Elimination Rate Constant Calculator
Convert a drug's half-life into its elimination rate constant, the percent eliminated per hour, and the percent remaining after any time you choose.
📉 What is the Elimination Rate Constant?
The elimination rate constant (ke) is the fractional rate at which a drug's plasma concentration declines under first-order kinetics, expressed in inverse time units such as per hour. It is mathematically the twin of half-life, related by the simple formula ke = ln(2) / t1/2, and either value can always be derived directly from the other.
Pharmacologists use ke to model a drug's full concentration-time curve, since the entire first-order decay equation C(t) = C0 x e^(-ke x t) is built directly on this single constant. Clinical pharmacists use it to predict how much drug remains in a patient's system at any point after dosing stops, which matters for surgery timing, drug interaction windows, and washout periods before switching medications. Pharmacokinetics students use ke as the connecting variable between half-life, clearance, and volume of distribution (ke = CL / Vd), since all three describe the same underlying elimination process from different angles.
A common point of confusion is treating ke as if it were itself a percentage. It is not, ke is a rate constant, and the actual percent eliminated in any given hour must be calculated separately using the exponential formula, since a constant fractional rate produces a shrinking absolute amount removed each successive hour.
This calculator converts a known half-life into ke instantly, then projects exactly how much of the drug is eliminated (and how much remains) at any time point you choose, useful for planning dosing schedules or estimating washout periods.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — Two Half-Lives Elapsed
Half-life = 4 hr, evaluate at t = 8 hr
Example 2 — One Half-Life Elapsed
Half-life = 6 hr, evaluate at t = 6 hr
Example 3 — Five Half-Lives Elapsed
Half-life = 2 hr, evaluate at t = 10 hr
❓ Frequently Asked Questions
🔗 Related Calculators
How do you find the elimination rate constant from half-life?
Use ke = ln(2) / t(1/2), where t(1/2) is the half-life in hours. Since ln(2) is approximately 0.693, a drug with a 4-hour half-life has ke = 0.693/4 = 0.1733 per hour.
What does the elimination rate constant actually mean?
It is the instantaneous fractional rate at which the drug concentration is declining, expressed per unit time (commonly per hour). A ke of 0.1733/hr means the concentration is momentarily falling at 17.33% of its current value per hour, not a fixed 17.33% of the original dose.
Is the percent eliminated per hour the same every hour?
No. The percent eliminated relative to the concentration at the start of that specific hour stays roughly constant, but since the starting concentration keeps shrinking, the absolute amount removed each hour keeps decreasing too. That's what makes elimination exponential rather than linear.
How do I calculate percent eliminated after a specific number of hours?
Use percent eliminated = (1 - e^(-ke * t)) x 100, where t is the elapsed time in hours. For example, after exactly 2 half-lives, this always works out to exactly 75% eliminated (25% remaining), regardless of the drug's specific half-life value.
Why use natural log (ln) and not log base 10 for ke?
First-order drug elimination is modeled with the natural exponential function e^(-ke*t), so its inverse, the natural logarithm, is what correctly relates ke to half-life. Using log base 10 would give a numerically wrong ke unless an extra conversion constant were applied.
What is a 'typical' elimination rate constant?
There is no single typical value, it varies enormously by drug, ke commonly ranges from under 0.01/hr for drugs with multi-day half-lives to over 1/hr for drugs eliminated within an hour or two. Always use the specific published half-life for the drug in question.
How many half-lives does it take to eliminate 99% of a drug?
About 6.6 half-lives, since 2^6.6 is approximately 100. In practice, 4 to 5 half-lives (about 94% to 97% eliminated) is the conventional clinical threshold for considering a drug essentially cleared.
Does a higher elimination rate constant mean a drug is more or less potent?
Elimination rate constant says nothing about potency, only about how fast the drug leaves the body. A fast-eliminating (high ke) drug can be just as potent per dose as a slow-eliminating one, it simply needs more frequent dosing to sustain its effect.
Can elimination rate constant change over time in the same patient?
For drugs that follow simple first-order (linear) kinetics, ke is treated as constant for a given patient under stable conditions. It can shift if kidney or liver function changes, or in rarer cases of saturation (zero-order, Michaelis-Menten) kinetics at very high doses.
What is the relationship between elimination rate constant and clearance?
Elimination rate constant relates to clearance (CL) and volume of distribution (Vd) by ke = CL / Vd. A drug can have the same clearance but a different ke if its volume of distribution differs, which is why ke alone doesn't fully describe a drug's disposition.