Half Life Reaction Calculator

Calculator Inputs

This page keeps a single-column content flow, while the input area expands to three columns on large screens, two on medium screens, and one on mobile.

Choose a goal first. The page will tell you which values are essential.

Calculation Goal Each goal uses the correct kinetic relationship.

Reaction Order Half-life depends on order and sometimes on initial concentration.

Time Unit Use one time unit consistently across all entries.

Concentration Unit Examples: mol/L, mmol/L, mg/L.

Initial Concentration [A]₀ Required for concentration, elapsed-time, and some half-life cases.

Remaining Concentration [A]ₜ Use when solving elapsed time or reconstructing the initial value.

Rate Constant k Units change with reaction order.

Elapsed Time t Use zero or positive time values only.

Half-life t½ Use this when solving directly for the rate constant.

Graph End Time Optional. Leave blank for an automatic range.

Graph Points Higher values make a smoother plotted curve.

Reset

Example Data Table

This example compares half-life behavior for identical starting concentrations under three common kinetic models.

Reaction Order	Initial Concentration [A]₀	Rate Constant k	Half-life Formula	Half-life Result
Zero-order	1.20 mol/L	0.10 mol/L·min⁻¹	t½ = [A]₀ / 2k	6 min
First-order	1.20 mol/L	0.12 min⁻¹	t½ = ln(2) / k	5.776 min
Second-order	1.20 mol/L	0.18 L·mol⁻¹·min⁻¹	t½ = 1 / k[A]₀	4.63 min

Formula Used

Different reaction orders use different kinetic laws. The calculator automatically applies the correct relationship after you choose the reaction order.

Zero-order kinetics

[A]t = [A]0 − kt t½ = [A]0 / 2k

First-order kinetics

[A]t = [A]0 e^(−kt) t½ = ln(2) / k t = ln([A]0 / [A]t) / k

Second-order kinetics

1 / [A]t = 1 / [A]0 + kt [A]t = [A]0 / (1 + k[A]0t) t½ = 1 / k[A]0

The graph plots concentration against time from the resolved values. Exported results include both summary metrics and graph data points.

How to Use This Calculator

Choose the calculation goal, such as half-life, rate constant, or remaining concentration.
Select the reaction order that matches your chemical system.
Enter concentration values, rate constant, half-life, or elapsed time as needed.
Keep all entries in one consistent time unit and concentration unit.
Press Calculate Now to show the result above the form under the header.
Review the computed table, decay graph, and derived percentages.
Use the export buttons to download the result as CSV or PDF.

FAQs

1. What does reaction half-life mean?

Reaction half-life is the time needed for a reactant concentration to decrease to half of its starting value under a defined kinetic model and fixed conditions.

2. Why does half-life depend on reaction order?

The governing rate law changes with order. Zero and second-order half-lives depend on starting concentration, while first-order half-life remains constant at a given temperature.

3. Can I use any concentration unit?

Yes. You can use mol/L, mmol/L, mg/L, or another consistent unit. The calculator treats the concentration unit as a label and keeps it throughout.

4. What unit should the rate constant use?

Zero-order uses concentration per time, first-order uses inverse time, and second-order uses inverse concentration-time. The calculator displays the matching rate-constant unit automatically.

5. Why can zero-order concentration reach zero on the graph?

Zero-order decay is linear. Once the calculated concentration falls to zero, the reactant is fully consumed, so the plotted concentration is held at zero.

6. Why does second-order initial concentration sometimes fail?

Some combinations of remaining concentration, rate constant, and time imply a mathematically impossible starting concentration. The calculator blocks those combinations and asks for adjusted inputs.

7. Can I export my calculated results?

Yes. The page includes CSV and PDF export buttons after a successful calculation. The exports include the result summary and a sample of graph data.

8. Is this calculator useful for teaching and lab work?

Yes. It helps compare orders, inspect decay trends, validate manual work, and produce quick output tables for classroom exercises or experimental reviews.