Rounding to the nearest mark

An exact calculation does not make an accurate measurement. The barrel has a resolution, and that resolution costs a percentage that climbs as the draw gets shorter.

Educational arithmetic only. Not medical advice and not a dosing protocol.

Where the precision runs out

The arithmetic on this bench is exact: quantities are held as fractions of whole numbers and rounded once, at the point of display. So a tool can tell you that the volume you want is 7.142857 units. A barrel marked every single unit can show you 7 units or 8 units, and nothing in between.

The nearest printed mark is the exact figure rounded to the smallest graduation on that barrel, half away from zero. Every tool here names it alongside the exact value rather than instead of it, because the difference between the two is a real quantity and a reader is entitled to see it.

Half a graduation as a share of the draw, on a 1 mL U-100 barrel marked every unit. The absolute uncertainty is the same on every row; only the draw changes.
Volume drawn	Units	Half a mark, as % of the draw	Band
0.01 mL	1.0	50.00%	over 5%
0.02 mL	2.0	25.00%	over 5%
0.03 mL	3.0	16.67%	over 5%
0.05 mL	5.0	10.00%	over 5%
0.08 mL	8.0	6.25%	over 5%
0.1 mL	10.0	5.00%	under 5%
0.2 mL	20.0	2.50%	under 5%
0.3 mL	30.0	1.67%	under 5%
0.5 mL	50.0	1.00%	under 5%

What the bench will not tell you

This is educational arithmetic on figures entered by the reader. It is not medical advice, not a dosing protocol, and not a recommendation that anything be prepared, obtained or administered.

Nothing here states what quantity is appropriate for anyone, and there is no function in it that produces an amount to administer. A question about anyone’s health belongs with a licensed clinician who can examine the person asking.

Compounds of the kind this arithmetic is used on are largely research chemicals that are not approved by the FDA for human use. An exact calculation is not an accurate measurement: what is actually in a syringe depends on the preparation and the device, neither of which this page can see.

No qualified clinical reviewer is recorded against this site, and no credential is claimed anywhere on it. the limits of this bench.

Why the percentage climbs

Half a graduation on a 1 mL U-100 barrel is five microlitres, and that figure does not change with the size of the draw. As a share of the draw it therefore grows as the draw shrinks: 2.5% of a 20-unit draw, 5% of a 10-unit draw, 25% of a 2-unit draw. At the bottom of the scale the uncertainty in the reading is a large fraction of what is being measured.

Below two graduations every tool on this bench flags the reading rather than printing it plainly. Not because the arithmetic has failed - it is as exact as ever - but because its precision has stopped carrying any information about the measurement.

The fix is liquid, not arithmetic

A short draw can be made into a long one by spreading the same amount through more solution. Half a milligram out of a 10 mg/mL preparation is 5 units on a U-100; the same half milligram out of a 2 mg/mL preparation is 25 units. The absolute reading error is identical and its share of the measurement has dropped by a factor of five.

That is what diluent for a strength and thinning a solution are for, and it is the only honest answer to an unreadable draw. More decimal places on the answer do not help.

Coarser barrels cost more

A U-40 barrel is marked every unit too, but each of its units is 25 microlitres rather than 10, so half a mark is 12.5 microlitres and every percentage above is two and a half times larger. The five barrel pages each carry this same column computed for their own calibration.