First-Order Reaction Calculator (Rate Constant, Half-Life)
First-order reaction calculator: concentration over time, rate constant, time or initial concentration, plus half-life.
[A] = [A]0 · e−kt
How to use this calculator
- Choose the quantity you want under “Solve for”.
- Type the known values and pick their units: any combination works.
- The result updates as you type. Open “Show the steps” to see the substitution.
For first-order kinetics [A] = [A]₀·e^(−kt), and the half-life t½ = ln 2 / k does not depend on concentration.
Formula
[A] = [A]0 · e−kt
| Symbol | Quantity | Units |
|---|---|---|
| [A]0 | Initial concentration | mol/L, mmol/L, µmol/L, nmol/L, mol/m³ |
| k | Rate constant | s⁻¹, min⁻¹, h⁻¹ |
| t | Time | s, ms, µs, ns, min, h, d, wk, yr |
| [A] | Concentration at t | mol/L, mmol/L, µmol/L, nmol/L, mol/m³ |
Worked example
Given: [A]0 = 0.1 mol/L · k = 0.01 s⁻¹ · t = 100 s
[A] = [A]0 e−kt
Result: [A] = 0.0367879 mol/L
Frequently asked questions
[A]₀ = 0.1 M and k = 0.01 s⁻¹: concentration after 100 s?
0.0368 M; the half-life is 69.3 s.