Dilution Mathematics Guide

Dilution means lowering the concentration of a solution by adding more liquid. This guide covers the arithmetic only and is not medical advice.

What the calculation means

You have a stock solution of known concentration. You take some of it and add liquid until the total reaches a chosen volume. The amount of dissolved material stays the same, so concentration times volume is the same before and after.

The formula

C1 × V1 = C2 × V2
C1 and V1: stock concentration and the volume of stock you take.
C2 and V2: final concentration and final volume.
Liquid to add = V2 − V1.

Worked example (mathematical example only)

Stock 10 mg/mL. You want 2 mg/mL in a final 5 mL. V1 = (2 × 5) ÷ 10 = 1 mL of stock. Liquid to add = 5 − 1 = 4 mL. Check: 10 × 1 = 10 and 2 × 5 = 10.

Rules the calculator checks

Final concentration cannot be higher than the stock concentration.
Final volume cannot be smaller than the stock volume.
Use the same units for both concentrations and both volumes.

Common mistakes

Treating V2 as the liquid to add. V2 is the total, and the added liquid is V2 − V1.
Mixing mg/mL with mcg/mL in the same calculation.

Dilution calculator · Concentration guide · Unit conversion guide

Mathematical calculation only. Not medical advice.