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Dose to Volume

Short draws and reading error

An exact calculation does not make an accurate measurement. The barrel has a resolution, and the shorter the draw, the larger a share of it that resolution is.

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

Where the precision runs out

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

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.

Half a graduation as a share of the draw, on a 1 mL U-100 barrel marked every unit. The absolute uncertainty is five microlitres on every row; only the draw changes.
Volume drawnUnitsHalf a mark, as % of the draw
0.01 mL1.050.00%
0.02 mL2.025.00%
0.03 mL3.016.67%
0.05 mL5.010.00%
0.08 mL8.06.25%
0.1 mL10.05.00%
0.2 mL20.02.50%
0.3 mL30.01.67%
0.5 mL50.01.00%

Before you act on that number

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.

Why two graduations is the line

Below two graduations every panel on this site flags the reading rather than printing it plainly. At that point the uncertainty in the measurement is at least a quarter of what is being measured, and the precision of the arithmetic has stopped carrying any information about the result.

Nothing has gone wrong with the calculation. It is as exact as ever. What has happened is that the limiting factor moved from the maths to the hardware, and a tool that keeps printing three decimal places without comment is implying a precision the syringe cannot deliver.

The fix is liquid, not decimal places

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

That is what making a solution weaker is for, and it is the only honest answer to an unreadable draw. The most dilute strength page is the other end of the same trade-off: long readable draws, and a ceiling on how large an amount will fit in the barrel.

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 in the table above is two and a half times larger on it. A U-50 sits in between, at double.

Which is the second reason the barrel is a required field on every panel here. The first is that the reading itself is wrong without it; this one is that the error attached to the reading is wrong too.