# Doing Calculations for a Taper

It can be helpful to read the following sections in order, since the math steps build upon each other. If you need to brush up on your introductory algebra, here's a handy reference page.

Note that in many cases we round numbers up or down to the nearest one hundredth for simplicity, and because common syringes don’t measure more accurately than hundredths. So 1.144 or below becomes 1.14,  and 1.115 or above becomes 1.12. You will likely also need to do the same at times when you are doing your calculations and measuring your amounts. But keep in mind that it’s best to only round up or down at the very end, once you’ve finished all your other calculations—that will make your final result more accurate.

For the sake of simplicity, we have described the calculations for hypothetical people named Jack or Jill throughout. And since a beginning taper rate commonly recognized as reasonably safe in the layperson psychiatric drug withdrawal community involves cutting 5% from each previous month’s dose, so that monthly reduction amounts become progressively smaller over time, we have used that rate in most of the examples. Also, we use the phrase “Starting Amount” of a dose simply to refer to the starting point for doing the calculations in these examples – in principle, this starting point could be any day of one’s choosing either right at the beginning of a taper, at the beginning of any new month, or at any other time part-way through a taper.

## Calculating a monthly taper cut

Jill is planning to start her taper by cutting 5% of her total daily dose over the course of the first month. What will the actual amount of her cut be?

There are two steps to calculating the amount of Jill’s monthly taper cut. First,  we must turn the monthly taper rate that Jill has chosen to follow into a decimal number. It’s simple to do when we remind ourselves that “x%” literally means “x per 100”. Here’s how to state that in a formula:

The Taper Rate Percentage as a Decimal = The Taper Rate / 100

So if Jill’s planned starting taper rate is 5% per month, then the equation looks like this:

x = 5 / 100
To solve the equation, we divide 5 by 100 and conclude:
x = 0.05
Therefore, 5% as a decimal number is 0.05.

An easy way to do this quickly is to remember the rule that to convert a percentage into a decimal number, we simply shift the decimal two places to the left. For example, 10.0% becomes 0.1

Next, to calculate the amount of Jill’s monthly cut, we add up the total amount of active drug that Jill is taking per day, then multiply it by Jill’s chosen monthly taper rate as a decimal number to get the amount of her cut.

For example, with a tablet or powdered capsule, the calculation might look like:
100mg X 0.05 = 5mg cut

With a beaded capsule it might look like:
300 beads X 0.05 = 15 beads cut

With a liquid it might look like:
300mL X 0.05 = 15mL cut

### Taper Schedule 1: Cut-and-hold

#### Once-monthly cut

Suppose Jack wants to make a 5% cut today and hold it for the next month using a once-monthly Cut-and-hold schedule. What will the amount of his cut be?

As described above, we calculate Jack’s cut by multiplying the amount of his daily dose by his taper rate in this way:

A tablet or powdered capsule:
100mg X 0.05 = 5mg
Therefore, Jack would remove 5mg of powder from his dose and take 95mg.

300 beads X 0.05 = 15
Therefore, Jack would remove 15 beads from his beaded capsule and take 285 beads.

A liquid mixture, manufacturer’s oral liquid, or compounded liquid:
300mL X 0.05 = 15mL
Therefore, Jack would remove 15mL from his liquid and take 285mL.

#### Weekly cut

Suppose Jill wants to make a 5% cut over the course of one month using a weekly Cut-and-hold schedule. In other words, Jill wants to make cuts at the beginning of each week over 4 weeks, until she reaches a 5% total cut by the end of the month. What will the amount of her cuts be?

In this case, we first divide the total monthly cut Jill wants to make by the number of cuts she wants to take to get there (in this case, 4 weekly cuts over the course of one month). Then we increase the calculated cut each week by that same amount.

If Jill is taking 100mg daily in a tablet or powdered capsule, the equation looks like this:

(100mg X 0.05) / 4 = 1.25mg
This means that Jill will remove 1.25mg from her dose on the first day of the first week, and then “hold” at that amount of cut through each day of that week.

This will also be the amount that she will increase the cut by cumulatively over the following weeks:

Cut 2 (starting on day eight, the first day of week two): 1.25mg + 1.25mg = 2.5mg
Cut 3 (starting on day fifteen, the first day of week three): 1.25mg + 1.25mg + 1.25mg = 3.75mg
Cut 4 (starting on day twenty-two, the first day of week four): 1.25mg + 1.25mg + 1.25mg + 1.25mg = 5mg

If Jill is using a 300mL volume of liquid mixture, manufacturer’s oral liquid, or compounded liquid, the basic approach is the same:

(300mL X 0.05) / 4 = 3.75mL
This means that on day one Jill will remove 3.75mL of the liquid dose in her jar each day and “hold” at that level of cut through the first week, taking 296.25mL daily.

This will also be the amount that she will increase the cut cumulatively each week:

Cut 2 (starting on day eight, the first day of week two): 3.75mL + 3.75mL = 7.5mL
Cut 3 (starting on day fifteen, the first day of week three): 3.75mL + 3.75mL + 3.75mL = 11.25mL
Cut 4 (starting on day twenty-two, the first day of week four): 3.75mL + 3.75mL + 3.75mL + 3.75mL = 15mL

And if Jill is counting beads, the basic approach is the same, though she may have to more frequently round up or down, since beads only come in whole numbers:

(300 beads X 0.05) /4 = 3.75 beads (which would be rounded up to 4 beads)
This means that on day one and each day through the first week, Jill will remove 4 beads, taking 296 beads daily.

This will also be the amount that Jill will cumulatively increase the cut by each week:

Cut 2 (starting on day eight, the first day of week two): 3.75 beads + 3.75 beads = 7.5 beads (which would be rounded up to 8 beads)
Cut 3 (starting on day fifteen, the first day of week three): 3.75 beads + 3.75 beads + 3.75 beads = 11.25 beads (which would be rounded down to 11 beads)
Cut 4 (starting on day twenty-two, the first day of week four): 3.75 beads + 3.75 beads + 3.75 beads + 3.75 beads = 15 beads

Note that we can also do all of these calculations with simple multiplication. Once we've calculated Cut 1, we know that Cut 3 is 3 times the size of the Cut 1, and Cut 4 is 4 times the size of Cut 1.

### Taper Schedule 2: Daily Microtaper

Instead of an immediate, one-time cut, or a series of Cut-and-hold reductions, suppose Jack wants to make a 5% cut over the course of one month using a Daily Microtaper schedule. What will the amount of his cuts be?

In this case, much like with the Cut-and-hold schedule, we will divide the total monthly cut Jack wants to make by the number of cuts he wants to take to get there.  Then we increase the calculated cut each day by that same amount.

If Jack is taking 100mg daily in a tablet or powdered capsule, the equation looks like this:

(100mg X 0.05) / 31 = 0.16mg (which is rounded down to the nearest hundredth)
This means that Jack will cut 0.16mg on the first day of the month.

Then he will increase the amount of the cut each day by that same amount:

Cut 2 (day two): 0.16mg + 0.16mg = 0.32mg
Cut 3 (day three): 0.16mg + 0.16mg + 0.16mg = 0.48mg

And so on until the end of the month:

Cut 31 (day 31): 0.16mg X 31 = 4.96mg
This is just under 5mg, since we were rounding down through the month. (As a general rule, though, remember that it's usually best to use a calculator and round up or down only on the final results rather than on every number every time a calculation is done, to ensure maximum accuracy.)

Again, this same approach works with a liquid mixture, manufacturer’s oral liquid, or compounded liquid, where we change the measurements to mL, and with counting beads, where we change the measurements to beads.

And note that, again, we can also do all of these calculations with simple multiplication. Once we've calculated Cut 1, we know that Cut 3 is 3 times the size of the Cut 1, and Cut 31 is 31 times the size of Cut 1.

## Summarizing taper calculations into simple formulas

Getting clear on the basics of what's involved in doing these calculations makes it possible to build a taper plan simply by putting any particular monthly taper rates and starting daily dose amounts into the examples above. It’s useful, though, to do these calculations using formulas that can make the calculations faster and more flexible.

Let's define the elements of the formulas first:

• We start with a person’s current daily dose at the beginning of the month dissolved or suspended in a liquid (in mL), weighed on a scale (in mg), or counted out in beads. Let's call this the "Total Starting Amount". (Note that when combining a manufacturer's oral liquid with a diluent liquid, the 'Total Starting Amount' is the amount of both liquids together in mL.)

• We then have a person’s monthly taper rate converted into a decimal. Let's call that the "Monthly Taper Rate".

• We then have the number of cuts that the person wants to make during a month, whether it be 1 (i.e. once-monthly Cut-and-hold), 4 (weekly Cut-and-hold), 30 or 31 (Daily Microtaper), or any other number of cuts. Let's call that the "Total Number of Cuts".

• If the person has a sequence of cuts planned – perhaps 2 bimonthly cuts, 4 weekly cuts, or 30 daily cuts in the month – let's call a particular number in this sequence "The Sequential Number of the Cut" e.g. Cut 2, Cut 4, or Cut 30.

• Finally, we'll call the cut that the person is going to make on the first day the "Initial Cut" and the cut that the person is going to make on any other day or week a "Next Cut".

So how do we determine how much of a drug dose to cut at the start of any taper? It's this formula:

(Total Starting Amount X Monthly Taper Rate)  / Total Number of Cuts = Initial Cut

Looking back at our previous examples, we can see how they all follow this formula:

100mg times 0.05 divided by 4 cuts = 1.25mg cumulative cuts each week
100mg X 0.05 / 31 = 0.16mg cumulative cuts each day
Etc.

And what if we want to quickly calculate how much Cut 3 (on day twenty-two) of a weekly Cut-and-hold will beOr the amount of the cut on the 23rd day of a 31-day Daily Microtaper? The formula is this:

((Total Starting Amount X Monthly Taper Rate) / Total Number of Cuts) X The Sequential Number of the Cut =  Next Cut

Again, looking back at our previous examples, we can see how they all follow this formula:

( (100mg times 0.05) divided by 4 cuts) all times 3 = 3.75mg

This means that Cut 3, on day twenty-two of this weekly Cut-and-hold schedule at this taper rate, would be 3.75mg.

OR

(100mg times 0.05) divided by 31 cuts) all times 23 = 3.71mg (which is rounded up to the nearest hundredth)

This means that if a person was doing the same taper but using a Daily Microtaper schedule, on the 23rd day the person would be cutting 3.71mg.

And again, if we simply insert the number of beads or the volume of liquid into these formulas, the results work equally well.

## Calculating how much to take instead of how much to cut

If for any reason we'd prefer to know exactly how much Jill should be taking instead of exactly how much she should be cutting at any particular time, we simply do the exact same formulas we just described, except that we subtract these results from the Total Starting Amount to calculate Jill’s "Amount to Take". The formulas are these:

Initial Cut Day:

Total Starting Amount - (Total Starting Amount X Monthly Taper Rate) / Total Number of Cuts = Amount to Take

Next Cut Day:

Total Starting Amount - ((Total Starting Amount X Monthly Taper Rate) / Total Number of Cuts) X The Sequential Number of the Cut = Amount to Take

## Keeping track of how much dose of a drug a person is actually taking

If we’re using these calculations to determine how much to cut from a volume of liquid (mL), weight of powder or beads (mg), or number of beads, then it's possible that we could at times lose track of exactly how much dose of active drug a person is taking as the person tapers down. Sometimes that can be disorienting! But there are some simple ways to figure it out.

Suppose for example at the beginning of the month Jack is dissolving 100mg of active drug in 300mL of water and taking it all. He has since then been following a 5% monthly taper rate and he’s on the 10th day of a 30-day Daily Microtaper schedule. Jack did his calculations each day correctly, so he knows that on the 10th day he is cutting 5mL from his 300 mL of liquid mixture and taking 295mL. But how much drug is Jack actually cutting?

There are two ways to determine how much active drug Jack is taking. One is to use the exact same formula we were using to calculate the reductions in liquid mixture, and apply it directly to the amount of drug, like this:

((Total Starting Amount X Monthly Taper Rate) / Total Number of Cuts) X The Sequential Number of the Cut =  Next Cut

Inserting Jack's amounts into the formula, we get:
((100 mg X 0.05) / 30) X 10 = 1.67mg (which is rounded up to the nearest hundredth)

This means that Jack is currently cutting 1.67mg of drug, and taking 98.33mg.

Another way to do the calculation is to do a conversion from liquid amount (mL) to drug amount (mg). Here is a formula to do that:

We fill in the formula with the numbers we know, and solve the equation for the number we don't know – the Current Amount of Drug Dose. In this case, it would look like this:

100mg/300mL = x/295mL

Solving for X, we get 300x = 29500
X = 98.33mg

This means that Jack is currently taking 98.33mg of drug in his 295mL of liquid mixture.

## Calculating future monthly reductions

Many in the layperson withdrawal community say that it’s important to not get too attached to a pre-determined timeline for how long it will take to taper off psychiatric drugs, and to instead let your body’s messages be your guide. That being said, there may be times when you’re feeling curious about how far along in your taper you might get if you are able to comfortably maintain a certain pace.

If Jack is following a taper rate of 5% per month, recalculated at the beginning of each month, he will be recalculating his monthly cuts on that basis for some length of time until his total dose becomes small enough that he feels capable of handling a slightly increased rate or some ”fixed” cut amounts that will bring him to the end of his taper. Until that time, though, while he’s still cutting at his ‘decelerating’ 5% rate, how can Jack know how much drug dose he’ll be taking after, say, 3, 6, 9 or 12 months?

Here’s an equation to help determine this (and if you’re in need of a useful online resource for calculating numbers to the power of an exponent, click here):

So if Jack is taking 100 mg and tapering at a rate of 5% per month recalculated at the start of each month, here’s what his dosing regimen would look like: