How the Half-Life Calculator works.
N(t) = N₀ × 2⁻ᵗ/ᵗ¹ᐟ²; t = t¹ᐟ² × log₂(N₀/N)N₀ is initial amount, N(t) is remaining amount, t is elapsed time, and t¹ᐟ² is the positive half-life.
Worked example for the Half-Life Calculator.
After three half-lives, 100 units become 12.5 units because 100 × 2⁻³ equals 12.5.
How to read this result.
Forward mode predicts remaining quantity. Inverse mode finds the elapsed time needed to reach a chosen positive remaining quantity.
How the calculation works
Remaining amount after time t is initial amount × 2 raised to −t divided by half-life; inverse time is half-life × log₂(initial divided by remaining amount). Formula or rule: N(t) = N₀ × 2⁻ᵗ/ᵗ¹ᐟ²; t = t¹ᐟ² × log₂(N₀/N). N₀ is initial amount, N(t) is remaining amount, t is elapsed time, and t¹ᐟ² is the positive half-life.
What this calculator does not prove
The model assumes a constant half-life and exponential decay. It does not model replenishment, multiple decay chains, changing conditions, or measurement noise. Use the result for the mathematical question shown here; a correct calculation does not by itself establish that the source data, sample, or real-world assumption is appropriate.
Inputs and edge cases to check.
Initial amount and half-life must be positive; time cannot be negative; inverse remaining amount must be greater than zero and no greater than the initial amount.
What this tool does not include.
The model assumes a constant half-life and exponential decay. It does not model replenishment, multiple decay chains, changing conditions, or measurement noise.
Reference guidance and methodology.
Half-Life Calculator questions.
What does the Half-Life Calculator calculate?
Calculate remaining amount after elapsed half-lives or solve backward for the time to reach a chosen amount.
Which formula or algorithm does it use?
N(t) = N₀ × 2⁻ᵗ/ᵗ¹ᐟ²; t = t¹ᐟ² × log₂(N₀/N). N₀ is initial amount, N(t) is remaining amount, t is elapsed time, and t¹ᐟ² is the positive half-life.
What limitations or edge cases matter?
Initial amount and half-life must be positive; time cannot be negative; inverse remaining amount must be greater than zero and no greater than the initial amount. The model assumes a constant half-life and exponential decay. It does not model replenishment, multiple decay chains, changing conditions, or measurement noise.