Free converters & iv tool
Dilution Calculator: C1V1 = C2V2 and Serial Dilutions
To calculate a dilution, use C1V1 = C2V2: stock concentration times stock volume equals final concentration times final volume. To make 5 mL at 2 mg/mL from a 10 mg/mL stock, V1 = (2 × 5) ÷ 10 = 1 mL of stock plus 4 mL of diluent. This calculator solves for any one of the four values and also builds serial dilution tables.
Prepared by Prospyr · Reviewed October 3, 2026 · Free, no sign-up, runs in your browser
Calculated for you
Any unit works if C1 and C2 match: mg/mL, %, mM.
V1 and V2 must use the same unit.
Stock volume to use (V1)
1mL
Diluent to add (V2 − V1)
4 mL
Dilution factor (C1 ÷ C2)
5×
1:4 stock to diluent
General lab and compounding arithmetic. It does not choose a stock, a final strength or a dose. Follow your protocol and the product label.
C1V1 = C2V2: the dilution formula
The dilution equation is C1V1 = C2V2. In OpenStax's Chemistry 2e, it follows from the fact that a dilution does not change the amount of solute, so the amount before equals the amount after.
- Stock volume: V1 = (C2 × V2) ÷ C1
- Final volume: V2 = (C1 × V1) ÷ C2
- Final concentration: C2 = (C1 × V1) ÷ V2
- Stock concentration: C1 = (C2 × V2) ÷ V1
- Diluent to add: V2 − V1
- Dilution factor: C1 ÷ C2
The concentrations just need the same unit as each other, and the volumes the same unit as each other. Any unit works, including mg/mL, percent or mM.
Worked example: how to dilute a stock solution
You have a 10 mg/mL stock and need 5 mL at 2 mg/mL. Solve for V1: (2 × 5) ÷ 10 = 1 mL. Measure 1 mL of stock, then add 5 − 1 = 4 mL of diluent. The dilution factor is 10 ÷ 2 = 5, so the result is a 5-fold dilution.
| Known | Solve for | Math | Answer |
|---|---|---|---|
| C1 10, C2 2, V2 5 | V1 | (2 × 5) ÷ 10 | 1 (add 4 of diluent) |
| C1 100, V1 1, V2 10 | C2 | (100 × 1) ÷ 10 | 10 |
| C2 1, V1 2, V2 10 | C1 | (1 × 10) ÷ 2 | 5 |
| C1 50, V1 2, C2 5 | V2 | (50 × 2) ÷ 5 | 20 (add 18 of diluent) |
Serial dilution calculator and table
A serial dilution repeats the same dilution step down a row of tubes. Enter the starting concentration, the dilution factor per step, the number of tubes and the final volume per tube, and the calculator lists each tube's concentration, how much diluent to add and how much to carry over.
Example: start at 1,000, dilute 10-fold, three tubes, 9 mL in each. Carry 9 ÷ 10 = 0.9 mL and add 8.1 mL of diluent per tube. The tubes read 100, 10 and 1, which are total dilutions of 10, 100 and 1,000.
Concentration calculator: amount per volume
The Concentration tab turns an amount and a volume into a concentration: concentration = amount ÷ total volume of solution. It shows the answer in mg/mL, mcg/mL, g/L and percent weight per volume (1% w/v = 1 g per 100 mL = 10 mg/mL). 50 mg in 10 mL is 5 mg/mL, or 0.5%.
Related tools: the mg to mL calculator turns an amount into a volume at a known concentration, and the mg to mcg converterconverts mass units. For neurotoxin vials, reconstitution follows each product's label; see the Botox reconstitution calculator.
Frequently asked questions
What is the C1V1 = C2V2 formula?
C1 is the stock concentration, V1 the stock volume, C2 the final concentration and V2 the final volume. The equation works because diluting adds solvent but does not change the amount of solute, so C1 × V1 = C2 × V2. Rearrange it to solve for whichever value you do not know.
How do I calculate how much diluent to add?
Find V1 with C1V1 = C2V2, then subtract it from the final volume: diluent = V2 − V1. For 5 mL at 2 mg/mL from a 10 mg/mL stock, V1 is 1 mL, so you add 5 − 1 = 4 mL of diluent.
What does a 1:10 dilution mean?
It is usually 1 part stock plus 9 parts diluent, a 10-fold dilution, so the final concentration is one tenth of the stock. Some people write 1:10 to mean 1 part stock to 10 parts diluent (an 11-fold dilution), so state which one you mean. This calculator uses the dilution factor, C1 ÷ C2.
How do I make a serial dilution?
Add the same volume of diluent to each tube, move a fixed volume from the stock into tube 1, mix, then move the same volume from tube 1 to tube 2, and so on. Each step divides the concentration by the dilution factor, so a 10-fold series from 1,000 goes 100, 10, 1. The serial dilution tab builds the table and the volumes.
Can the final concentration be higher than the stock?
No. Dilution only lowers concentration, because you are adding solvent. If the calculator says the final concentration is higher than the stock, one of the numbers is in the wrong box or the wrong unit.
How do I calculate concentration from an amount and a volume?
Divide the amount by the total volume of the finished solution. 50 mg dissolved to make 10 mL is 50 ÷ 10 = 5 mg/mL, which is 0.5% weight per volume. Use the Concentration tab to see it in mg/mL, mcg/mL, g/L and percent.
Does this calculator tell me what strength or dose to prepare?
No. It does general lab and compounding arithmetic on the numbers you enter. The stock, the final strength and any patient dose come from your protocol, the product label and the treating provider.
Sources and scope
- OpenStax, Chemistry 2e, section 3.3: Molarity (Feb 14, 2019)
The dilution equation C1V1 = C2V2 and why it holds: dilution does not change the amount of solute.
- NIST: Metric (SI) Prefixes
Definitions of the milli and micro prefixes used in the concentration conversions.
General lab and compounding arithmetic, not medical advice. It does not choose a stock, a final strength or a dose and is not a substitute for the product label or your protocol. Dosing decisions belong to the treating provider.