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Reconstitution Math Explained
Understand the relationship between mass, concentration, volume, and syringe markings. A step-by-step arithmetic guide with free browser calculators.
This guide explains the arithmetic, not how to prepare or administer a substance.
1. Put mass into the same units
Before dividing, make sure both mass values use mg or both use mcg. Multiply mg by 1,000 to get mcg. Use the mg to mcg converter. Reference: NIST: Metric prefixes.
2. Calculate mass per unit of volume
Concentration = mass ÷ final solution volume
For example, 12 mg distributed through 3 mL gives 4 mg/mL. Use the actual final volume. The calculation assumes a fully dissolved, uniform solution. Open the concentration calculator.
3. Relate an already specified mass to volume
Volume = specified mass ÷ concentration
As a purely numerical example, 1 mg divided by 4 mg/mL equals 0.25 mL. The unit mg cancels, leaving mL. These sample numbers are not a suggested dose or preparation.
4. Understand the scale
Volume and syringe markings are different ways of expressing the same volume on a specified scale. A U-100 scale uses 100 markings per mL: 0.25 mL corresponds to 25 markings. Use the U-100 converter.
Common arithmetic mistakes
- Mixing mg and mcg in the same division without converting them.
- Treating the amount in a container as its concentration.
- Using liquid added as final volume without checking that assumption.
- Using a U-100 conversion on a different syringe scale.
- Rounding intermediate results before finishing the calculation.
Check your calculation
Multiply your resulting volume by concentration. You should recover the mass you started with, allowing for display rounding. This checks arithmetic only; it does not validate a dose or whether a substance should be used.