About the Dilution Calculator
Laboratories rarely make every solution from solid. Instead they keep stock solutions at high concentration and dilute them to the strength they need. Diluting adds solvent but never removes solute, which leads to one of the most used equations in chemistry and biology: C₁V₁ = C₂V₂. Know any three of the four values and the fourth follows.
This dilution calculator solves C₁V₁ = C₂V₂ for the stock volume, the final concentration, the final volume or the stock concentration. It also tells you how much solvent to add, the dilution factor, and checks that the amount of solute is the same before and after. Concentrations and volumes can be in any units, as long as each pair matches.
How to Use the Dilution Calculator
Choose what to find: stock volume, final concentration, final volume or stock concentration.
Enter the three known values.
Choose the concentration unit — M, mM, µM, percent, mg/mL or fold — and the volume unit.
The Formula
C₁ × V₁ = C₂ × V₂
C₁ = stock concentration V₁ = volume of stock used
C₂ = final concentration V₂ = final total volume
solvent to add = V₂ − V₁
dilution factor = C₁ ÷ C₂ = V₂ ÷ V₁Step-by-Step Examples
Making 250 mL of 0.1 M from a 1 M stock.
V₁ = C₂ × V₂ ÷ C₁ = 0.1 × 250 ÷ 1 = 25 mL
solvent = 250 − 25 = 225 mL
dilution factor = 10Diluting 5 mL of 10 M to 100 mL.
C₂ = C₁ × V₁ ÷ V₂ = 10 × 5 ÷ 100 = 0.5 M
dilution factor = 20How far can 10 mL of 12 M acid be diluted to reach 1 M?
V₂ = C₁ × V₁ ÷ C₂ = 12 × 10 ÷ 1 = 120 mLWhy the Equation Works
Concentration × volume is the amount of solute. For molar concentrations, mol/L × L = mol. Adding solvent increases the volume, but the number of moles stays the same, so C₁V₁ before dilution equals C₂V₂ after. The same logic applies to any concentration unit — grams per litre, percent, or times-concentrated stocks — which is why the calculator lets you use any unit for both concentrations.
Dilution Factors and Ratios
The dilution factor is how many times more dilute the final solution is. A tenfold dilution — 25 mL made up to 250 mL — has a factor of 10. In biology this is often written as 1:10, meaning one part stock in ten parts total. Be careful: some people use 1:10 to mean one part stock plus ten parts solvent, which is really an 11-fold dilution. When following a protocol, check which convention it uses, or work from the concentrations directly.
Serial Dilutions
To reach very low concentrations accurately, labs use serial dilutions: a series of smaller dilutions, each made from the previous one. Four tenfold steps give a 10,000-fold dilution without measuring impossibly tiny volumes. Each step uses the same equation, and the overall dilution factor is the product of the individual factors. Serial dilutions are used for standard curves, bacterial counts and preparing drug doses.
Working Safely with Concentrated Stocks
When diluting concentrated acids, especially sulfuric acid, always add acid to water, slowly and with stirring, never water to acid. Mixing releases a great deal of heat, and adding a small amount of water to a large amount of acid can make it boil and spit. Wear eye protection and gloves, work in a fume cupboard for volatile acids and bases, and let the solution cool before making it up to the final volume, because hot liquids occupy slightly more space.
Accuracy Tips
Use a volumetric pipette or accurate micropipette for V₁ and a volumetric flask for V₂, filling to the mark after mixing. Avoid measuring very small volumes — below about a hundredth of the final volume — in one step; use a serial dilution instead. Label every diluted solution with its concentration, date and the stock it came from.
Dilution in Everyday Life
Dilution is not only a laboratory skill. Concentrated garden feeds, cleaning products, squash drinks, photographic chemicals and disinfectants are all sold as concentrates meant to be diluted. The label usually gives a ratio — for example 1 part to 50 parts water — or a dose such as 20 mL per litre. The same C₁V₁ = C₂V₂ reasoning applies: to make 5 litres of a solution at one-fiftieth of the concentrate's strength, you need 5,000 ÷ 50 = 100 mL of concentrate made up to 5 litres. Getting dilutions right matters, because too strong a mixture can damage plants, surfaces or skin, and too weak a mixture may not work. For disinfectants in particular, follow the manufacturer's dilution exactly, since a solution that is too dilute may not kill germs in the stated contact time.
Checking Your Answer
A quick sanity check catches most mistakes. The stock volume V₁ must always be smaller than the final volume V₂, and the final concentration C₂ must always be smaller than the stock C₁. The ratio between the volumes must equal the ratio between the concentrations, only upside down: if the concentration falls tenfold, the volume rises tenfold. If a result breaks one of these rules, a value has probably been entered in the wrong box or the wrong unit. The calculator's check line multiplies each side out so that you can see at a glance that the amount of solute is the same before and after dilution.
Mixing Ratios Like 1:200 and 1:400
Cleaning products, disinfectants, garden sprays and photographic chemicals usually give a dilution ratio on the label instead of a concentration. Choose Mix a ratio in the calculator, enter the ratio and the total amount you want, and it gives the concentrate and water to measure.
Most labels mean 1 part concentrate plus 400 parts water, so a 1:400 mix has 401 parts in total. Some scientific protocols mean 1 part in 400 parts total. For large ratios the two readings differ by well under 1%, so either is fine for cleaning; for laboratory work, check which one your protocol uses.
| Ratio (1 part + water) | Concentrate per 1 litre | Concentrate per US gallon |
|---|---|---|
| 1:10 | 90.9 mL | 344.1 mL (11.64 fl oz) |
| 1:20 | 47.6 mL | 180.3 mL (6.10 fl oz) |
| 1:32 | 30.3 mL | 114.7 mL (3.88 fl oz) |
| 1:50 | 19.6 mL | 74.2 mL (2.51 fl oz) |
| 1:64 | 15.4 mL | 58.2 mL (1.97 fl oz) |
| 1:100 | 9.9 mL | 37.5 mL (1.27 fl oz) |
| 1:128 | 7.8 mL | 29.3 mL (0.99 fl oz) |
| 1:200 | 5.0 mL | 18.8 mL (0.64 fl oz) |
| 1:256 | 3.9 mL | 14.7 mL (0.50 fl oz) |
| 1:400 | 2.5 mL | 9.4 mL (0.32 fl oz) |
| 1:500 | 2.0 mL | 7.6 mL (0.26 fl oz) |
| 1:1000 | 1.0 mL | 3.8 mL (0.13 fl oz) |
Example: 1:400 in a 1 litre spray bottle. 1,000 mL ÷ 401 = 2.49 mL of concentrate, about half a teaspoon, topped up with 997.5 mL of water. 1:200 in a US gallon needs 3,785 mL ÷ 201 = 18.8 mL, a little over a tablespoon.
Understanding Your Result
The headline is the value you asked for.
The recipe line tells you how much stock to take and how much solvent to add.
The dilution factor line shows how many times more dilute the final solution is.
The check line confirms that C₁ × V₁ equals C₂ × V₂.
When Should You Use This Calculator?
Use it to prepare working solutions from stock in the lab.
Use it to plan serial dilutions for experiments.
Use it for chemistry and biology homework on concentration.
Use it to dilute cleaning or garden concentrates at home.
Common Mistakes
Mixing units between the two sides. Use the same unit for both concentrations and for both volumes.
Adding V₂ of solvent instead of making up to V₂. The final volume includes the stock.
Confusing 1:10 conventions. Check whether it means 1 in 10 or 1 plus 10.
Trying to concentrate by dilution. The final concentration is always lower than the stock.