Rate Constant Calculator
Use this Rate Constant Calculator to quickly find the reaction rate constant (k), the rate of reaction, a missing concentration, or the half-life – for zero, first, and second-order kinetics. It works both ways. Enter what you know, pick the reaction order, and the tool solves the rest with clean units and clear explanations.
What is the rate constant k?
The rate constant k links concentration to rate in a rate law. It captures everything that doesn’t change with concentration: the chemistry of the step, the temperature, and the chosen units. For a general elementary step
A + B → products with a rate law
rate = k[A]a[B]b,
a + b is the total order. The value of k depends on that order and the time units you pick.
Chemists measure rate in concentration per time—typically M·s−1. If you switch to minutes or hours then the number for k changes accordingly, which is why a good calculator lets you choose units explicitly.
How to use the Rate Constant Calculator
- Step 1: Choose the elementary type: unimolecular, bimolecular, or trimolecular. The tool shows the matching rate law instantly.
- Step 2: For each reactant, set the order with respect to that species—zero, first, or second—and type the initial concentration (leave one blank if you want the calculator to find it).
- Step 3 (optional): If you’re analyzing a single-reactant case, you can enter the half-life T½. The calculator uses the correct half-life formula for the chosen order.
- Step 4: Under Kinetics values, you may enter k or the rate, or leave both blank. The solver computes whichever values it can deduce from the information provided.
- Step 5: Read the results card. You’ll see the total reaction order, the correct k units for that order, and the computed values (k, rate, or a missing concentration) in the units you selected.
Rate laws by order (with equations)
Because reaction order changes how rate depends on concentration, each case has its own algebra and “straight-line” plot. Here’s the short, practical list you’ll actually use.
| Order | Differential rate law | Integrated form | Linear plot |
|---|---|---|---|
| Zero | rate = k | [A] = [A]0 − k t | [A] vs t → slope = −k |
| First | rate = k[A] | ln[A] = ln[A]0 − k t | ln[A] vs t → slope = −k |
| Second | rate = k[A]2 | 1/[A] = 1/[A]0 + k t | 1/[A] vs t → slope = k |
For multi-reactant steps, the general form is
rate = k[A]a[B]b[C]c.
The total reaction order is
n = a + b + c.
Units of k by reaction order
Units keep calculations honest. They also explain why different orders need different units of k. If rate uses M·time−1 and concentrations use M, then
| Total order (n) | k units | Example |
|---|---|---|
| 0 | M·time−1 | M·s−1, M·min−1 |
| 1 | time−1 | s−1, min−1, hr−1 |
| 2 | M−1·time−1 | M−1·s−1 |
| 3 | M−2·time−1 | M−2·s−1 |
The calculator displays these automatically as you change the total order or the time unit. That way you never wonder if a result is off by a factor of sixty.
Half-life formulas (T½) you can trust
Half-life behaves differently in each order. In first-order kinetics, it stays constant. In zero and second order, it depends on concentration.
- Zero order: T½ = [A]0 / (2k)
- First order: T½ = ln 2 / k
- Second order: T½ = 1 / (k[A]0)
Give the calculator T½ and the order, and it backs out k. Or enter k and it predicts the half-life that matches your units.
Worked examples you can follow
Example 1 — Find k from half-life (first order)
You monitor a unimolecular decomposition where T½ is 57 s. What’s k?
- Pick unimolecular, set order to first.
- Enter T½ = 57 s. You can leave the concentration blank.
- The calculator uses T½ = ln 2 / k, so k ≈ 0.01216 s−1.
Example 2 — Compute rate for a bimolecular step
Consider rate = k[A][B] with [A] = 5.0 M, [B] = 7.0 M, and k = 0.0105 M−1·s−1.
- Choose bimolecular. Set both orders to first.
- Enter the concentrations, pick seconds, and type k.
- The tool returns rate = 0.3675 M·s−1.
Example 3 — Solve a missing concentration
A trimolecular step shows k = 1.2×10−3 M−2·s−1 and rate = 3.0×10−2 M·s−1, with [A] = 0.45 M and [B] = 0.80 M, all first order. What is [C]?
Rearrange the rate law:
[C] = rate / (k[A][B]) = (3.0×10−2) / (1.2×10−3 × 0.45 × 0.80) ≈ 69.4 M
Typing these in the calculator yields the same value and reports consistent units automatically.
Temperature and the Arrhenius connection
The rate constant depends strongly on temperature. Arrhenius captured that with
k = A · exp(−Ea / (R T))
where A is the pre-exponential factor, Ea is the activation energy, R is the gas constant, and T is temperature. If you raise T, k grows exponentially. For a deeper dive, see the IUPAC Gold Book entry on the Arrhenius equation and this concise overview from LibreTexts.
Common pitfalls and pro tips
- Mind the order. If your total order is two then k needs units of M−1·time−1. If you see s−1 then you selected a first-order model by accident.
- Don’t mix unit systems. Millimolar and seconds give a different numeric k than molar and minutes. The calculator’s unit badges change as you switch; follow them.
- Half-life works only for single-reactant kinetics. When two reactants control the rate, half-life depends on both, so it can’t identify a unique k without extra constraints.
- Beware of initial rate traps. If you use the initial rate method, the very first seconds matter. Make sure your “initial” really means “before the reaction changes appreciably.”
- Look for linearity. If your first-order plot of ln[A] vs t curves, the mechanism or the order probably differs from what you assumed.
Rate constant FAQs
What does the rate constant mean physically?
It’s the proportionality factor that converts concentrations raised to their orders into a rate. At fixed temperature, larger k means a faster process under the same concentrations.
How do I determine reaction order?
Use method of initial rates, integrated plots, or isolation experiments. When you plot the right function—[A], ln[A], or 1/[A]—against time, a straight line reveals the order and k.
Can k be negative?
No. The sign of the slope in the integrated plot may be negative, yet k itself is a positive constant.
Does k change with concentration?
For an elementary rate law at a fixed temperature, k stays constant. Only temperature, solvent, and catalytic effects shift it, which Arrhenius captures.
Why are my units different from my textbook?
Time or concentration units differ. Convert everything to the same base, and the calculator’s k unit badge will match the order you selected.
Further reading
- IUPAC Gold Book: Rate constant – short, authoritative definitions.
- LibreTexts: Rate laws – in-depth yet readable.
- Khan Academy: Chemical kinetics – visual lessons with practice questions.
- Royal Society of Chemistry teacher notes on kinetics (PDF) – worked classroom activities and plots.
Quick reference cards
Zero-order summary
- rate = k
- [A] vs t → straight line; slope −k
- k units: M·time−1
- T½ = [A]0 / (2k)
First-order summary
- rate = k[A]
- ln[A] vs t → straight line; slope −k
- k units: time−1
- T½ = ln 2 / k (constant)
Second-order summary
- rate = k[A]2
- 1/[A] vs t → straight line; slope k
- k units: M−1·time−1
- T½ = 1 / (k[A]0)
How the calculator decides what to compute
The solver follows a simple, transparent playbook:
- If you give k: It calculates the rate from the rate law, as long as the required concentrations are present.
- If you give the rate: It calculates k.
- If you give a half-life for a single-reactant case: It computes k directly from the proper T½ formula.
- If exactly one required concentration is missing: It solves that concentration from the rate law when k and the rate are known.
- If nothing is solvable yet: It shows a friendly hint telling you what to add or clear.
The algorithm also converts all values to base units internally (M and seconds), performs the math, then converts back to the units you chose. That guarantees consistent numbers in the output chips.
Practical lab checklist
- Record temperature with each dataset. If the lab warms up, k does too.
- Note the solvent and ionic strength. They influence mechanisms and orders.
- Use fresh standard solutions. Concentration drift scrambles orders.
- Sample early and often for initial-rate experiments. The “initial” window closes fast.
- Plot the integrated forms to confirm order. Visual checks are powerful.
Why reaction order isn’t always the stoichiometric coefficient
Elementary steps often match. Complex mechanisms don’t. A measured first-order dependence might hide a pre-equilibrium or a rate-determining step. When data and stoichiometry disagree, follow the data. Mechanistic modeling then explains the numbers.
From classroom to industry
Pharmaceutical chemists rely on k to predict shelf life. Environmental scientists use it to model pollutant decay. Process engineers tune temperature to hit target rates without runaway reactions. Wherever molecules move, kinetics guides the timing.
