Here we go again with some baffling stuff. I wanted to understand the implications of drug (i.e., medicine or medication) half-lives, in particular for drugs taken daily. The half-life calculators that I found were not useful at all, so I created my own (including an interactive graph), for use on a desktop or laptop, with a keyboard and biggish screen:

http://com.hemiola.com/half-life/

This page does **not** explain the basics of half-lives. There are plenty of other sites that do that.

For drugs with a short half-life (e.g., a few hours), I can see how if taken daily, there is no buildup because the daily residual is negligible. It was intuitively obvious to me that with a long half-life (e.g., a half-day or more), taking the drug daily would cause an overlap and buildup—convergent, but still, you would have more drugs in your system than you take daily, and I wanted to know that number.

## The basics

Wikipedia recently instituted a format for its drug entries that includes the drug’s half-life. That makes it easy and convenient to look up the half-life for all the drugs I’ve checked.

There seems to be an assumption that drugs with a long half-life are slower acting. Mathematically, they stabilize in the system at a higher dose than what you take. I find that interesting.

## The math

There is the Wikipedia page on biological half-life, but the math there is way beyond me. Here is what was obvious to me:

After x hours with half-life H (in hours) and dose D_{1}, the fractional amount D_{2} leftover is:

When you take drugs at regular intervals, there might be some nonnegligible amount left over from previous doses. Here is essentially what my calculator is doing, where p is the hours between doses:

## The disclaimers

Yes, I realize the real-world implications of drugs and their half-lives are way more complicated than a simple power-of-two equation. Still, I wanted a quick and easy way to compute the oversimplified numbers.

This was exactly what I needed! I am titrating up on a drug with a half-life of 26hrs – the drug has side effects initially – so I wanted to know where roughly the peak was for each movement upwards

Thank you so much! I knew what i was looking for and was so happy when i found your calculator. In am on Intuniv for ADHD and know it’s building up in the body over time. T 1/2 is 18 hours and i wanted to know what blood levels i had of the drug when i was feeling the best. This is an easy formula like you say yourself, not including bio availability (which should not be hard to add) although it is a very useful one.

Don’t see the need for factoring in bioavailability Aleksander. Especially when you are looking at how it affects you or as you state “when I was feeling the best”.

It doesn’t matter if the bioavailability is 10% or 90%. Sure it affects plasma concentration but unless your changing ROA, the actual noticeable effects will remain constant. Since you are used to this constant you want to know what percentage of a drug is in your system over time whether you are titrating, tapering, or taking a consistent dose. Once you’re used to taking a drug you know it’s effects on your system…and that’s all we really care about right?

I mean if your doing a study on blood plasma concentration levels that’s a different story…and even that is going to vary from person to person.

I spoke too soon (before I tried it). This won’t help if your titrating or tapering as it assumes a consistent dose.

Thanks exactly what i was searching for. You would think other people who built calculators would understand that what people are actually interested in is knowing the residual accumulation but you are the only one who figured it out. Well done.