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C1V1 = C2V2 Dilution Calculator

Calculator

Enter the three known values, then choose what to solve for. Volume units (e.g., mL)

Educational use only. Always interpret results in clinical context and verify with local policies.

Written by George Lambroglou, RN • Formula checked against listed references • Last reviewed 21 Jun 2026

Solve the dilution equation for the missing concentration or volume. Enter the three known values and choose what you want to calculate.

Jump to:Calculator|How it works|Formula|Examples|Test questions|FAQs|References & Further Reading

How C1V1 = C2V2 Works

The C1V1=C2V2 equation represents conservation of solute: the amount of drug/solute before dilution equals the amount after dilution. When you add diluent, you increase the final volume (V2), so the final concentration (C2) decreases.

Key safety point: use final total volume (V2) — not the volume of diluent added. Diluent volume is calculated separately as V2 − V1.

Quick checks (avoid the classic errors):

  • C1 and C2 must be the same concentration units (convert first if needed).
  • V1 and V2 must be the same volume units.
  • For a typical dilution, C2 should be lower than C1.

Formula

C1 × V1 = C2 × V2

Worked Examples

Example 1: You have 10 mg/mL stock. You want 1 mg/mL in a final volume of 50 mL. What volume (V1) of stock do you need?

10 × V1 = 1 × 50
V1 = 50 ÷ 10 = 5 mL
Diluent = 50 − 5 = 45 mL
Answer: 5 mL stock + 45 mL diluent = 50 mL at 1 mg/mL

Example 2: You take 20 mL of 5 mg/mL solution. What concentration (C2) do you get if you make it up to 100 mL?

5 × 20 = C2 × 100
C2 = (5 × 20) ÷ 100 = 1 mg/mL
Answer: 1 mg/mL

Test questions

Quick practice checks to reinforce setup and avoid the most common C1V1=C2V2 mistakes (education only).

1) In C1V1=C2V2, what does V2 represent?
Answer: V2 is the final total volume after mixing (stock + diluent).
2) True/False: C1 can be in mg/L while C2 is in mg/mL if you’re careful.
Answer: False. C1 and C2 must be the same concentration units before you calculate.
3) If C1=8 mg/mL, V1=10 mL, and V2=40 mL — what is C2?
Answer: C2=(C1×V1)/V2=(8×10)/40=2 mg/mL.
4) If C1=20 mg/mL, C2=5 mg/mL, V2=60 mL — what is V1?
Answer: V1=(C2×V2)/C1=(5×60)/20=15 mL.
5) Using Q4, how much diluent is added?
Answer: Diluent = V2 − V1 = 60 − 15 = 45 mL.
6) Sanity check: for a typical dilution where C2 < C1, should V1 be smaller than V2?
Answer: Yes. V1 should be smaller than V2 for a dilution.
7) If your calculator shows negative diluent, what’s the first thing you check?
Answer: Unit mismatch or that you accidentally entered diluent volume instead of final total volume (V2), or that C2 > C1.
8) Can dilution achieve a higher concentration target (C2 > C1) by adding diluent?
Answer: No. Adding diluent can only reduce concentration.

When This Is Used

  • •Preparing diluted solutions from concentrated stock
  • •Adjusting medication concentrations for paediatric dosing
  • •Pharmacy compounding and aseptic preparation
  • •Double-checking dilution and concentration arithmetic

Clinical safety note: Always confirm concentrations, units, and local protocols. Use independent double-checks for high-risk medications and small-volume dilutions.

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C1 → C2 Final Volume

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Dose to final volume

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Frequently Asked Questions

Clinical reminder: Always follow local protocols and consult medication information sheets. These examples are for calculation practice only.

References & Further Reading

This calculator is based on established dilution and pharmaceutical standards from authoritative sources across healthcare disciplines.

International Standards

SI Prefixes (milli-, micro-, etc.)PDF

BIPM (Bureau International des Poids et Mesures)

Authoritative reference for metric prefixes used in unit conversions.

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Australia Resources

Drug Calculations PDF

Flinders University – Student Learning Support Service

Shows the standard “volume required” method and worked examples used in healthcare training.

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Medication Calculations PDF

University of Southern Queensland (USQ)

Provides formula-based approaches consistent with dilution and dose-to-volume calculations.

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Finding the Volume Required Web

RMIT Learning Lab (Nursing)

Explains stock strength/stock volume concepts that underpin dilution calculations.

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United Kingdom Resources

Intravenous Drug and Fluid Administration Training PDF

Gloucestershire Hospitals NHS Foundation Trust

Includes practical calculation methods used in IV preparation and dilution scenarios.

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United States Resources

Medication Calculations PDF

SUNY Upstate Medical University

Explains ratio/proportion style approaches relevant to dilution and dose-to-volume problems.

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Pharmacy Calculations Web

NCBI Bookshelf (StatPearls Publishing)

Covers solution/mixture calculation structures consistent with C1V1=C2V2 style dilution methods.

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Tip: If your answer looks wrong, it’s almost always a unit mismatch (e.g., mg/mL vs mg/L) or using diluent volume instead of final total volume (V2).

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