t is the elapsed time, and t1/2 is the half-life. Rearranged: N0 = N / (1/2)^(t / t1/2), t = t1/2 x log2(N0 / N), and t1/2 = t x ln(2) / ln(N0 / N). The decay constant is lambda = ln(2) / t1/2.
Which units should I use?
Use the same unit for the initial and remaining amounts. They can be mass, atom count, activity such as becquerels, or a percentage, as long as they match. The half-life and elapsed time must also share one time unit, such as hours or days. The decay constant is reported per one time unit.
What is the decay constant?
The decay constant lambda is the probability of decay per unit time. It relates to the half-life by lambda = ln(2) / t1/2, so a shorter half-life means a larger decay constant. For example, a 5-hour half-life gives a decay constant of about 0.1386 per hour.
Which inputs are accepted?
Enter positive amounts and half-life values and a non-negative elapsed time, all up to 1,000,000,000,000. To find a time, the remaining amount cannot exceed the initial amount. To find a half-life, the remaining amount must be strictly less than the initial amount and the elapsed time must be greater than zero. Missing, non-numeric, or invalid entries show a clear error instead of a result.
Is this a substitute for a lab measurement?
No. It applies the ideal exponential decay model to the numbers you enter and assumes a single, constant half-life. Real samples can follow more complex decay chains or be affected by measurement error. Use it as a general estimate and verify critical work with measured data. The calculation and copy run locally in your browser; CodeASystem does not upload or store your values.