What is the dilution formula?

The dilution formula is C₁V₁ = C₂V₂, where C₁ is the initial concentration, V₁ is the initial volume taken, C₂ is the final concentration, and V₂ is the final total volume. Rearranging: C₂ = (C₁ × V₁) / V₂. This formula works for any concentration unit as long as both concentrations are in the same unit.

What is the dilution factor?

The dilution factor is V₂/V₁ — the ratio of the final volume to the initial volume taken. A 10× dilution means V₂ = 10 × V₁. For example, taking 1 mL of stock and adding 9 mL of diluent gives a final volume of 10 mL, so the dilution factor is 10 and the final concentration is 1/10 of the original.

How do you make a 1:10 dilution?

A 1:10 dilution means 1 part sample in 10 total parts (1 part sample + 9 parts diluent). Take 1 mL of your stock solution and add 9 mL of diluent (water or buffer), giving 10 mL total. The dilution factor is 10 and the final concentration is C₁/10. In the lab, this is often written as a 10× dilution.

What is a serial dilution?

A serial dilution is a series of step-by-step dilutions where each step uses the product of the previous step. For a 1:10 serial dilution, you dilute 1 mL into 9 mL three times to get concentrations of 1/10, 1/100, and 1/1,000 of the original. Serial dilutions are used in microbiology (plate counts), immunology (antibody titers), and pharmacology (dose-response curves).

How do you calculate how much stock to add for a target concentration?

Use C₁V₁ = C₂V₂ rearranged to V₁ = (C₂ × V₂) / C₁. For example, to make 100 mL of 0.1 M HCl from 12 M concentrated HCl: V₁ = (0.1 × 100) / 12 = 0.833 mL. Add 0.833 mL of concentrated HCl to enough water to make 100 mL total. Use the "Find V1" mode in this calculator.

Does C1V1 = C2V2 work for percent solutions?

Yes — C₁V₁ = C₂V₂ works for any concentration unit as long as both C values are in the same unit. For percent (% w/v, % v/v), use the same % notation for both. For example, diluting 70% ethanol to 30%: V₁ = (30 × 500 mL) / 70 = 214 mL of 70% ethanol, brought to 500 mL total with water.

What is a 1:10 dilution?

A 1:10 dilution means 1 part sample in 10 total parts (1 part sample + 9 parts diluent). The dilution factor is 10×, meaning the final concentration is 1/10 of the original. For example, 1 mL of a 100 mM stock solution diluted to 10 mL total gives 10 mM — a 1:10 dilution. Some fields (serology, bacteriology) define 1:10 as 1 part in 11; always clarify the convention in your lab.

Why do you add acid to water and not water to acid?

When diluting concentrated acids, you must always add acid to water — never pour water into concentrated acid. Concentrated sulfuric acid (H₂SO₄) generates enormous heat when it contacts water. Adding water to concentrated acid causes rapid steam generation and can violently splatter acid on the person performing the dilution. Adding acid slowly to a large volume of water distributes the heat safely. This rule applies to all strong acids: H₂SO₄, HCl, HNO₃, and HF.

How do you make a 1 molar solution from a 10 molar stock?

Use C₁V₁ = C₂V₂ with C₁ = 10 M, C₂ = 1 M. To make 1 liter of 1 M from 10 M stock: V₁ = (1 × 1,000 mL) / 10 = 100 mL. Pipette 100 mL of 10 M stock into a 1 L volumetric flask, then add water to the 1 L mark. This is a 10× dilution. For acids, always add the 100 mL of acid to ~800 mL of water first, mix, then bring to 1 L.

Dilution Calculator — C1V1 = C2V2

Calculates final concentration and dilution factor using C1V1 = C2V2 — solve for any variable.

Understanding the Dilution Formula C₁V₁ = C₂V₂

The dilution calculator on this page uses the C₁V₁ = C₂V₂ equation to find final concentration, initial volume, dilution factor, or final volume. The dilution equation states that the amount of solute remains constant when you dilute a solution — since no solute is added or removed, C₁V₁ always equals C₂V₂:

C₁ × V₁ = C₂ × V₂

You can solve for any of the four variables. For finding final concentration: C₂ = (C₁ × V₁) / V₂. For finding initial volume needed: V₁ = (C₂ × V₂) / C₁.

How to Make a Diluted Solution — Step-by-Step

Determine your target concentration (C₂) and final volume (V₂)
Enter your stock concentration (C₁) in the calculator
Use "Find V1" to calculate how much stock to take
Pipette that volume of stock into your vessel
Add diluent (buffer or water) to bring to V₂ total volume
Mix thoroughly before use

AdvertisementResponsive Ad

Dilution Factor vs. Dilution Ratio

These terms are often used interchangeably but have a subtle difference:

Dilution factor — the number you divide the original concentration by. A 10× dilution factor means C₂ = C₁/10. It equals V₂/V₁.
Dilution ratio — written as 1:10, meaning 1 part sample in 10 total parts. A 1:10 ratio equals a 10× dilution factor.
1:10 vs 1 in 10 — some fields (serology, pharmacy) use "1:10" to mean 1 part in 11 total. Always clarify the convention in your lab.

Common Lab Dilutions

2× dilution — 1 part sample + 1 part diluent → 2× volume, half concentration
5× dilution — 1 part sample + 4 parts diluent → 5× volume
10× dilution — 1 part sample + 9 parts diluent → 10× volume
100× dilution — 10 µL in 990 µL, or two 1:10 dilutions in series
1000× dilution — three serial 1:10 dilutions

Tips for Accurate Dilutions

Use calibrated micropipettes — pipetting error is the #1 source of dilution error
Add diluent to tube first, then add sample for best mixing
For very large dilutions (1:1,000 or more), do serial dilutions in 2–3 steps
Use volumetric glassware (not graduated cylinders) for precise final volumes
Label all dilutions with concentration, date, and diluent used

For preparing solutions from scratch (weighing out solute), use our molarity calculator to find the mass needed for a target concentration. If your stock solution concentration is expressed as g/mL or mg/mL rather than molarity, our density calculator can help convert between mass and volume to determine the correct starting concentration.

AdvertisementResponsive Ad

Serial Dilutions in Microbiology and Pharmacology

A serial dilution is a step-by-step series of dilutions where the product of each step is used as the starting material for the next. Serial dilutions are essential when the required final dilution factor is too large to achieve accurately in a single step.

Microbiology plate counts: To count bacteria in a culture that might contain 10⁸ cells/mL, serial 10× dilutions bring the count into the countable range (30–300 colonies per plate). Three successive 1:10 dilutions give a 1:1,000 final dilution.
Antibody titers: Serum is serially diluted to find the highest dilution that still shows a positive reaction — the titer. Common starting dilutions are 1:8 or 1:10, with 2× or 10× steps.
Drug dose-response: Pharmacology experiments use serial dilutions (often 2× or 10× steps) to test a drug across multiple concentration decades in a single experiment.

The total dilution factor of a serial dilution is the product of each step. Three 1:10 dilutions give 10 × 10 × 10 = 1:1,000 (1,000× dilution factor). Two 1:2 dilutions give 1:4.

Safety When Working with Concentrated Solutions

Dilution safety is particularly important when working with concentrated acids, bases, and toxic reagents. Key rules:

Always add acid to water — never add water to concentrated acid. Adding water to concentrated H₂SO₄ causes violent heat generation and acid spatter.
Use appropriate PPE — chemical-resistant gloves, eye protection, and a lab coat for all acid/base dilutions. A face shield is required for fuming acids (HCl, HF, HNO₃).
Work in a fume hood — volatile concentrated acids (hydrochloric, nitric, acetic acid) must be diluted in a ventilated fume hood to avoid inhaling fumes.
Label immediately — every diluted solution must be labeled with compound, concentration, date, and diluent before you step away from the bench.
Cool before transferring — some dilutions generate significant heat. Allow concentrated acid solutions to cool to room temperature before transferring or capping.

Concentration Units Supported

This calculator supports any concentration unit — as long as both C₁ and C₂ use the same unit, the math is identical. Supported units include:

M (molar) — mol/L, standard for solutions
mM / µM / nM — millimolar, micromolar, nanomolar for dilute solutions
% (percent) — % w/v, % v/v for reagents and disinfectants
mg/mL, µg/mL, ng/mL — mass concentration for proteins, drugs, standards

Sources & References

IUPAC Compendium of Chemical Terminology — Dilution — International Union of Pure and Applied Chemistry
CDC Laboratory Dilution and Concentration Guidelines — Centers for Disease Control and Prevention

Dilution Calculator

Dilution Calculator (C₁V₁ = C₂V₂)