Medication Dilution Calculator (C1V1 = C2V2)
Calculate stock solution volume, final concentration, starting concentration, or final total volume for a verified medication-dilution setup.
Dilutions
Calculate a medication dilution
Choose the missing value. C1 and C2 must describe the same medicine or solute using the same concentration basis, and V2 must be the final total volume.
Medication dilution arithmetic only
Solve for the missing value
Stock solution volume required (V1) is calculated. Enter the other three values.
Both values must describe the same medicine or solute and use the same concentration unit and basis.
Both volume values must use the same unit.
Enter the verified concentration of the starting medicine or solution.
This is the value the calculator will solve.
Enter the intended final concentration from the medicine source or preparation instruction.
Enter the verified total volume after preparation, not only the diluent volume.
How C1V1 = C2V2 works for medication dilution
C1 × V1 = C2 × V2 links the verified starting medicine concentration and stock volume with the intended final concentration and final total volume. The arithmetic assumes the same medicine or solute is represented on both sides and that concentration × volume is conserved.
Match medicine and concentration basis
C1 and C2 must describe the same medicine or solute and use the same concentration unit and basis. V1 and V2 must use the same volume unit.
Use final total volume for V2
V2 is the total volume after preparation. It is not merely the amount of diluent added.
Medication dilution formula and rearranged equationsShowHide
Find V1 stock volume
V1 = (C2 × V2) ÷ C1
Find V2 final total volume
V2 = (C1 × V1) ÷ C2
Find C1 starting concentration
C1 = (C2 × V2) ÷ V1
Find C2 final concentration
C2 = (C1 × V1) ÷ V2
Worked medication-dilution examplesShowHide
Find V1: dilute 10 mg/mL to 1 mg/mL in a final 50 mL
V1 = (C2 × V2) ÷ C1
V1 = (1 × 50) ÷ 10
V1 = 5 mL
Arithmetic difference = 50 − 5 = 45 mL
Stock solution volume: 5 mL. The verified preparation instruction determines how the final 50 mL is made.
Find C2: 20 mL of 5 mg/mL made up to a final 100 mL
C2 = (C1 × V1) ÷ V2
C2 = (5 × 20) ÷ 100
C2 = 1 mg/mL
Final concentration: 1 mg/mL.
Find V2: 10 mL of 8 mg/mL diluted to 2 mg/mL
V2 = (C1 × V1) ÷ C2
V2 = (8 × 10) ÷ 2
V2 = 40 mL
Arithmetic difference = 40 − 10 = 30 mL
Final total volume: 40 mL.
Medication dilution safety checks
Same medicine and basis
Confirm C1 and C2 refer to the same medicine or solute and use matching concentration units and definitions.
Concentration direction
For a standard dilution by adding diluent, C2 should be lower than C1. A stronger target cannot be made by adding diluent alone.
Final total volume
Confirm whether the medicine source says add a stated diluent volume or make up to a stated final volume. Those are not always the same.
Product-specific requirements
Check the permitted diluent, compatibility, route, final concentration, stability, aseptic process, and required independent check.
Practice questions with answersShowHide
1. If C1 = 20 mg/mL, C2 = 5 mg/mL, and V2 = 60 mL, what is V1?
Answer: V1 = (5 × 60) ÷ 20 = 15 mL.
2. If C1 = 8 mg/mL, V1 = 10 mL, and V2 = 40 mL, what is C2?
Answer: C2 = (8 × 10) ÷ 40 = 2 mg/mL.
3. If 5 mL of stock is made up to a final 50 mL, what is V2 and what is the arithmetic difference?
Answer: V2 is 50 mL. The arithmetic difference V2 − V1 is 45 mL, but the medicine source determines the actual preparation sequence.
4. Can a 2 mg/mL stock be diluted with fluid to make 10 mg/mL?
Answer: No. Adding diluent cannot create a stronger concentration. Recheck the inputs and use the verified product-specific preparation.
Medication dilution and C1V1 = C2V2 FAQShowHide
What does C1V1 = C2V2 mean?
C1V1 = C2V2 is a concentration-volume equation. It states that the amount represented by concentration multiplied by volume is the same before and after a dilution.
- C1 is the starting or stock concentration
- V1 is the stock-solution volume used
- C2 is the intended final concentration
- V2 is the final total volume after preparation
- C1 and C2 must describe the same medicine or solute using the same concentration basis
Example: A 10 mg/mL medicine diluted to 1 mg/mL has the same drug amount spread through a larger final volume.
Can C1V1 = C2V2 be used for medication dilution?
Yes, it can check medication-dilution arithmetic when the verified starting concentration, intended final concentration, and final total volume are known. It does not decide whether or how a medicine should be diluted.
- Use the medication order, product label or monograph, pharmacy guidance, and local policy to obtain the permitted preparation
- The calculator does not select the diluent, route, concentration, stability period, or aseptic method
- Product-specific instructions override generic arithmetic
- High-risk preparations may require an independent check
Example: The equation can calculate a stock volume, but the medicine source still controls the permitted diluent and final concentration.
Which value can the medication dilution calculator solve?
It can solve for V1, V2, C1, or C2 when the other three positive values are known.
- Solve V1 to find the stock-solution volume
- Solve V2 to find the final total volume
- Solve C1 to find the implied starting concentration
- Solve C2 to find the final concentration
Example: If C1, C2, and V2 are known, select V1 to calculate the stock volume required.
Is V2 the final volume or the amount of diluent added?
V2 is the final total volume. It is not only the amount of diluent added.
- V2 includes the stock solution within the final prepared volume
- The arithmetic difference V2 − V1 may be shown separately
- Do not automatically treat V2 − V1 as a preparation instruction
- Some products require making up to final volume or accounting for displacement
Example: If 5 mL of stock is made up to 50 mL, V2 is 50 mL and the arithmetic difference is 45 mL.
How do I calculate stock volume V1 and the diluent difference?
Calculate V1 with V1 = (C2 × V2) ÷ C1. The arithmetic difference is then V2 − V1.
- V1 is the volume withdrawn from the starting solution
- Use the verified final total volume as V2
- For a standard dilution, C2 is usually lower than C1 and V1 is smaller than V2
- Preparation instructions may not equal simple volume addition
Example: For 10 mg/mL to 1 mg/mL in a final 50 mL: V1 = 5 mL and V2 − V1 = 45 mL.
Do C1 and C2 need matching units?
Yes. C1 and C2 must use matching concentration units and definitions, while V1 and V2 must use matching volume units.
- Convert mg/L and mg/mL before using them together
- For percentages, confirm the same basis, such as both % w/v
- A matching symbol alone does not prove two percentage definitions are equivalent
- Unit mismatch can produce a plausible-looking but incorrect result
Example: Do not combine C1 in mg/mL with C2 in mcg/mL until one concentration has been converted.
Is medication dilution the same as reconstitution?
No. Dilution starts with a known concentration and reduces or changes that concentration. Reconstitution usually creates a liquid concentration from a powder using product-specific instructions.
- Use C1V1=C2V2 when a starting concentration already exists
- Use the product label or monograph to establish a reconstituted final concentration
- The volume of diluent added may differ from the final vial volume
- After reconstitution, a separate dose-to-volume or final-bag calculation may be required
Example: A powder vial reconstituted to 100 mg/mL first creates C1; a later dilution may then use C1V1=C2V2.
What if the target concentration is higher than the stock concentration?
Adding diluent cannot create a stronger concentration. A target C2 above C1, or a calculated V1 above V2, does not describe a standard dilution by adding diluent.
- Recheck that C1 and C2 were not swapped
- Confirm concentration units and percentage basis
- Confirm that V2 is the final total volume
- Use a different verified starting concentration or preparation instruction if a stronger solution is required
Example: A 1 mg/mL stock cannot be diluted with fluid to make 10 mg/mL.
Continue calculating
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Open calculatorReferences and sourcesShowHide
Molarity and the Dilution Equation
WebOpenStax Chemistry 2e
Explains conservation of solute amount and the stock-to-final dilution relationship.
Dosage Calculations
WebOpenStax Pharmacology for Nurses
Nursing guidance on medication calculation setup, volume, concentration, and unit consistency.
Preparing Unit-Dose Packaged Medications
WebOpenStax Clinical Nursing Skills
States that reconstitution diluent type and amount should come from the label, package insert, or medication record.
Safety Considerations for Container Labels and Carton Labeling
PDFU.S. Food and Drug Administration
FDA guidance on clearly presenting reconstitution instructions, diluent volume, and resulting concentration.
High Risk Medicines and Systems
WebAustralian Commission on Safety and Quality in Health Care
Australian medication-safety guidance on concentrated medicines, dilution controls, and independent checks.
References support the dilution equation, medication-calculation principles, and safety boundaries. The current product label or monograph, pharmacy guidance, medication order, and local policy control real preparation.