Dilution Calculator — Chemistry, Lab and Serial Dilutions
What is Dilution?
Dilution is the process of reducing the concentration of a solute in a solution by adding more solvent. The amount of solute stays constant — only the volume changes. Dilution is described by the equation C1V1 = C2V2, where C is concentration and V is volume. Explore other related concepts in our chemistry tools index or return to the homepage.
Dilution Definition in Chemistry
In chemistry, dilution specifically refers to lowering the molarity of a solution. This is governed by the conservation of moles principle: the number of moles of solute before dilution equals the number of moles of solute after dilution. Because moles can be calculated as concentration multiplied by volume, this fundamental principle gives us the relationship C1V1 = C2V2. The behaviour of these dissolved solutes is often determined by their electronegativity and molecular polarity.
Note the difference between dilution and dissolution. Dissolution is the process of dissolving a solid solute into a solvent to make a solution, whereas dilution involves adding more solvent to an already existing solution. In these calculations, concentration is typically measured in mol/L (M) and volume in L or mL. This equation is sometimes called the dilution equation, the dilution formula, or the C1V1 = C2V2 equation — they all refer to the exact same mathematical relationship.
Dilution Formula
Initial concentration
Initial volume
Final concentration
Final total volume
To solve for any unknown, simply rearrange the formula algebraically:
- Solving for C₂ (Final Concentration): C₂ = (C₁ × V₁) / V₂
- Solving for V₁ (Stock Volume): V₁ = (C₂ × V₂) / C₁
- Solving for C₂ with unit conversion: Always ensure V₁ and V₂ use the same units before calculating. If your initial concentration is in M but you need the answer in mM, calculate C₂ in M first, then multiply by 1000.
What is a Dilution Factor?
The dilution factor is defined as the ratio of the final volume to the initial volume. The formula is: DF = Vf / Vi. For example, if you dilute 10 mL of stock to a total volume of 100 mL, your dilution factor is 10 (often written as 1:10).
Crucial Distinction: A dilution factor of 10 means the concentration is divided by 10, not multiplied. The solution is 10 times less concentrated. This direction confusion is the most common mistake students make on exams.
What is Serial Dilution?
A serial dilution is a stepwise, sequential series of dilutions. It is used when the required dilution factor is too large to achieve accurately in a single step, or when you need to create a range of known concentrations for a standard curve.
To calculate the final concentration, you multiply the starting concentration by the dilution factor at each step. For example, starting with a 1 M stock solution and performing three 1:10 serial dilutions results in: 1 M → 0.1 M → 0.01 M → 0.001 M.
How to Calculate Dilution — Step by Step
Note: For gas phase reactions involving concentration, pressure, and volume changes, use our Ideal Gas Law Calculator. For aqueous liquid solutions, use the standard C₁V₁ = C₂V₂ examples below.
1Solving for final concentration
You have 50 mL of a 2.0 M NaCl solution. You add water to make 250 mL total. What is the final concentration?
Step 1: Identify the variables. C₁ = 2.0 M, V₁ = 50 mL, V₂ = 250 mL, C₂ = unknown.
Step 2: Apply C₁V₁ = C₂V₂.
Step 3: Rearrange for C₂ = (C₁ × V₁) / V₂.
Step 4: Substitute. C₂ = (2.0 × 50) / 250 = 100 / 250 = 0.40 M.
2Solving for stock volume
20 mL of saline is diluted to a total volume of 100 mL, giving a final concentration of 1.0 M. What was the initial concentration?
C₁ = unknown, V₁ = 20 mL, C₂ = 1.0 M, V₂ = 100 mL.
C₁ = (C₂ × V₂) / V₁
C₁ = (1.0 × 100) / 20 = 100 / 20 = 5.0 M.
3Serial dilution calculation
You need a 1:400 dilution of an antibody stock. How do you achieve this in two steps?
Step 1: 1:20 dilution — take 1 part stock, add 19 parts buffer.
Step 2: 1:20 dilution again — take 1 part of step 1 solution, add 19 parts buffer.
Total dilution: 20 × 20 = 1:400.
4Calculating water to add
How much water must be added to 150 mL of a 7.5 M solution to produce a concentration of 5.25 M?
C₁V₁ = C₂V₂
7.5 × 150 = 5.25 × V₂
V₂ = 1125 / 5.25 = 214.3 mL.
Volume of water to add = V₂ − V₁ = 214.3 − 150 = 64.3 mL.
Dilution Ratios — 1:10, 1:100, 1:1000 and How to Make Them
The table below demonstrates standard laboratory dilution ratios and how to physically prepare them starting with 1 mL of stock solution.
| Dilution Ratio | Parts Stock | Parts Diluent | Final Volume (from 1 mL) | Example Use Case |
|---|---|---|---|---|
| 1:2 | 1 | 1 | 2 mL | Blood typing, basic lab prep |
| 1:5 | 1 | 4 | 5 mL | Household cleaning products |
| 1:10 | 1 | 9 | 10 mL | Standard serial dilution step |
| 1:20 | 1 | 19 | 20 mL | Antibody dilution step 1 |
| 1:100 | 1 | 99 | 100 mL | Bacterial culture dilution |
| 1:200 | 1 | 199 | 200 mL | Antibody dilution (1:20 × 1:10) |
| 1:400 | 1 | 399 | 400 mL | Antibody dilution (1:20 × 1:20) |
| 1:1000 | 1 | 999 | 1000 mL | Trace element solutions |
Note on conventions: This calculator and table use the standard scientific convention where a "1:10 dilution" means 1 part stock in 10 parts total (a dilution factor of 10). In some non-scientific fields, 1:10 means 1 part stock to 10 parts diluent (a dilution factor of 11). Always check which convention your specific textbook or laboratory uses to avoid critical errors.
Dilution Calculations on the AP Chemistry Exam
In AP Chemistry, dilution calculations are heavily tested in Unit 4 (Chemical Reactions) and Unit 9 (Applications of Thermodynamics). Dilution frequently appears in free-response questions where students must justify the physical laboratory procedure for preparing a standard solution using volumetric glassware.
AP Problem Example:
Calculate the volume of 12.0 M HCl stock solution required to prepare 500.0 mL of a 0.150 M HCl solution.
V₁ = (C₂ × V₂) / C₁ = (0.150 M × 500.0 mL) / 12.0 M = 6.25 mL
AP Procedure Example:
Describe how you would prepare this solution.
Using a volumetric pipet, transfer exactly 6.25 mL of 12.0 M HCl into a 500 mL volumetric flask containing some distilled water. Then, add distilled water dropwise until the bottom of the meniscus rests exactly on the 500.0 mL calibration mark. Cap and invert to mix.
Dilution for JEE Main and Advanced
As per NCERT Class 11 Chemistry (Some Basic Concepts of Chemistry), JEE tests dilution in the context of molarity, normality, and equivalent concentration. JEE Advanced problems often combine dilution with limiting reagent concepts or require tracking ion concentrations across multiple mixing steps.
Note that JEE uses normality (N₁V₁ = N₂V₂) extensively in acid-base titrations in addition to molarity. The mathematical relationship is identical because equivalent equivalents are conserved just as moles are conserved.
JEE Main Integer Type:
What volume of water (in mL) must be added to 200 mL of 0.5 M NaCl to make a 0.2 M solution?
M₁V₁ = M₂V₂ → 0.5 × 200 = 0.2 × V₂ → V₂ = 500 mL.
Volume to add = V₂ − V₁ = 500 − 200 = 300 mL.
Dilution for CBSE Class 11 and 12
In the CBSE curriculum, dilution questions are typically 3 to 5 mark numericals. CBSE examiners look for specific steps: you must state the formula explicitly, show the substitution with units, and state the final answer with correct units. Failure to show units at the final step will result in a 0.5 mark deduction.
Frequently Asked Questions — Dilution Calculator
What is the dilution equation?
The dilution equation is C₁V₁ = C₂V₂, where C₁ is the initial concentration, V₁ is the initial volume, C₂ is the final concentration, and V₂ is the final volume. The equation works because the moles of solute remain constant during dilution: moles = concentration × volume.
How do you calculate a 1:10 dilution?
For a 1:10 dilution, take 1 part of your stock solution and add 9 parts diluent to give 10 parts total. The final concentration is one-tenth of the original. Example: take 1 mL stock and add 9 mL water to give 10 mL at 1/10th the original concentration. Note: some textbooks define 1:10 as 1 part stock to 10 parts diluent — check your convention.
What is a dilution factor?
A dilution factor is the ratio of the final volume to the initial volume of the stock solution. Formula: DF = Vf / Vi. A dilution factor of 10 means the concentration has been reduced ten-fold. It is the inverse of the concentration factor.
How do you make a serial dilution?
To make a serial dilution: decide your dilution factor per step (commonly 1:10). Take 1 part of your stock and add 9 parts diluent — this is step 1. Take 1 part of step 1 solution and add 9 parts diluent — this is step 2. Repeat until you reach your desired concentration. Each step multiplies the total dilution factor.
What does a 1:400 dilution mean?
A 1:400 dilution means 1 part stock in 400 parts total, so the final concentration is 1/400th of the original. Achieve it in two steps: first a 1:20 dilution (1 mL stock into 19 mL diluent), then a 1:20 dilution of that result. 20 × 20 = 400.
How do you calculate the final concentration after dilution?
Rearrange C₁V₁ = C₂V₂ to solve for C₂: C₂ = (C₁ × V₁) / V₂. Example: 50 mL of 2.0 M solution diluted to 250 mL total: C₂ = (2.0 × 50) / 250 = 0.40 M. The units of concentration must match on both sides. Volume units must also match.
What is the difference between dilution and concentration?
Dilution reduces concentration by adding solvent — moles of solute stay constant, volume increases. Concentration (or concentrating) increases concentration by removing solvent or adding solute. The dilution equation C₁V₁ = C₂V₂ applies to both processes. For a dilution, C₂ is less than C₁. For concentrating, C₂ is greater than C₁.
How do you dilute bleach safely?
For general surface disinfection, dilute household bleach (5.25% NaOCl) to 0.1%: add 20 mL bleach to 1 litre of water. For blood spill disinfection use 0.5%: add 100 mL bleach to 1 litre of water. Always add bleach to water, never water to bleach. Never mix bleach with ammonia or acidic cleaners.
By Emmanuel TUYISHIMIRE · April 2026 · Last Reviewed April 2026
Emmanuel TUYISHIMIRE (Toni)
Principal Software Engineer & STEM Educator · Toni Tech Solution · Kigali, Rwanda
Toni cross-references every data value on this site against at least three authoritative sources: PubChem, NIST Chemistry WebBook, and the Royal Society of Chemistry. When sources conflict, all three are cited and the discrepancy is explained. Read the full methodology →
Data Sources & References
All numerical values on this page are sourced from and cross-referenced against the following authoritative databases:
- PubChem (National Library of Medicine)— Element property database, NCBI/NIH
- NIST Chemistry WebBook— National Institute of Standards and Technology
- Royal Society of Chemistry — Periodic Table— RSC authoritative element data
- Pauling, L. (1932)— The Nature of the Chemical Bond, original electronegativity scale