Medication Dilution Calculator (C1V1 = C2V2)
Dilutions
How much stock solution do you need?
Enter the stock concentration, intended final concentration, and verified final total volume. MedMaths will calculate the stock volume to withdraw.
What do you need to calculate?
Stock solution to withdraw (V1) is calculated. Enter the other three values.
Both values must describe the same medicine or solute and use the same compatible 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.
Dilution arithmetic only — product information controls preparation
Simple answer
How do you use C1V1 = C2V2 for medication dilution?
Use C1 × V1 = C2 × V2 when the same medicine or solute is being diluted and three of the four values are already known from a verified source. Rearrange the equation for the one missing value.
V2 means the verified final total volume, not simply the amount of diluent added. C1 and C2 must use a compatible concentration basis; a generic percent sign is not enough. The equation checks dilution arithmetic; it does not choose the medicine, diluent or preparation method.
Clinical use and safety
When to use this calculator — and its limits
The arithmetic can be correct while the clinical decision is still wrong. These boundaries show what the calculator can and cannot establish.
When to use
- Use when the same medicine or solute is being diluted and three of C1, V1, C2 and V2 are already known from a verified source.
- Use when C1 and C2 use concentration expressions compatible with the same conserved quantity and the volume terms, and V1/V2 use matching volume units.
- Use V2 as the verified final total volume of the preparation, not simply the amount of diluent added.
Key limitations
- C1V1 = C2V2 assumes the amount of the same solute is conserved during dilution. It is not valid if the concentration basis changes, the values describe different substances, or a mass-per-mass value such as % w/w is treated as though it were volume-based without an appropriate mass/density method.
- The arithmetic difference V2 − V1 is not automatically the real-world amount of diluent to add. Product-specific preparation instructions may require withdrawal of carrier fluid, staged reconstitution, displacement allowances, or another sequence.
- The equation does not establish solubility, compatibility, stability, sterility, route suitability, storage conditions, or whether the final concentration is permitted for the medicine.
- Very small calculated stock volumes may not be accurately measurable with the available device and may require a product- or pharmacy-approved alternative preparation.
What MedMaths does not decide
- Which medicine, diluent or final concentration should be used.
- Whether the medicine is suitable for dilution or whether a proposed admixture is compatible or stable.
- Aseptic preparation steps, labelling requirements, storage time, route, infusion rate, filter, line or monitoring requirements.
Evidence and method checks
- Molarity — dilution relationship — OpenStax Chemistry 2e
- Strength Conversion in Drug Listing — U.S. Food and Drug Administration
- Pharmacy Calculations — NCBI Bookshelf / StatPearls
- Preparing Unit-Dose Packaged Medications — OpenStax Clinical Nursing Skills
Formula logic and known-value examples are checked as part of the MedMaths review process.
See how MedMaths checks calculator methods →Formula, examples and learning guide
Review C1V1 = C2V2, worked examples, unit checks, dilution safety points, and FAQs.
Formula, examples and learning guide
Review C1V1 = C2V2, worked examples, unit checks, dilution safety points, and FAQs.
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 the amount of that solute is conserved through the dilution. It is not a generic equation for mixing different active substances or for overriding product-specific reconstitution and displacement instructions.
If your verified workflow starts with a reconstituted vial, then transfers a stated medicine-solution volume into a known final IV preparation volume, use the Final IV Bag Concentration Calculator instead.
Match medicine and concentration basis
C1 and C2 must describe the same medicine or solute and use a compatible concentration unit and basis so concentration × volume represents the same conserved quantity. % w/v and % v/v must stay on the same verified basis; % w/w is not supported by this volume-based model without an appropriate mass/density method. 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.
Want to practise medication dilution calculations?
Use the calculator for the immediate C1V1=C2V2 arithmetic. The Dilution lesson provides stepped examples, final-volume wording and repeated practice across all four solve paths.
Medication dilution safety checks
Same medicine and compatible basis
Confirm C1 and C2 refer to the same medicine or solute and use concentration expressions that are compatible with the same conserved quantity and the volume terms. Do not treat % w/w as interchangeable with % w/v or % v/v.
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. V2 − V1 is an arithmetic difference, not automatically the exact diluent volume to add.
Product-specific requirements
Check the permitted diluent, compatibility, route, final concentration, stability, aseptic process, and required independent check.
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 much diluent do I add using C1V1 = C2V2?
C1V1=C2V2 calculates concentration-volume relationships, not a universal diluent instruction. After calculating V1, V2 − V1 is only the arithmetic volume difference.
- V1 is the volume withdrawn from the starting solution
- V2 is the verified final total volume, not automatically the diluent volume
- V2 − V1 may equal the diluent volume only in a simple additive preparation where the governing instructions support that assumption
- Displacement, overfill, reconstitution instructions, or a specified make-up-to process can change the volume actually added
Example: For 10 mg/mL to 1 mg/mL in a final 50 mL, V1 is 5 mL and V2 − V1 is 45 mL; the product instructions still determine how that final 50 mL is prepared.
Do C1 and C2 need matching units?
Yes. C1 and C2 must use concentration expressions that are compatible with the same conserved quantity and the volume terms in the equation, while V1 and V2 must use matching volume units.
- Convert mg/L and mg/mL before using them together
- For percentages, use the same verified basis on both sides
- % w/v and % v/v are volume-compatible when used consistently; % w/w is mass-per-mass and is not interchangeable with a volume-based percentage
- A matching symbol alone does not prove two concentration definitions are dimensionally compatible
Example: Do not combine C1 in mg/mL with C2 in mcg/mL until one concentration has been converted.
Can I use percentages in C1V1 = C2V2?
Yes, but only when C1 and C2 use the same verified percentage basis and that basis is compatible with the volume terms. This calculator supports % w/v and % v/v; it does not treat % w/w as a volume-based concentration.
- % w/v means mass per volume and can be used consistently with volume terms
- % v/v means volume per volume and can be used consistently when the same definition is used on both sides
- % w/w means mass per mass; a volume-based equation cannot safely substitute for the required mass/density information
- Check the exact product strength definition rather than assuming that every percent concentration is interchangeable
Example: A 10% w/v stock and a 2% w/v target use the same percentage basis; a 10% w/w product is a different concentration definition.
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.
Equation basis
C₁V₁ = C₂V₂ is the general dilution equation, following from conservation of solute amount during dilution. It is not presented by MedMaths as a formula belonging to a single researcher.
Supporting references
- Chemistry 2e — Molarity: derivation of the dilution equation C₁V₁ = C₂V₂ — OpenStax
- Strength Conversion in Drug Listing — U.S. Food and Drug Administration
- Pharmacy Calculations — NCBI Bookshelf / StatPearls
Safety and quality guidance
- Preparing Unit-Dose Packaged Medications — OpenStax Clinical Nursing Skills
- Allowable Excess Volume and Labeled Vial Fill Size in Injectable Drug and Biological Products — U.S. Food and Drug Administration
- Assessing risks when reconstituting injectable medicines — NHS Specialist Pharmacy Service
- High risk medicines and systems — Australian Commission on Safety and Quality in Health Care
Why there is no historical formula author
Unlike a named clinical equation such as Cockcroft-Gault or Mosteller BSA, this calculator uses standard arithmetic or unit relationships rather than a formula that MedMaths can reliably trace to one historical researcher or publication. MedMaths therefore identifies who wrote and reviewed the page instead of assigning a historical formula author.
The calculation uses concentration-volume or final-concentration arithmetic from verified inputs. It does not select the medicine, diluent, route, compatible concentration, preparation technique, stability period, storage conditions, or administration plan.
Want the equation explained rather than another solve? Read why C₁V₁ = C₂V₂ works and why V₂ means final total volume →
Not sure whether the preparation is reconstitution or dilution? Read Reconstitution vs dilution: what's the difference? →
Continue calculating
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Open calculatorReferences and sources
Open the calculation and medication-safety sources used for this dilution calculator.
References and sources
Open the calculation and medication-safety sources used for this dilution calculator.
Molarity and the Dilution Equation
MethodOpenStax Chemistry 2e
Derives the concentration-volume dilution relationship from conservation of solute amount.
Strength Conversion in Drug Listing
US strength definitionsU.S. Food and Drug Administration
Defines w/w, w/v and v/v strength expressions and supports making the concentration basis explicit rather than using an ambiguous percent symbol.
Pharmacy Calculations
Pharmacy methodNCBI Bookshelf / StatPearls
Covers pharmacy dilution relationships and distinguishes percent weight/volume, volume/volume and weight/weight concentration expressions.
Preparing Unit-Dose Packaged Medications
Medication preparationOpenStax Clinical Nursing Skills
Supports obtaining reconstitution diluent, volume and resulting concentration from verified product directions or medication references.
Allowable Excess Volume and Labeled Vial Fill Size
US preparation boundaryU.S. Food and Drug Administration
Supports the boundary that labelled fill, excess volume and real preparation volumes are product-specific rather than idealised arithmetic assumptions.
Assessing risks when reconstituting injectable medicines
Injectable safetyNHS Specialist Pharmacy Service
Guidance emphasising product- and process-specific risk assessment for injectable preparation.
High Risk Medicines and Systems
Medication safetyAustralian Commission on Safety and Quality in Health Care
Guidance covering concentrated injectable medicines and safer medication-preparation systems.
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.