Reaction Rate Calculator
Calculate average chemical reaction rate, reactant consumption rate, apparent rate constant k, and half-life from initial and final molarity and Δt.
Open toolIntegrated Rate Law Calculator
Enter experimental time and molar concentration pairs (`t, [A]`) to simultaneously regress Zero-Order (`[A]` vs. `t`), First-Order (`ln[A]` vs. `t`), and Second-Order (`1/[A]` vs. `t`) integrated rate laws, compare `R²` goodness-of-fit, and extract rate constant `k` and half-life `t₁/₂`.
Free to useNo sign-upRuns in your browser
Enter your details
Enter the inputs, then select Fit Integrated Rate Laws.
Your result
Enter your details
Result will appear here
How the Integrated Rate Law Regression Works
Instead of guessing the reaction order in advance, this calculator transforms your `(t, [A])` dataset into all three canonical kinetic coordinates and performs ordinary least-squares (OLS) linear regression on each.
0th: [A]_t = [A]_0 - k*t; 1st: ln[A]_t = ln[A]_0 - k*t; 2nd: 1/[A]_t = 1/[A]_0 + k*t.
Performs ordinary least-squares regression on [A] vs. t, ln[A] vs. t, and 1/[A] vs. t simultaneously, reporting R², residual RMSE in concentration units, fitted [A]_0, rate constant k with exact units, and half-life t_{1/2}.
Zero, First & Second-Order Integrated Rate Law Equations & Half-Life Table
Reference equations, linear plots, slope meanings, rate constant units, and half-life formulas for single-reactant kinetics (`A -> Products`).
| Reaction Order | Differential Rate Law | Integrated Linear Form | Linear Plot (y vs. x) | Slope & Units of k | Half-Life (t₁/₂) |
|---|---|---|---|---|---|
| Zero Order (`n = 0`) | `Rate = k` | `[A]_t = -k*t + [A]_0` | `[A]` vs. `t` | `Slope = -k` (`M·s⁻¹`) | `[A]_0 / (2k)` |
| First Order (`n = 1`) | `Rate = k[A]` | `ln[A]_t = -k*t + ln[A]_0` | `ln[A]` vs. `t` | `Slope = -k` (`s⁻¹`) | `ln(2) / k ≈ 0.693 / k` |
| Second Order (`n = 2`) | `Rate = k[A]²` | `1/[A]_t = k*t + 1/[A]_0` | `1/[A]` vs. `t` | `Slope = +k` (`M⁻¹·s⁻¹`) | `1 / (k*[A]_0)` |
How to use Integrated Rate Law Calculator step by step
Enter the values for your scenario, verify the units, and run the calculation.
Enter the inputs
Start by entering the required fields in the Integrated Rate Law Calculator form above.
Verify units and assumptions
Match each value to the unit or format shown next to the input box before running the calculation.
Run and export your result
Select Fit Integrated Rate Laws, inspect the primary metric and breakdown cards, then use Copy result or Download result.txt.
Worked examples for Integrated Rate Law Calculator
Compare baseline and alternative runs for Integrated Rate Law Calculator before exporting the result.
Baseline example
Determine reaction order (0th, 1st, or 2nd) from time-concentration data by linearizing [A], ln[A], and 1/[A] vs. time t, comparing R² and RMSE, and calculating rate constant k and half-life.
Comparison scenario
0th: [A]_t = [A]_0 - k*t; 1st: ln[A]_t = ln[A]_0 - k*t; 2nd: 1/[A]_t = 1/[A]_0 + k*t.
Boundary check before exporting
Performs ordinary least-squares regression on [A] vs. t, ln[A] vs. t, and 1/[A] vs. t simultaneously, reporting R², residual RMSE in concentration units, fitted [A]_0, rate constant k with exact units, and half-life t_{1/2}.
How to interpret the Integrated Rate Law Calculator output
Review the calculated output alongside your entered parameters and unit conventions.
Performs ordinary least-squares regression on [A] vs. t, ln[A] vs. t, and 1/[A] vs. t simultaneously, reporting R², residual RMSE in concentration units, fitted [A]_0, rate constant k with exact units, and half-life t_{1/2}.
Experimental Verification Checklist
Check these three conditions before reporting kinetic parameters.
0th: [A]_t = [A]_0 - k*t; 1st: ln[A]_t = ln[A]_0 - k*t; 2nd: 1/[A]_t = 1/[A]_0 + k*t. Performs ordinary least-squares regression on [A] vs. t, ln[A] vs. t, and 1/[A] vs. t simultaneously, reporting R², residual RMSE in concentration units, fitted [A]_0, rate constant k with exact units, and half-life t_{1/2}.
Order Fill Rate Analyzer
Analyze warehouse fulfillment performance from order line data: compute unit fill rate, line fill rate, order fill rate, and backorder recovery with explicit gross vs. net denominators.
Open tool
Cycle Time Analyzer (Bottleneck, Takt Time & Little's Law WIP)
Calculate bottleneck cycle time, Takt time margin, hourly and shift throughput, line balance efficiency, flow efficiency, and Little's Law WIP from workstation times.
Open toolMore free tools to try
Choose another tool for your next calculation, conversion, or text task.
Lawn Mowing Time Calculator (Deck Width, Overlap, Speed & Acres/Hr)
Calculate how long it takes to mow any lawn size by deck width, mowing speed, pass overlap, and turn/obstacle field efficiency.
Open tool
Metal Removal Rate Calculator
Calculate CNC milling and turning Metal Removal Rate (MRR in cm³/min and in³/min), estimated spindle power (kW / HP), and chip load.
Open tool
Hiking Time Calculator (Naismith's Rule, Elevation Gain & Pace)
Calculate hiking time from trail distance, elevation gain, elevation loss, base flat pace, and terrain difficulty using Naismith's Rule, Langmuir descent adjustments, and Tobler's function.
Open tool
Reverberation Time Calculator (Sabine & Eyring RT60 Acoustic Formula)
Calculate room reverberation time (RT60) using Sabine (0.161 V / A) and Norris-Eyring formulas from room volume and surface absorption coefficients.
Open toolIntegrated Rate Law Calculator: common questions
Answers about using Integrated Rate Law Calculator and understanding its results.
How do you determine reaction order using integrated rate laws?
Plot your experimental time-concentration data in three linearized forms: [A] vs. t (zero-order), ln[A] vs. t (first-order), and 1/[A] vs. t (second-order). Whichever transformation yields a straight line with the highest coefficient of determination (R² closest to 1.0000) and random residuals identifies the reaction order.
What are the units of the rate constant k for 0th, 1st, and 2nd order reactions?
For a zero-order reaction, k has units of M·s⁻¹ (mol·L⁻¹·s⁻¹). For a first-order reaction, k has units of s⁻¹. For a second-order reaction, k has units of M⁻¹·s⁻¹ (L·mol⁻¹·s⁻¹).
Why is first-order half-life independent of initial concentration [A]_0?
In a first-order reaction, t_{1/2} = ln(2) / k ≈ 0.6931 / k. Because concentration decays exponentially, taking 50% of any starting concentration always requires the exact same time interval. By contrast, zero-order half-life (t_{1/2} = [A]_0 / 2k) decreases as the reaction proceeds, and second-order half-life (t_{1/2} = 1 / (k·[A]_0)) doubles with each successive half-life.
Can I include zero or negative concentrations in the dataset?
No. Because first-order linearization requires ln[A] and second-order linearization requires 1/[A], every experimental concentration point must be strictly positive ([A] > 0).
Try your own values
Choose another tool for your next calculation, conversion, or text task.