Dilution Calculator

Dilution is the process of adding more solvent to a given solution in order to decrease its concentration. The amount of solute remains unchanged. By spreading it out over a larger volume, the concentration decreases. This tool calculates these values using the same formula that applies for all dilutions.

If you enter three of the four values, this calculator will complete the fourth value and show how much solvent to add and what the concentration will be after dilution. It is a standard tool for making working solutions from concentrated stock solutions in laboratories, workshops or at home.

The formula for dilution:

If you multiply the concentration of a solution by its volume, you get the amount of solute present in it. Since this quantity remains constant during dilution, the product of initial concentration and initial volume is equal to the product of final concentration and final volume. This relation is called the dilution formula.

In this case C1 is the concentration of the starting solution, V1 is the volume that will be taken from the starting solution. C2 is the desired final concentration and V2 is the total volume of the solution after preparation. When chemists work with concentrations in moles they often write it as M1V1 = M2V2 but the meaning is exactly the same.

Example:

Suppose you have a stock solution with a concentration of 10 mM and need to make a solution with a concentration of 50 μM at a volume of 20 mL. The formula is as follows: the amount of stock solution needed = (desired concentration (C2) x desired volume (V2)) / starting concentration (C1). This means you multiply 50 μM by 20 mL and then divide that answer by 10 mM.

So, you take 0.1 mL of the stock solution (i.e., 100 microliters) and dilute it with a solvent to give a final volume of 20 mL. The amount of solvent added is 19.9 mL, which is the difference between 0.1 mL and 20 mL. The dilution factor is the ratio of the starting concentration (10 mM) to the target concentration (50 uM), which is 200. This corresponds to a dilution by a factor of 200.

How to use this calculator.

Enter three of the four values and leave the value you want to calculate blank. The calculator will solve for the blank value and update it instantly. In most cases, you know the starting concentration, the target concentration, and the final volume. So if you leave the volume of the starting solution blank, you'll get information on how much of the starting solution is needed.

Each input field has separate unit conversions. You can use millimoles for the starting solution and micromoles for the target solution, while volume can be entered in microliters, milliliters or liters. The calculator will do the conversions during calculation and show the amount of solvent to add along with the dilution factor next to the result.

This is how you determine missing values.

An equation links four quantities together so that if three of them are known, the fourth can be found. Each variation corresponds to a different practical problem.

If you leave the volume of the stock solution blank, it will calculate the volume to be removed. If you leave the final volume blank, it will calculate the volume that can be made from a given amount of stock solution. If you leave the final concentration blank, it will calculate the resulting concentration. If you leave the concentration of the stock solution blank, it will calculate the required concentration of the stock solution backwards.

Dilution factor and dilution ratio

The dilution factor indicates the factor by which the final solution has been diluted compared to the starting solution. It is the result of dividing the concentration of the initial solution by that of the final one and, according to the law of dilution, also the result of dividing the volume of the final solution by that of the initial one.

A dilution factor of 200 means that the concentration of the final solution is 200 times lower than the concentration of the starting solution. The dilution can also be expressed as a ratio, such as 1:10. This usually means that one part of the original solution is removed and diluted with a certain amount so that the final volume is ten parts; the dilution factor would then be 10. However, it's best to explicitly state the factor, since this notation isn't always unambiguous. There are also other tools for calculating dilutions that can work directly with the ratio of concentrate to water.

Required amount of solvent

The amount of solvent used is the difference between the final volume and the volume of the withdrawn stock solution. It is not the same amount of solvent added as V2. Enough solvent is added to ensure that the total volume reaches V2, the volume of the withdrawn stock solution.

In the example above 0.1 mL of stock solution is removed and diluted to a volume of 20 mL by adding 19.9 mL of solvent. For accurate performance, either add solvent up to the mark or weigh it out. Avoid mixing a fixed volume of stock with a fixed volume of solvent as volumes do not always add exactly when liquids are mixed.

Areas of application for dilution:

Preparing a working solution from a concentrated stock solution is one of the most common laboratory tasks in chemistry and biology. The same calculation can be applied to many different fields.

In sample preparation, biological samples are often diluted because their concentration is too high to be measured directly and must be brought into the range of the analytical method. In reagent manufacturing, enzymes, buffers, dyes and antibiotics are supplied in concentrated form and must be diluted to working concentrations. In cell culture, growth factors or inhibitors are diluted in media to desired concentrations. For calibration standards for chromatography and spectroscopy, stock solutions are serially diluted to known concentrations.

The same formula can be used outside the lab to determine dilution ratios for home or industrial use, such as when diluting concentrated cleaning products, making a 3% hydrogen peroxide solution (stock is 30%) or diluting antifreeze. The following safety notes are especially important when working with strong acids and oxidizing agents.

Formulas with other concentration measures:

The dilution equation does not ask what unit you use for concentration, but it is required that the initial and final solutions have the same units. This can be molarity, percent, parts per million or mass/volume (e.g., milligrams per milliliter). The volume of the initial solution and the final volume must also be in the same units.

This tool's concentration conversion supports ranges from nanomolar to molar. If the concentration is given as a percentage or milligrams per milliliter, enter the concentration value in both input fields and select the same unit for both fields. As only the ratio of the two concentrations is used in the calculation, volume and dilution factor will be calculated correctly.

Continuous dilution:

When very high dilution factors or a series of standard solutions are required, it is difficult to dispense the correct amount in one step. With serial dilutions, the goal is achieved by breaking it up into several steps with the same dilution factor. A 1000-fold dilution can be broken down into three simple 10-fold dilutions for example. The formula C1V1 = C2V2 applies to each step and a special tool for calculating serial dilutions illustrates these steps.

Safe dilution of acids.

When you mix a strong acid with water heat is released. When water is added to an acid the heat can build up quickly at the surface causing the water to boil and the acid solution to splash out of the container.

Always pour the acid into water slowly and stir constantly to spread the heat evenly in the larger volume of water. Work in a well-ventilated area, wear safety glasses and gloves. Only use the solution when it has cooled down. Even strong oxidizing agents like concentrated hydrogen peroxide must be handled with great care.

Tips for accurate dilution:

Use the same units for both concentrations, and also use the same units for both volumes before checking your result. Alternatively you can convert in the individual input fields of a calculator tool. Mixing up units is the most common mistake when diluting.

Use appropriate equipment to measure small volumes of stock solution. It is inaccurate to dispense only a few milliliters with a large graduated cylinder. If the amount of stock solution required falls below one or two microliters at some point, switch to serial dilution. Instead of adding a fixed volume of solvent, fill the solution up to the final volume. This will ensure that the total volume is exactly V2.

This tool is for general educational purposes and normal solution preparation. For clinical applications, pharmaceutical industry or dangerous substances you must follow the procedures, classification standards and safety data sheets that apply to your particular environment.