Ratio strength

Convert between ratio strength (1 : X) and percentage strength for dilute preparations.

What is this for?

Ratio strength expresses concentration as one part of solute in X parts of total preparation. It is conventionally reserved for very dilute solutions, where a percentage would be an awkward string of leading zeros. The classic example is epinephrine, historically labelled 1:1000 and 1:10,000.

How to use it

Choose the direction of conversion.
For a ratio strength, enter only the denominator: for 1:5000, enter 5000.
For a percentage, enter the number without the percent sign.

Worked example

An older ampoule is labelled "epinephrine 1:1000". Express this as a percentage strength and as mg/mL.

Answer: 100 ÷ 1000 = 0.1% w/v, which is 1 mg/mL. The 1:10,000 presentation is 0.01% = 0.1 mg/mL.

Clinical pearls & pitfalls

Ratio labelling of epinephrine was a recognised source of ten-fold errors in cardiac arrest. The FDA required single-entity epinephrine to be relabelled in mg/mL, and ratio expressions have been removed from US labelling — but they persist in older references, exam questions, and international products.
For a weight-in-volume ratio, the denominator is directly the number of millilitres containing 1 gram: 1:1000 means 1 g in 1000 mL.
Ratio strength always refers to solute in total preparation, not solute to solvent. 1:10 is one part in ten total, not one part to ten parts.

Assumptions & limitations

Assumes weight-in-volume unless stated otherwise. For a solid mixture the same arithmetic applies but the units are g in g.
The convention is only meaningful for dilute preparations; for concentrated ones, percentage strength is clearer and less error-prone.

References

US Food and Drug Administration. Epinephrine injection labelling: removal of ratio expression. FDA Drug Safety Communication.
Institute for Safe Medication Practices. ISMP Medication Safety Alert: Epinephrine ratio expressions.
United States Pharmacopeia. General Notices, 8.140 Percentage Measurements.