Why a formula cannot be written in drops: weighing, percentages, and a 1% solution you can reproduce

Recipes online look like this:

5 drops bergamot, 3 drops lavender, 1 drop patchouli

That formula cannot be reproduced. Someone else will fail with it, and so will you, next month, with the same bottles on the same bench.

A drop is not a unit

In 2017 Moore, Beck and Kryscio published a thorough measurement in BMC Ophthalmology. They tested 192 bottles across 32 different bottle designs and manufacturers of glaucoma medication, counting drops with an automated counter and determining drop volume by weighing on a 0.0001 g analytical balance.

The result:

Significant variability in the estimated drop size of studied formulations, ranging from 0.024 to 0.221 mL.

Twenty-four microlitres to 221 microlitres. Ninefold.

There is a more intuitive figure too. Bottles all labelled 5 mL delivered between 111 and 209 drops. Same nominal volume, nearly twice the count.

And these are pharmaceutical dropper bottles: containers designed for reproducible dosing, regulated, made by specialist manufacturers. The glass pipette you bought from a lab supplier is not better than they are.

Even with every condition controlled, 3.3% remains

What if you are careful? Same pipette, same posture, slow and steady?

In 2005 Sklubalová and Zatloukal measured the contributing factors systematically in Pharmazie. Comparing rubber against plastic dropper tips, they found that tip design, dispensing angle and dispensing rate all significantly affect drop volume, with plastic tips giving more consistent results.

And under defined dispensing conditions, in the best case:

The variability of the drop volume could be expressed by a variability coefficient of 3.3%.

3.3% is the best you will ever do, the ceiling of your precision. And tilting the dropper 45° from vertical decreased drop volume and increased variability, through air bubble formation.

Even doing everything right, a drop carries 3.3% uncertainty. Change the pipette, change the material, hold it at a slightly different angle, and you are back to tens of percent.

And equal volumes are not equal masses

Everything above concerns one liquid whose delivered volume wanders. The deeper problem is that different materials of equal volume do not weigh the same. Specific gravity is the field that records this, and it sits on every datasheet next to four other numbers worth knowing how to read.

Taking materials in our database that have supply information, a recorded specific gravity, and an appearance that is not solid leaves 3,863 liquids:

	Specific gravity
Minimum	0.706
5th percentile	0.823
Median	0.941
95th percentile	1.134
Maximum	1.560

The middle 90% spans a factor of 1.38; the full range a factor of 2.21.

One drop of an aldehyde at 0.82 and one drop of an ester at 1.18 differ in mass by 44%, even if the two drops were identical in volume (and the sections above establish they are not).

A formula works on ratios. The article on odour thresholds showed that something at 0.1% can dominate something at 30%. In a system where a single drop may be 1% of the whole, a 40% weighing error is not a rounding question.

One data-cleaning step to declare. Of the 4,011 raw specific gravity values, 31 (0.8%) are plainly digit errors in the source — for example 0.88600 to 8.90000 (should be 0.890) and 0.99200 to 0.09970 (should be 0.997), where a decimal point has shifted. Left in, the maximum becomes 9.0 and the range becomes a spurious 7.8×. The table above is restricted to the plausible band 0.70–1.60.

The measurement temperature is also inconsistent (mostly 25 °C, with 872 entries at 20 °C). Organic liquid density changes roughly 0.1% per degree, negligible against the 38% and 121% figures above, but worth recording.

Incidentally: specific gravity is itself a range

Every one of those 3,863 raw values is a range, e.g. 0.85100 to 0.87000 @ 15.00 °C. Not a single entry is a lone number.

The median band width is 0.0080, about 0.85% of the value; the 90th percentile is 0.0400.

The conclusion of the previous article on batch variation reappears here: a supplier gives you a band. Even for a quantity as basic as density.

So: weigh, and work in percent

The conclusion is simple; getting it right has a few details.

Write formulae as percent by weight (% w/w), summing to 100. Skip volume percent, drops, and "parts".

Bergamot oil          35.0 %
Lavender oil          20.0 %
Linalool              15.0 %
Dihydromyrcenol       12.0 %
Patchouli oil          8.0 %
Iso E Super            9.0 %
Coumarin 10% solution  1.0 %
                     ------
                      100.0 %

The advantage is that this is independent of batch size. Five grams or five hundred, the ratios hold, and anyone who receives it can reproduce it.

Also record the mass you actually weighed. You aimed for 3.500 g and the pan settled at 3.512 g: write 3.512, then back-calculate the true percentages. This is the step most often skipped and the most important one. A formula record documents what you did, not what you planned.

How many decimal places does your balance need?

Do not go by the advertised figure. Derive it from your requirement.

Separate two things first: readability, the smallest displayed increment, is no guarantee of accuracy. A balance's repeatability is typically ±1 to ±2 in the last digit, so a 0.001 g balance carries roughly ±0.002 g of uncertainty per reading.

That gives the minimum usable weight directly. For an error under 1%:

minimum weight = 0.002 g ÷ 1% = 0.2 g

Below 0.2 g, stop weighing. Dilute.

In practice:

Balance	Reliable minimum (within 1%)	Suitable for
0.01 g (2 dp)	about 2 g	Not enough. In a 10 g formula a 1% component is 0.1 g, which this cannot weigh
0.001 g (3 dp)	about 0.2 g	The correct starting choice. With dilutions it covers almost everything
0.0001 g (4 dp)	about 0.02 g	Buy when you need it. This is the class Moore's study used

A three-decimal balance plus disciplined dilution beats a four-decimal balance used to weigh traces directly, and it is far cheaper and much harder to get wrong.

Making a 1% solution that comes out the same every time

One rule: weigh both components. Never measure by volume.

To make a 10% solution of linalool in DPG or 95% ethanol:

1. Put the empty bottle on the balance and tare.
2. Weigh in the linalool and record the actual figure, say 1.024 g.
3. Weigh in solvent to a total of 10.240 g (ten times the material weight), recording the actual figure.
4. Label it: Linalool 10.0% w/w in DPG | 1.024 g + 9.216 g | 2026-10-10 | batch ABC

Every part of step 4 earns its place. The concentration is what you calculate formulae with. The actual weights let you trace an error later; the date tells you when a remake is due. And the batch number connects back to the batch variation of the previous article.

Why insist on w/w over v/v? Because your formula is written by weight. A volume-based solution feeding a weight-based formula forces a density conversion in the middle, and that is exactly where the 2.21× spread above bites. Stay in mass throughout and there is no conversion.

Handling trace materials

Some materials are used at 0.01% or below (the ones from the article on odour thresholds). In a 10 g formula, 0.01% is one milligram. On a three-decimal balance that is "0.001 g", the last digit flickering. It cannot be accurate.

The answer is serial dilution, keeping the balance in the range where it is good:

neat → 10% solution → 1% solution → 0.1% solution

To place 0.01% (1 mg) of neat material in a 10 g formula, add 1.0 g of the 0.1% solution instead, which contains that 1 mg. One gram is comfortable territory for a three-decimal balance, an error of 0.2%.

Three warnings:

1. The solvent takes up formula space. That 1.0 g of solution is 0.999 g of DPG; in a 10 g formula it occupies 10%, and it must be counted in the total. This is the classic beginner error, and I have made it myself: dilution after dilution goes in, and when you finally add it up, a third of the formula is solvent.

2. Dilutions age, so date them. Ethanol ones die faster than DPG ones; aldehyde dilutions faster still.

3. Dilution is for precision; any money saved is incidental. Treat your dilutions as your measuring instrument.

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Drops are a kitchen unit; percentages are a formulation unit. The day you switch is the day your formulae first become reproducible, modifiable and scalable. Before that, you are running one-off experiments.

References

D. B. Moore, J. Beck & R. J. Kryscio, An objective assessment of the variability in number of drops per bottle of glaucoma medication, BMC Ophthalmology, 17, 78 (2017). PMID 28532424

Z. Sklubalová & Z. Zatloukal, Systematic study of factors affecting eye drop size and dosing variability, Pharmazie, 60(12), 917–921 (2005). PMID 16398268

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Next: solvents. What DPG, ethanol, IPM and TEC are each good for, why a solvent is not an odourless background, and how it changes the evaporation curve you smell.