Short teaching lessons
Veterinary dilution calculations: how to use C1V1 = C2V2
Prepared 23 October 2026 · VetQ
For a straightforward dilution, the amount of solute is conserved while total volume increases. C1V1 = C2V2 expresses that relationship when concentration units are consistent. The exercise values below are fictional and do not establish compatibility, stability or a clinical preparation method.
For veterinary exam study. These short examples do not prescribe treatment for an individual patient.
Name the four quantities
C1 is the starting concentration, V1 the volume of stock needed, C2 the target concentration and V2 the final total volume. Rearrange to V1 = C2 × V2 ÷ C1. Before calculating, make sure both concentrations use the same kind of units.
Work an example
To make a theoretical final volume of 100 mL at 2 mg/mL from a 10 mg/mL stock, calculate V1 = 2 × 100 ÷ 10 = 20 mL. In this simplified exercise, the remaining volume is 80 mL of diluent. The final mixture contains 200 mg in 100 mL.
Avoid the final-volume trap
Adding 100 mL of diluent to 20 mL of stock produces 120 mL, not the requested 100 mL. The final concentration would be 200 ÷ 120, approximately 1.67 mg/mL. Always distinguish “make up to” a final volume from “add” a specified volume.
A second worked check: matching units
An exercise gives a 1% weight-per-volume solution. By definition that is 1 g in 100 mL, which equals 1,000 mg in 100 mL, or 10 mg/mL. If a target uses mg/mL, convert the starting percentage before applying the dilution equation. Do not assume every percentage label uses the same convention; identify the type of concentration in the question. To check the earlier example, calculate solute amount from both sides: starting concentration times stock volume should equal target concentration times final volume. If the values differ, either the arithmetic or the interpretation of final volume is wrong. These checks concern a simplified calculation, not real-world formulation instructions.
Check your understanding
How much 20 mg/mL stock is needed for a theoretical final mixture of 50 mL at 4 mg/mL? How much diluent is needed under the exercise’s simple volume-addition assumption?
Read the answer and reasoning
V1 = 4 × 50 ÷ 20 = 10 mL stock. Add 40 mL diluent to reach 50 mL total. Check: 10 mL × 20 mg/mL = 200 mg; 200 mg ÷ 50 mL = 4 mg/mL.