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chemistry

Half-Life Calculator

Calculate the half-life of a first-order chemical reaction from the rate constant, or determine how much substance remains after a given time.

Reviewed by Christopher FloiedPublished Updated

This free online half-life calculator provides instant results with no signup required. All calculations run directly in your browser — your data is never sent to a server. Enter your values below and see results update in real time as you type. Perfect for everyday calculations, homework, or professional use.

First-order rate constant.

Starting quantity (any units).

Time elapsed in the same unit as k.

Results

Half-Life

27.726

Amount Remaining

47.237

Percent Remaining

47.2%

How to Use This Calculator

1

Enter your input values

Fill in all required input fields for the Half-Life Calculator. Most fields include unit selectors so you can work in your preferred unit system — metric or imperial, whichever matches your problem.

2

Review your inputs

Double-check that all values are correct and that you have selected the right units for each field. Incorrect units are the most common source of calculation errors and can produce results that are off by factors of 2, 10, or more.

3

Read the results

The Half-Life Calculator instantly computes the output and displays results with units clearly labeled. All calculations happen in your browser — no loading time and no data sent to a server.

4

Explore parameter sensitivity

Try adjusting individual input values to see how the output changes. This is a quick and effective way to develop intuition about how different parameters influence the result and to identify which inputs have the largest effect.

Formula Reference

Half-Life Calculator Formula

See calculator inputs for the governing equation

Variables: All variables and their units are labeled in the calculator interface above. Input fields accept values in multiple unit systems — select your preferred unit from the dropdown next to each field.

When to Use This Calculator

  • Use the Half-Life Calculator when you need accurate results quickly without the risk of manual computation errors or unit conversion mistakes.
  • Use it to verify calculations made by hand or in spreadsheets — an independent check can catch errors before they lead to costly decisions.
  • Use it to explore how changing input parameters affects the output — a quick way to develop intuition and identify the most influential variables.
  • Use it when collaborating with others to ensure everyone is working from the same numbers and applying the same assumptions.

About This Calculator

The Half-Life Calculator is a free, browser-based calculation tool for engineers, students, and technical professionals. Calculate the half-life of a first-order chemical reaction from the rate constant, or determine how much substance remains after a given time. It implements standard formulas and supports both metric (SI) and imperial unit systems with automatic unit conversion. All calculations are performed instantly in your browser with no data sent to a server. Use this calculator as a quick reference and sanity-check tool during design, analysis, and learning. Always verify results against primary engineering references and applicable standards for any safety-critical application.

About Half-Life Calculator

The half-life calculator for chemical reactions determines the time required for half of a reactant to be consumed in a first-order process, and also calculates how much substance remains after a given elapsed time. First-order kinetics apply to radioactive decay, many drug metabolism pathways, unimolecular decomposition reactions, and pseudo-first-order processes. The half-life of a first-order reaction is unique in being independent of the initial concentration — it depends only on the rate constant k. This makes it a convenient single parameter for characterizing reaction speed.

The Math Behind It

For a first-order reaction A → products, the rate law is −d[A]/dt = k[A], which integrates to [A] = [A]₀ · e^(−kt). Setting [A] = [A]₀/2 and solving for t gives t½ = ln(2)/k ≈ 0.6931/k. Notably, each successive half-life reduces the remaining amount by half: after one half-life, 50% remains; after two, 25%; after three, 12.5%; and so on. This geometric decay is characteristic of first-order processes. For zero-order reactions, t½ = [A]₀/(2k) and depends on initial concentration. For second-order reactions, t½ = 1/(k[A]₀) and also depends on concentration. Thus, the concentration-independent half-life is a hallmark of first-order kinetics. In pharmacology, the elimination half-life of a drug describes how quickly it is cleared from the body, guiding dosing intervals.

Formula Reference

First-Order Half-Life

t½ = ln(2) / k

Variables: t½ = half-life; k = first-order rate constant; ln(2) ≈ 0.6931

Worked Examples

Example 1: Drug elimination

A drug has k = 0.025 min⁻¹. Starting dose: 100 mg. Time: 30 min.

Step 1:t½ = 0.6931 / 0.025 = 27.7 min.
Step 2:Remaining = 100 × e^(−0.025 × 30) = 100 × 0.472 = 47.2 mg.

The half-life is 27.7 minutes. After 30 minutes, 47.2 mg remains (47.2%).

Common Mistakes & Tips

  • !Applying the first-order half-life formula to zero- or second-order reactions.
  • !Confusing the rate constant k with the half-life — they are inversely related.
  • !Using inconsistent time units between k and elapsed time.

Related Concepts

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Frequently Asked Questions

Why doesn't concentration affect the half-life of a first-order reaction?

Because the rate is proportional to concentration: as concentration drops, the rate drops proportionally, so the fraction consumed per unit time remains constant.

How many half-lives until a substance is essentially gone?

After 7 half-lives, less than 1% remains (0.78%). After 10 half-lives, only 0.098% remains. In practice, 5–7 half-lives is often considered sufficient for near-complete elimination.