Half-Life Calculator (Chemistry)

Calculate half-life of chemical reactions for first order kinetics: t-half = 0.693/k. Find k from half-life, or determine concentration remaining after any number of half-lives.

⏱️ Kinetics📐 t½ = 0.693/k (first order)🧪 Chemistry

Rate constant k (s^-1 for 1st order)

OR half-life t1/2

Initial concentration [A]0

Time elapsed t

Please enter valid values.

Formula & Reference

Variable	Symbol	Formula	Units
Half-Life Calculator (Chemistry)	See formula	t½ = 0.693/k (first order)	seconds or same as 1/k

Step-by-Step Examples

Example 1

Find t1/2 from k

First order reaction: k=0.0500 s^-1.

t_half = 0.693/k = 0.693/0.0500
t_half = 13.86 s

✓ t1/2 = 13.86 s

Example 2

Find k from t1/2

Drug with t1/2 = 6 hours. Find k.

k = 0.693/t_half = 0.693/(6x3600)
k = 0.693/21600 = 3.21x10^-5 s^-1

✓ k = 3.21x10^-5 s^-1

Example 3

Concentration After Time

First order, t_half=10 min. [A]0=1.00 M. [A] after 30 min?

30 min = 3 half-lives
[A] = [A]0 x (1/2)^3 = 1.00 x 0.125 = 0.125 M
Or: [A] = [A]0 x e^(-kt) = 1.00 x e^(-0.0693x30) = 0.125 M

✓ [A] = 0.125 M after 30 min (3 half-lives)

Real-World Applications

💊

Pharmacokinetics

Drug half-life determines dosing frequency. Aspirin: ~15 min. Ibuprofen: ~2 hours. Aspirin prodrug: ~6h.

☢️

Radioactive Decay

Chemical and nuclear first-order kinetics: same math. C-14 t1/2=5730 years for radiocarbon dating.

🌍

Environmental Chemistry

Pesticide half-lives in soil determine persistence and environmental impact.

🧪

Enzyme Kinetics

Michaelis-Menten kinetics reduces to first order at low substrate concentration.

Common Mistakes to Avoid

⚠️

t1/2 = 0.693/k only for first order

Zero order: t1/2 = [A]0/(2k). Second order: t1/2 = 1/(k[A]0). Only first order t1/2 is concentration-independent.

⚠️

k and t1/2 units must be compatible

If t_half in seconds, k in s^-1. If t_half in hours, k in h^-1. Same time units throughout.

⚠️

Each half-life reduces [A] by exactly half

After n half-lives: [A] = [A]0 x (0.5)^n. After 10 half-lives: ~0.1% remains.

Frequently Asked Questions

Why is it called a half-life? ▾

The time for exactly half of the substance to react or decay. For first order, this is constant regardless of starting concentration.

Why is first order t1/2 constant? ▾

Because the rate is proportional to current [A]. The same fraction reacts per unit time regardless of how much you start with.

What is the relationship between t1/2 and k? ▾

t1/2 = ln(2)/k = 0.6931/k. Derived from: [A] = [A]0*exp(-kt); set [A] = [A]0/2 and solve for t.

How many half-lives to reach 1% of original? ▾

[A]/[A]0 = 0.01 = 0.5^n. n = log(0.01)/log(0.5) = 6.64 half-lives. About 6-7 half-lives to reach 1%.

What is a biological half-life? ▾

Time for half of a drug to be eliminated from the body. Affected by absorption, distribution, metabolism, and excretion. Different from chemical half-life.

Related Chemistry Calculators

Formula Explorer connections

Interpretation: This formula connects concentration, time, temperature or transport to the speed of a chemical process. Assumption: The reaction order and mechanism must match the model. Temperature, catalyst, mixing and mass-transfer limitations can alter the observed rate.

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