How do you calculate a dilution with C1V1 = C2V2?
Multiply the concentration by the volume on each side and set them equal. Diluting does not change the amount of drug; it only spreads it through more liquid. The amount is concentration × volume, so the amount in the stock you draw up equals the amount in the finished solution.
C1 × V1 = C2 × V2
C1 is the stock concentration, V1 the stock volume you take, C2 the final concentration and V2 the final volume. Rearranged for each unknown:
- V1 = C2 × V2 ÷ C1
- V2 = C1 × V1 ÷ C2
- C2 = C1 × V1 ÷ V2
- C1 = C2 × V2 ÷ V1
The diluent to add is the difference between the two volumes: diluent = V2 − V1.
How to use the dilution calculator
- Under Solve for, choose the value you are missing: V1, V2, C2 or C1.
- Fill in the three fields that appear. Concentrations are in mg/mL and volumes in mL.
- Read the result. When you solve for V1 or V2, you also get the Diluent to add.
- If a warning says the final concentration is higher than the stock, it’s worth rechecking the numbers.
Worked examples
Example 1 – stock volume to draw up. You need 50 mL at 1 mg/mL from a 10 mg/mL stock. V1 = 1 × 50 ÷ 10 = 5 mL of stock. Diluent = 50 − 5 = 45 mL.
Example 2 – final volume. You have 2 mL of a 40 mg/mL solution (80 mg) and want 2 mg/mL. V2 = 40 × 2 ÷ 2 = 40 mL in total. Diluent = 40 − 2 = 38 mL.
Example 3 – final concentration. 1 mL of a 1 mg/mL ampoule is made up to 10 mL with diluent. C2 = 1 × 1 ÷ 10 = 0.1 mg/mL. The diluent added is 10 − 1 = 9 mL.
Quick reference
Stock volume (V1) to draw up from a 10 mg/mL stock for a given final concentration and final volume.
| Final concentration | 10 mL final | 20 mL final | 50 mL final |
|---|---|---|---|
| 5 mg/mL | 5 mL | 10 mL | 25 mL |
| 2 mg/mL | 2 mL | 4 mL | 10 mL |
| 1 mg/mL | 1 mL | 2 mL | 5 mL |
| 0.5 mg/mL | 0.5 mL | 1 mL | 2.5 mL |
The diluent in each case is the final volume minus the stock volume.
Common mistakes
- Adding V2 of diluent instead of making up to V2. “Dilute to 50 mL” means 50 mL in total. The stock is part of that volume, so the diluent is 50 mL minus the stock.
- Mixed units. A stock in mg/mL and a target in mcg/mL, or litres next to mL, gives an answer off by a factor of a thousand. Convert first; the medication unit conversions guide also covers percentages and ratio strengths.
- Swapping C1 and C2. The stock is always the stronger solution. If C2 comes out larger than C1, the fields are probably the wrong way round.
A quick sense check
The dilution factor is C1 ÷ C2, and V2 ÷ V1 must match it. Going from 10 mg/mL to 1 mg/mL is a tenfold dilution, so the final volume must be ten times the stock volume. If the two ratios differ, a value is wrong. Once the bag or syringe is made up, the IV bag concentration calculator confirms its strength, and the mcg/kg/min infusion calculator turns it into a pump rate.
Frequently asked questions
What does C1V1 = C2V2 mean?
It means the amount of drug is the same before and after you dilute. C1 and V1 are the concentration and volume of the stock you start with; C2 and V2 are those of the solution you end up with. Diluent changes the volume, not the amount, so concentration × volume stays equal.
How much diluent do I add?
Subtract the stock volume from the final volume: diluent = V2 − V1. To make 50 mL at 1 mg/mL from a 10 mg/mL stock, draw up 5 mL of stock and add 45 mL of diluent, not 50 mL. The calculator shows this figure as Diluent to add.
Do the units have to match?
Yes. C1 and C2 must be in the same concentration unit, and V1 and V2 in the same volume unit. The calculator works in mg/mL and mL, so convert g, mcg or litres before you enter them. A mixed pair gives an answer that is off by a factor of a thousand.
Why does the calculator warn that the final concentration is higher than the stock?
Because adding diluent can only lower a concentration. If C2 is larger than C1, one of the values has been entered wrongly, often a mg/mcg slip or two fields swapped. The calculator then shows the warning instead of a diluent volume, so it’s worth rechecking the numbers before going on.
Can I use it for percentage solutions?
Yes, as long as C1 and C2 use the same unit. The equation works with any concentration unit, even though the calculator labels the fields in mg/mL. To convert a percentage, remember that 1% w/v equals 10 mg/mL, so a 2% stock is 20 mg/mL.
Why is the diluent amount not shown when I solve for a concentration?
Because the calculator shows Diluent to add only when you solve for V1 or V2. If you solve for C1 or C2 you have already entered both volumes, so the diluent is simply V2 − V1, which you can work out at a glance.