Chemistry

Dilution Calculator

Solve C₁V₁ = C₂V₂ for stock or diluted concentration and volume when preparing solutions.

Dilution calculator

C₁V₁ = C₂V₂ · serial dilution

Ratio
Lab

Enter any three values and leave one blank. Concentrations must share the same unit; volumes use the unit selected below.

Solved for V₁ (stock volume)

C₁
2 M
V₁
62.5 mL
C₂
0.5 M
V₂
250 mL

Dilution factor C₁/C₂ = 4×

What is the Dilution Calculator?

Dilution is the process of lowering a solution’s concentration by adding solvent. In teaching labs and homework, the working relation is almost always C₁V₁ = C₂V₂: the amount of solute is conserved when you dilute, so the product of concentration and volume stays constant if concentration units are consistent.

Typical tasks include preparing a working solution from a concentrated stock, finding how much stock to pipette into a volumetric flask, or checking what concentration results after combining a known aliquot with solvent up to a final volume. The Dilution Calculator solves for whichever one of C₁, V₁, C₂, or V₂ you leave blank.

Keep units consistent. If volumes are in milliliters, both V₁ and V₂ should be in milliliters (or both in liters). Concentrations may be molarity, percent, or another shared unit—the algebra is the same. Use the serial dilution mode for 1:10 / 1:100 series, or lab presets such as alcohol, bleach, and hydrogen peroxide dilutions.

  • Solute amount is conserved: moles before = moles after (for non-reactive dilution)
  • C₁V₁ = C₂V₂ with matching concentration units and matching volume units
  • Stock concentration C₁ is greater than or equal to the diluted concentration C₂

Mathematical / chemical formulas

For a dilution that does not consume or produce solute, the conserved quantity is concentration × volume.

C₁V₁ = C₂V₂

Solve for one unknown, for example:
  V₁ = (C₂V₂) / C₁
  C₂ = (C₁V₁) / V₂

Dilution factor = C₁ / C₂ = V₂ / V₁
  • Volumes may be mL or L as long as both sides match.
  • Do not mix mass percent with molarity in the same equation without converting first.

Step-by-step example: Preparing 250 mL of 0.50 M HCl from 2.0 M stock

You have 2.0 M HCl stock and need 250 mL of 0.50 M HCl. What volume of stock should you measure before diluting to the mark?

  1. Identify knowns: C₁ = 2.0 M, C₂ = 0.50 M, V₂ = 250 mL; solve for V₁.
  2. V₁ = (C₂V₂) / C₁ = (0.50 × 250) / 2.0 = 62.5 mL.
  3. Measure 62.5 mL of stock and dilute with water to 250 mL total volume.
  4. Check: dilution factor = 2.0 / 0.50 = 4, and 250 / 62.5 = 4.

In the Dilution Calculator, enter C₁ = 2.0, leave V₁ blank, C₂ = 0.50, V₂ = 250 (mL). Confirm V₁ ≈ 62.5 mL.

Frequently asked questions

Can I use mL and L in the same calculation?

Only if you convert so both volumes use the same unit. 250 mL is 0.250 L. Mixing units without converting gives a wrong V₁ by a factor of 1000.

Does C₁V₁ = C₂V₂ work for mass percent?

It works when both concentrations are the same type and the density does not change much, which is reasonable for dilute aqueous solutions. For precise work with concentrated solutions, convert to moles or use mass of solute instead.

What is a serial dilution?

A serial dilution repeats dilution in steps (for example, 1:10 three times). Each step still obeys C₁V₁ = C₂V₂. The overall dilution factor is the product of the step factors. Switch the Dilution Calculator to Serial dilution, set factor = 10 with transfer 1 into final 10, and read each tube concentration.

How do I do a 1:10 dilution calculator workflow?

A 1:10 step means the diluted concentration is one-tenth of the stock for that step (dilution factor 10). In simple mode, leave V₁ blank with C₁ known, set C₂ = C₁/10, and enter V₂. In serial mode, choose the 1:10 chip so transfer/final volumes match the factor.

Keep learning with more calculators and study guides on Online Science Tools.

Practice problems & worked examples

Practice alongside the dilution calculator above. Each problem includes a full worked solution so you can check your reasoning step by step.

Practice problem 1

Stock volume for a lab dilution

How many mL of 6.0 M H₂SO₄ are needed to prepare 500. mL of 0.15 M H₂SO₄?

Show solution

Worked solution

  1. C₁V₁ = C₂V₂ → V₁ = (C₂V₂)/C₁.
  2. V₁ = (0.15 × 500) / 6.0 = 12.5 mL.

Answer: 12.5 mL of 6.0 M stock

Practice problem 2

Find final concentration

25.0 mL of 0.80 M NaOH is diluted to 100.0 mL. What is C₂?

Show solution

Worked solution

  1. C₂ = (C₁V₁)/V₂ = (0.80 × 25.0) / 100.0 = 0.20 M.

Answer: 0.20 M

Practice problem 3

Dilution factor

A stock is 2.5 M and the working solution is 0.050 M. What is the dilution factor?

Show solution

Worked solution

  1. Factor = C₁/C₂ = 2.5 / 0.050 = 50.
  2. Equivalently V₂/V₁ = 50 if volumes are consistent.

Answer: 50×

Practice problem 4

1:10 serial dilution

Start with 1.0 M stock. Do three successive 1:10 dilutions (1 mL into 10 mL each time). What is the concentration after the third tube?

Show solution

Worked solution

  1. Each step multiplies concentration by 1/10.
  2. After 3 steps: C = 1.0 / 10³ = 0.0010 M.
  3. Overall factor from stock = 1000×.

Answer: 0.0010 M (1000× from stock)

Practice problem 5

Alcohol dilution (v/v)

How much 95% ethanol is needed to prepare 100 mL of 70% ethanol (same % units)?

Show solution

Worked solution

  1. V₁ = (C₂V₂)/C₁ = (70 × 100) / 95 ≈ 73.7 mL.
  2. Dilute the aliquot to 100 mL with water.

Answer: ≈ 73.7 mL of 95% stock

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