Rate Constant Calculator
The rate constant for a zero, first or second order reaction — from concentrations and time, or from the half-life.
Each reaction order has its own integrated rate law.
How the rate constant calculator works
Each reaction order has its own integrated rate law. Zero order: k = (C₀ − C)/t. First order: k = ln(C₀/C)/t. Second order: k = (1/C − 1/C₀)/t.
The orders behave quite differently. Only first order has a half-life independent of concentration, which is why radioactive decay and most drug elimination are described that way.
Formula: first order: k = ln(C₀/C) / t
Worked examples
| Inputs | Rate constant k | Note |
|---|---|---|
| First order, 1 M to 0.25 M in 100 s | 0.01386294 | two half-lives — k = 0.01386 s⁻¹ |
| From a 50 s half-life | 0.01386294 | the same k |
| Second order instead | 0.03 | k = 0.03 L·mol⁻¹·s⁻¹ |
FAQFrequently asked questions
What is a rate constant?
The proportionality constant in the rate law. Its units depend on the reaction order, which is a useful check that you have the order right.
Why is first order special?
Because its half-life does not depend on concentration. Radioactive decay and most drug elimination are first order, which is why half-life is such a useful number there.
How do I find the order?
Plot the data: concentration against time is linear for zero order, ln(C) for first, 1/C for second. Whichever gives a straight line is the order.
Do the units really differ?
Yes, and it matters. First order is s⁻¹, second order L·mol⁻¹·s⁻¹. A rate constant quoted without units is ambiguous.
How does temperature affect k?
Strongly, through the Arrhenius equation. A rough rule is that k roughly doubles for every 10 °C rize.
Where these figures come from
- IUPAC — Standard atomic weights (2021 conventional values) — the molar-mass table
- NIST — CODATA 2018 fundamental physical constants — Avogadro constant, gas constant, speed of light
- NIST Chemistry WebBook — thermochemical data
- National Institute of Standards and Technology — the US measurement and reference-data authority
Last checked: September 2026. Atomic masses are the IUPAC conventional values; constants are CODATA 2018; equations are the standard textbook forms.