# Serial Dilution Calculator

Created by Jack Bowater
Reviewed by Bogna Szyk
Last updated: Feb 02, 2023

If you are wondering how to do serial dilutions, this serial dilution calculator is the tool for you. Here, we provide you with every imaginable piece of information regarding serial dilutions; from calculations for the required volume of solution at the end of each dilution, to the exact amount of stock solution and dilutant needed to make the first solution, to the dilution factor of the first nine solutions with respect to the starting solution. We have even provided two different methods - dilution factor or concentration range. Please read on to find a serial dilution definition in the what is a serial dilution section as well as some serial dilution examples!

## What is a serial dilution

A serial dilution is a kind of solution dilution: if you need to refresh the topic, visit our solution dilution calculator. A more exact serial dilution definition is that it is a stepwise dilution of a solution, that is repeated a certain number of times and in which the concentration decreases with each step. The dilution factor calculated at each step does not have to be constant, but it is for this tool**. Serial dilutions have many uses that are mainly related to chemistry and biology.

It may be useful to you if we elucidate some of the terms in this serial dilution calculator:

• Method - You have two choices, dilution factor and concentration range. Dilution factor allows you to input the dilution factor that separates one solution and the next. The dilution factor between solutions is the same for all dilutions. Concentrations range requires you to provide the concentration of the initial and final solutions. Each dilution separated by the same dilution factor, which is calculated for you.
• Number of dilutions - This is the number of solutions you are preparing. A $1$ in this field calculates if you are making the starting solution from the stock solution, and will alter the fields accordingly. Any other number will be the number of solutions you are making, including the starting solution. Please input integer values into this field.
• Starting solution concentration - The concentration of the first solution in the series, not the concentration of the stock solution.
• Volume per use - How much solution you need per concentration for your experiment.
• Number of uses per dilution - The number of repeats per solution.
• Error type - Either percentage error or pipette error. The former will add that percent onto the volume to be left, while the latter will add the pipetting error (you can find this on your pipette) on to the volume. If you don't know how to calculate percentage error, check our percent error calculator.
• Minimum volume required - The volume that should be left in your dilution after you have removed an amount of it for the next dilution. The calculation for this is volume per use times number of uses per dilution times error. This value can be inputted directly if you already know it.
• Starting solution composition - This section deals with the creation of the starting solution. It tells you the starting volume needed, and tells you how to make that from the volume of stock solution required and the volume of dilutant to be added, provided you know the stock solution concentration.
• Repeat solutions - This section tells you how to create each of the dilutions past the starting solution. It gives you the volume to be transferred from one dilution to the next, the amount of dilutant you need to add to each dilution, and the total amount of dilutant needed - so you don't need to keep pouring out more!
• Dilution factor with respect to the starting solution - This field will appear once you input the number of dilutions and the dilution factor (or the starting solution concentration and the final solution concentration if you're using the concentration range method. Here you will find the cumulative dilution factor as it relates to the starting solution.
• Concentration of solutions - the concentration of up to the first ten solutions.

## How to do serial dilutions

Serial dilutions are not as intuitive as we'd like. So, in this section, we provide you with a step-by-step guide of how to do serial dilutions. We hope this will help you, along with the serial dilution definition we provided above:

1. Determine the number of dilutions, dilution factor (or range) and starting solution concentration. In this example, we are making $6$ dilutions of sulphuric acid diluted with water. The starting concentration is $10\ \text{M}$ and the dilution factor is $4$. This experiment will then require $6$ test tubes, one for each of the dilutions.

2. Work out how much of the solution you require for each dilution. For our experiment we are using $9\ \text{cm}^3$ of each dilution, with $3$ repeats. This means we need $3\ \text{cm}^3\cdot 9\ \text{cm}^3 = 27\ \text{cm}^3$ of solution total. If we assume a total pipette error of $\pm3\ \text{cm}^3$, the total minimum value is $27\ \text{cm}^3 + 3\ \text{cm}^3 = 30\ \text{cm}^3$.

3. Calculate how much of the solution you need to pipette from one dilution to the next. This is given by minimum volume / (dilution factor - 1) = move volume. In our example we need to move $30\ \text{cm}^3 / (4 - 1) = 10\ \text{cm}^3$. Grab a pipette of an appropriate size.

4. Make the starting solution. The volume of this is equal to minimum volume + move volume = starting volume. In our case it is equal to $30\ \text{cm}^3 + 10\ \text{cm}^3 = 40\ \text{cm}^3$. The next step is to calculate how much of the stock solution you need to get the desired concentration. This equation is given by (starting volume * starting concentration) / stock concentration = stock volume. If our stock solution of sulphuric acid has a strength of $50\ \text{M}$, then the calculation becomes $(40\ \text{cm}^3 \cdot 10\ \text{M}) / 50\ \text{M} = 8\ \text{cm}^3$. So we need $8\ \text{cm}^3$ of our stock solution and the remaining $32\ \text{cm}^3$ of our dilutant to make the correct concentration. Pipette this amount of stock solution and water into the first test tube. Remember to use clean pipettes for both and to stir the solution thoroughly but gently.

5. With a clean pipette, remove the move volume, from the starting solution into the next test tube. In our example, pipette $10\ \text{cm}^3$ of the solution into the next test tube, add $32\ \text{cm}^3$ of water and mix gently but thoroughly. With clean pipette repeat this step with the solution you just created. Repeat this a further $3$ times, so you have $6$ solutions of decreasing concentration.

6. Perform your experiment.

7. Dispose of all chemicals correctly and safely.

As you can see, several calculations are required to carry out a serial dilution correctly. Instead of having to worry about this, just input the number of dilutions, dilution factor, starting solution concentration, stock solution concentration and the minimum volume required into this serial dilution calculator to receive all the other values you need!

If you are using the concentration range method, the steps are the same as above, but you will need to calculate the dilution factor using the following equation:

$f_\text{d} = (c_\text{initial} - c_\text{final})^{\frac{1}{n_{\text{d}}- 1}}$

Where:

• $f_{\text{d}}$ — The dilution factor;
• $c_{\text{initial}}$ and $c_{\text{final}}$ — The initial and final concentration; and
• $n_{\text{d}}$ — The number of dilutions.

From that point onwards the steps are the same.

## Serial dilution examples

Serial dilutions are a common practice in the natural sciences. Due to the period decrease in concentration, this method is very useful when performing many types of experiments, from chemistry to biology to medicine. You can plot the information they provide onto a graph to find the gradient and intercepts (or calculate them with our slope intercept form calculator), so that information about any trends can be spotted. They are also useful when you want to experiment at a certain concentration, but are unsure what the concentration is. For example, you want to perform UV spectrometry on a sample of furan you made, but you do not know which strength will get you the best result. So, to find this, you take your $5\ \text{M}$ solution and perform a serial dilution with a dilution factor or 1:5. From this you get concentrations of $5\ \text{M}$, $1\ \text{M}$, $0.2\ \text{M}$, $0.04\ \text{M}$, and $0.008\ \text{M}$. You run each of these samples through a UV spectrometry, and find that you get the best result at $0.2\ \text{M}$. You now know that concentrations around this mark will give you the best result.

This serial dilution calculator also has applications in microbiology. Let's say you have a colony of bacteria made up of 100000 cells. You want to test the effectiveness of your new antibiotics on different amounts of cells. You take 10% off from each of the serial dilutions (i.e., a 1:10 dilution factor) and, after 4 dilutions, have a solution with approximately 10 cells. With this known number you can get a better understanding of the effectiveness of your drug.

Doctors and nurses also often use serial dilutions. Sometimes, patients require a very small dose of medicine - for example, you need to adjust the paracetamol dosage by weight of the child. Other drug dosages vary based on body surface area. As such doses may be too small to be made up with a pipette and the stock solution, medical staff will carry out a series of dilutions to get to the correct concentration.

If you need help in chemistry, check out the other tools in the , like the calibration curve calculator!

Jack Bowater
Method
Dilution factor
Number of dilutions
Dilution factor
:1
Starting solution concentration
M
Volume to be left for each dilution
Volume per use
cm³
Number of uses per dilution
Error type
Percentage
Percentage error
%
Minimum volume required
cm³
Starting solution composition
Starting volume needed
cm³
Stock solution concentration
M
Volume of stock solution required
cm³
Volume of dilutant to be added
cm³
Repeat solutions
Volume to be moved at each step
cm³
Dilutant needed at each step
cm³
Total amount of dilutant needed
cm³
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