Dilution Calculator: How to Dilute Solutions (Formula & Examples)

Dilution is the process of reducing the concentration of a solution by adding more solvent (usually water or a buffer). The total amount of solute (dissolved substance) stays the same — only the volume changes, which spreads the solute over a larger volume and reduces the concentration.

Dilution is used everywhere in chemistry, biology, medicine, and everyday life: making juice from concentrate, preparing reagents in a lab, calibrating analytical instruments, and dosing medications.

Key principle: the amount of solute before dilution equals the amount after dilution. This conservation law is what makes the C₁V₁ = C₂V₂ formula work.

The dilution equation:

C₁ × V₁ = C₂ × V₂

Where:

• C₁ = initial (stock) concentration
• V₁ = volume of stock solution to use
• C₂ = final (desired) concentration
• V₂ = final total volume after dilution

You can rearrange this to solve for any of the four variables:

• V₁ = (C₂ × V₂) ÷ C₁ — how much stock to take
• C₂ = (C₁ × V₁) ÷ V₂ — what concentration you will end up with
• V₂ = (C₁ × V₁) ÷ C₂ — what final volume you need

Units must be consistent within each variable pair: C₁ and C₂ must use the same units (both in mg/mL, both in M, etc.), and V₁ and V₂ must use the same units (both mL, both L, etc.).

Example 1 — How much stock solution to use?

Problem: You have a 10 mg/mL stock solution. You want to make 50 mL of a 2 mg/mL solution. How much stock do you need?

• C₁ = 10 mg/mL, C₂ = 2 mg/mL, V₂ = 50 mL, V₁ = ?
• V₁ = (C₂ × V₂) ÷ C₁ = (2 × 50) ÷ 10 = 100 ÷ 10 = 10 mL
• Action: Take 10 mL of stock, add 40 mL of solvent to reach 50 mL total.

Example 2 — What concentration will you end up with?

Problem: You add 5 mL of a 0.1 M NaCl solution to 45 mL of water. What is the final molarity?

• C₁ = 0.1 M, V₁ = 5 mL, V₂ = 50 mL (5 + 45), C₂ = ?
• C₂ = (C₁ × V₁) ÷ V₂ = (0.1 × 5) ÷ 50 = 0.5 ÷ 50 = 0.01 M

Example 3 — What final volume do you need?

Problem: You have 3 mL of a 500 µg/mL solution. You want to dilute it to 50 µg/mL. What total volume do you need?

• C₁ = 500 µg/mL, V₁ = 3 mL, C₂ = 50 µg/mL, V₂ = ?
• V₂ = (C₁ × V₁) ÷ C₂ = (500 × 3) ÷ 50 = 1500 ÷ 50 = 30 mL
• Action: Add 27 mL of solvent to the 3 mL of stock.

Dilution factor (DF) is the ratio of final volume to initial volume:

Dilution factor = V₂ ÷ V₁ = C₁ ÷ C₂

Common notation formats:

• 1:10 — take 1 part stock, add 9 parts solvent (total = 10 parts). DF = 10.
• 1:100 — take 1 part stock, add 99 parts solvent. DF = 100.
• 1:2 — mix equal volumes of stock and solvent. DF = 2.

Note: different fields use "1:10" to mean different things. In microbiology, 1:10 usually means 1 part in 10 total (final volume 10×). In some clinical contexts, 1:10 can mean 1 part added to 10 parts solvent (final volume 11×). Always clarify the convention in your context.

Serial dilution is a series of repeated dilutions, where each step uses the previous diluted solution as the new "stock." It is used to achieve very low concentrations that would require impractically small volumes if done in a single step.

Example: 1:10 serial dilution from a 1 M solution over 4 steps:

• Step 1: 1 M → 0.1 M (1:10)
• Step 2: 0.1 M → 0.01 M (1:10)
• Step 3: 0.01 M → 0.001 M (1:10)
• Step 4: 0.001 M → 0.0001 M (1:10)

Final concentration = initial concentration ÷ (dilution factor)ⁿ, where n is the number of steps.

Serial dilutions are essential for:

• Creating standard curves for ELISA, PCR, and spectrophotometry
• Counting bacteria (colony-forming units per mL)
• Diluting very concentrated stock reagents to working concentrations
• Determining minimum inhibitory concentrations (MIC) in antibiotics testing

The C₁V₁ = C₂V₂ formula works with any consistent concentration unit. Common types:

• Molarity (M or mol/L) — moles of solute per liter of solution. Most common in chemistry labs.
• mg/mL or µg/mL — mass concentration. Common in biology, pharmacology, and clinical labs.
• % (w/v) — grams of solute per 100 mL of solution. Common for solutions like 0.9% NaCl (saline) or 70% ethanol.
• % (v/v) — volume of liquid solute per 100 mL of solution. Used for alcohol concentrations and liquid-liquid dilutions.
• ppm/ppb — parts per million/billion. Used in environmental and trace analysis.

As long as C₁ and C₂ are in the same units, and V₁ and V₂ are in the same units, the formula works regardless of which units you choose.

• Preparing working solutions from stock reagents — most lab reagents are stored as concentrated stocks and diluted before use to extend shelf life.
• Drug dosing — pharmacists dilute concentrated drugs to specific dosage concentrations for patient administration.
• Blood alcohol content — breathalyzer tests use a standard blood-to-breath dilution ratio to estimate BAC from exhaled air.
• Food and beverage — juice concentrates, cleaning products, and disinfectants all use dilution instructions on the label.
• Microbiology plate counts — bacterial samples are serially diluted so that countable numbers of colonies appear on plates.
• Analytical calibration — serial dilutions create concentration standards against which unknown samples are compared.

Use the dilution calculator to solve for any variable in the C₁V₁ = C₂V₂ equation without doing the algebra manually — enter three known values and it calculates the fourth.