First-Order Half-Life Calculator
Compute the half-life and remaining concentration of a first-order reaction from its rate constant.
1/s
M
s
Time for the concentration to fall by half
- 1
ln(2)
0.6931The natural logarithm of 2 appears because the concentration falls by half each half-life. - 2
Half-life t½ = ln(2) ÷ k
0.6931 ÷ 0.05 = 13.8629
How does this calculator work?
For a first-order reaction the half-life is t½ = ln(2)/k ≈ 0.693/k and depends only on the rate constant, not the starting amount. The remaining concentration after time t follows [A]t = [A]0·e^(−k·t). Enter k (and optionally [A]0 and t) to get the half-life, remaining concentration, and a decay curve.
Formula
How this is calculated
A first-order reaction has a rate that is directly proportional to the concentration of a single reactant. Its half-life depends only on the rate constant k (in inverse seconds), not on the starting concentration, so each successive half-life takes the same amount of time. The half-life is t½ = ln(2)/k ≈ 0.693/k. Enter k to get the half-life directly.
To find how much reactant is left after a given time, the calculator uses the integrated first-order rate law [A]t = [A]0·e^(−k·t). Provide the optional initial concentration [A]0 (in molarity) and a time t (in seconds) to evaluate the remaining concentration [A]t and the fraction remaining (e^(−k·t)). The mean lifetime, τ = 1/k, is the time at which the concentration falls to 1/e (about 37%) of its initial value.
Units must be consistent: k is given in 1/s and t in seconds here, so concentrations are reported in the same units as [A]0. The model assumes a single elementary first-order step at constant temperature with no reverse reaction. k must be positive; a zero or negative k is invalid because the half-life would be undefined or unphysical. The decay curve samples [A] versus time across roughly five half-lives, by which point about 97% of the reactant has been consumed.
Frequently asked questions
No. For a first-order reaction the half-life t½ = ln(2)/k depends only on the rate constant, so it is constant regardless of how much reactant you start with.
For a first-order reaction k has units of inverse time. This calculator uses 1/s, so times are in seconds. If your k is in 1/min or 1/hr, convert it (or your time) to keep units consistent.
It uses the integrated rate law [A]t = [A]0·e^(−k·t). After one half-life half remains, after two half-lives a quarter remains, and so on.
Also known as
TG we-Calculate Editorial Team. (2026). First-Order Half-Life Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/first-order-half-life-calculator
TG we-Calculate Editorial Team. "First-Order Half-Life Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/first-order-half-life-calculator.
TG we-Calculate Editorial Team, "First-Order Half-Life Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/first-order-half-life-calculator
@misc{wecalculate_first_order_half_life_calculator, title = {First-Order Half-Life Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/first-order-half-life-calculator}}, year = {2026}, note = {TG we-Calculate} }
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