# Elimination Rate Constant Calculator (k = ln2 / t½)

Convert an elimination half-life to the first-order elimination rate constant: k = ln2 / t½ = 0.693 / t½. Also reports the fraction of drug remaining after 1/2/3/4/5 half-lives (50%, 25%, 12.5%, 6.25%, 3.125%), the number of half-lives required to reach steady state (≈4 for 94%, ≈5 for 97%), and the time to ~99% elimination (≈6.64 half-lives). Valid only for first-order (linear) elimination — NOT for zero-order or Michaelis-Menten kinetics (phenytoin, high-dose ethanol, high-dose aspirin). Not medical advice.

> Canonical page: https://elysiatools.com/en/tools/elimination-rate-constant

- **Category:** Health

- **Keywords:** elimination rate constant, k, kel, half-life, first-order, ln2, exponential decay, steady state, pharmacokinetics, pk, drug, medicine

## Overview

The Elimination Rate Constant Calculator converts a positive elimination half-life in hours into the first-order rate constant k using k = ln(2) / t½. It also reports the fraction remaining after 1 to 5 half-lives, estimated steady-state timing, and the time for approximately 99% elimination.

## Inputs

- **Half-life t½ (h)** (number): Elimination half-life in hours. Must be positive.
- **Decimal Places** (number)

## When to use

- Calculate k or kel from a known elimination half-life.
- Estimate how much drug remains after several half-lives.
- Estimate steady-state timing or approximately 99% elimination under first-order kinetics.

## How it works

- Enter the elimination half-life in hours.
- The calculator applies k = ln(2) / t½.
- It calculates the remaining fraction after 1, 2, 3, 4, and 5 half-lives.
- It estimates steady state at about 4 to 5 half-lives and approximately 99% elimination at 6.64 half-lives.

## Use cases

- Pharmacokinetic calculations using a known drug half-life.
- Comparing how shorter and longer half-lives affect the elimination rate constant.
- Estimating remaining drug fraction and approximate accumulation or washout timing.

## Frequently asked questions

### What formula does the calculator use?

It uses k = ln(2) / t½, which is approximately 0.693 / t½.

### What unit does k use?

Because the half-life is entered in hours, k is reported in h⁻¹.

### What happens after five half-lives?

Approximately 3.125% remains, meaning about 96.875% has been eliminated.

### How many half-lives are needed for steady state?

About 4 half-lives corresponds to approximately 94% and 5 half-lives to approximately 97%.

### When is this calculator not appropriate?

It is for first-order, linear elimination only and is not appropriate for zero-order or Michaelis-Menten kinetics. It is not medical advice.

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