How to use the first-order reaction calculator
Find concentration and half-life for a first-order reaction. Enter initial concentration, rate constant, time in the fields above; the concentration at t, half-life, fraction remaining are computed instantly and plotted on the chart so you can see how the answer changes.
Formula
Variables
- A0 — Initial concentration (mol/L)
- k — Rate constant (1/s)
- t — Time (s)
Worked example
With initial concentration = 1 mol/L, rate constant = 0.02 1/s, time = 60 s, the calculator gives concentration at t ≈ 0.3011942 mol/L; half-life ≈ 34.65736 s; fraction remaining ≈ 30.11942 %.
Frequently asked questions
What is the formula for the first-order reaction calculation?
Concentration at t (mol/L) = A0 × exp(-k × t). Half-life (s) = ln(2) / k. Fraction remaining (%) = 100 × [Concentration at t] / A0. Here A0 is initial concentration (mol/L), k is rate constant (1/s), t is time (s).
What inputs do I need for the first-order reaction calculator?
You need initial concentration in mol/L, rate constant in 1/s, time in s. Each field is pre-filled with a typical example so you can see how the result responds as you edit the numbers.
How do I use this calculator?
Type values into the input fields. Results and the chart update instantly. Use Reset to restore the example values, Copy results to paste them elsewhere, or Share to copy a link that preserves your inputs.
Is the result exact?
Calculations use standard formulas and double-precision arithmetic, then display about seven significant figures. Real-world measurements carry uncertainty, so treat results as estimates unless your inputs are exact.