Injections and infusions — drug calculations
Dilution calculator: using the
C1V1 = C2V2 formula
Dilution is one of the most common steps in drug calculations for injections and infusions. Here you get the formula C1×V1=C2×V2, a clear explanation and a calculator you can use straight away, whether you are practising or just need to check a calculation quickly.
The dilution formula
The amount of drug stays the same before and after dilution, so concentration multiplied by volume gives the same result on both sides.
V1 = (C2 × V2) ÷ C1 = (20 × 50) ÷ 100 = 10 ml stock solution
Diluent: 50 − 10 = 40 ml
Dilution calculator
Fill in the values below to work out how much stock solution and diluent you need.
Work out a dilution
The calculator is a study tool for practising drug calculations and should not be used as the basis for clinical dosing.
What do C1, V1, C2 and V2 mean?
The dilution formula relies on the total amount of drug being the same before and after dilution. Only the concentration and the volume change.
Stock solution (C1 and V1)
The starting solution, at a high concentration, that you dilute. V1 is the unknown volume you usually solve for.
Finished solution (C2 and V2)
The diluted, lower-concentration solution that is actually given to the patient, in the total volume that has been prescribed.
Is the solution given as an infusion? Work out drops per minute →
Is the solution stated as a percentage? Work out a percentage solution →
Need to calculate the amount of drug as well? See the dosage calculator →
Frequently asked questions about dilutions
How do you calculate a dilution?+
A dilution is calculated with the formula C1×V1=C2×V2, where C1 and V1 are the concentration and volume of the stock solution, and C2 and V2 are the required concentration and total volume after dilution. Rearranged: V1 = (C2 × V2) ÷ C1.
What do C1, V1, C2 and V2 mean?+
C1 is the concentration of the stock solution, V1 is the volume of stock solution to draw up, C2 is the required concentration after dilution, and V2 is the total volume the finished solution should have.
What do you top the dilution up with?+
The rest of the volume (V2 − V1) is made up with a diluent, for example sodium chloride (NaCl) or glucose solution, depending on what has been prescribed or what the question states.
Why are dilutions part of drug calculations?+
Many drugs, such as injections and infusions, have to be diluted to the right concentration before they are given, so that the dose is safe and correct. Dilution is a standard topic in drug calculation courses.
Practise dilutions in Dos
Dos is a practice app for drug calculations, with practice tests of ten questions, a built-in calculator next to each question and statistics per topic so you can follow your progress.
