# Dilution Factor Calculator

Created by Jack Bowater
Reviewed by Bogna Szyk and Steven Wooding
Last updated: Dec 30, 2022

You will find this dilution factor calculator useful if you have ever performed a dilution: from chemical experiments and the preparation of medicine to making the perfect cup of coffee! As you've almost certainly used the dilution factor formula before, we have written this article to help you learn what a dilution factor is and how to calculate the dilution factor of any dilution you prepare.

So, read on so you no longer need to wonder how to find the dilution factor!

## What is dilution factor?

The dilution factor (or dilution ratio) is the notation used to express how much of the original stock solution is present in the total solution after dilution. It is often given as a ratio but can also be given as an exponent; however, this calculator will only show it as a ratio. Regardless if the dilution factor is a ratio or exponent, it has two forms, either describing the parts of the stock solution to the parts of the dilutant added ($\small S:D$) or the parts of the stock solution to the parts of the total solution ($\small S:T$).

❓ What exactly is a dilution? The solution dilution calculator at Omni Calculator has the answer! ⚗

As the difference between these two representations is very slight, an example would help ensure you don't get the wrong answers and mess up your experiment!

Let's say you have a $\small 10\ \text{cm}^3$ aqueous solution of acyl chloride. However, this is too concentrated for your experiment, so you add $\small90\ \text{cm}^3$ of water to further dilute the solution. You end up with $\small100\ \text{cm}^3$ of acyl chloride. As you have $\small 10$ parts of the stock solution, and $\small90$ parts of the dilutant, the $\small S:D$ ratio is $\small 1:9$ (canceling down from $\small10:90$). In the $S:T$ notation the dilution factor is $\small1:10$, you have $\small 10\ \text{cm}^3$ of the stock solution that now makes up a $\small100\ \text{cm}^3$ solution.

It is also worth noting that dilution factors only represent a loss of concentration – no molecules themselves are lost, just the number of them per mL decreases. This can be useful in several experimental situations. Although the dilution factor is just a handy way of thinking about dilutions, dilutions are very common, both in science and your day-to-day life. If you've ever made gravy, you've done a dilution. Ever washed your hands with soap? You've done a dilution.

They are also useful in the lab. If you wanted to replicate experiments over a range of decreasing concentrations, you would prepare what is known as a serial dilution: visit our serialdilution calculator to learn the math of this technique. They're also used in practically every chemical and most biological experiments, as the stock solution of your chemical is often far more concentrated than you desire.

Dilution is often used in the administration of medicine – for example, in order to administer the proper paracetamol dose for a child per kg of their body weight, it's sometimes required to dilute the initial solution.

## Dilution factor formula

Now that we've discussed what the dilution factor is, let's get down to brass tacks and talk about the dilution factor formula. But first, a brief section on how to represent the dilution factor. As we mentioned above, the dilution factor is often expressed as a ratio of volumes. The simplest formula for both types of dilution factor is as follows:

• $S:D = V_\text{stock }:V_\text{dilutant}$; and
• $S:T = V_\text{stock}:V_\text{total}$.

If these volumes are expressed in the same units, you can cancel each side down using their greatest common factor, and you will end up with the simplest integer expression of the dilution factor. Some of you, however, may wish to express this ratio in the form 1:X, where X is how many parts of the dilutant/total solution there are for one part of the stock solution. This may leave you with some funny (not haha funny, but oh no funny) ratios, but their formulas are:

• $S:D = 1:(V_\text{stock }/V_\text{dilutant})$; and
• $S:T = 1:(V_\text{stock }/V_\text{total})$

Due to the limitations in current technology, this is also how our calculator expresses your results. We hope you can forgive us for making you do extra work. You may also see the dilution factor expressed as an exponent, such as $3^{-1}$, $5^{-3}$, or $10^{-4}$. Now, do not be frightened by this new form! The exponent merely represents the ratio of the parts of the dilutant/total to the parts of the stock. Use the order of the ratio above:

• $S:D = \text{exponent}:1$; and
• $S:T = \text{exponent}:1$

Now, you may or may not know that a number with a negative exponent is the same as putting that number as the denominator when the numerator is 1 and removing the negative sign. Our exponent calculator can help you understand this further, but for now, let's go through the examples we set out above:

$\scriptsize \begin{split} &3^{-1}\rightarrow \frac{1}{3^1}:1\rightarrow\frac{1}{3}:1\rightarrow1:3 \\[1.5em] &5^{-3}\rightarrow \frac{1}{5^3}:1\rightarrow\frac{1}{125}:1\rightarrow1:125 \\[1.5em] &10^{-4}\rightarrow \frac{1}{10^4}:1\rightarrow\frac{1}{10,\!000}:1\rightarrow1:10,\!000 \\ \end{split}$

## How to calculate dilution factor

If you're still asking yourself, "how to find the dilution factor?", then we hope this section will answer all of your questions. So, just follow the steps below if you want to calculate the dilution factor by hand:

1. Find any two of the following three values: volume of the stock solution (stock), volume of the dilutant (dilutant), and total volume of the solution (total). This can either be done theoretically (before your experiment) or experimentally (after your experiment).

2. Use the two volumes to find the third. Use this equation: $\small \text{stock} + \text{dilutant} = \text{total}$. If you know which notation you would prefer to use ($\small S:D$ or $\small S:T$), then you may not need this step, but we shall include it for completeness.

3. Be sure that all the volumes in the ratios use the same unit. If you need help, visit our volume converter!

4. Decide which notation you require:

• $\small S:D$ = set the values of the stock and dilutant amount as a ratio — $\text{stock}:\text{dilutant}$; or

• $\small S:T$ = set the values of the stock and total amount as a ration — $\text{stock}:\text{total}$.

5. If required, cancel down the fractions by finding the greatest common factor. You can use the equivalent fractions calculator to speed up this task.

We have already provided an example in the What is dilution factor? section above, so please check that again if you are still wondering how to find the dilution factor. We will, however, tell you how to calculate the volumes you need from the dilution factor:

1. Choose your desired dilution factor, its notation ($\small S:D$ or $\small S:T$), and one of the variables on either side of the colon.

2. Divide the number after the colon ($\small D$ or $\small T$) by the number before the colon ($S$). We will name this value will be known as the factor.

3. Use the following equations depending on your choice of notation:

• $\small S:D = \text{stock}\cdot\text{factor}= \text{dilutant}$ or $\small \text{dilutant}/\text{factor} = \text{stock}$; or

• $\small S:T = \text{stock}\cdot\text{factor} = \text{total}$ or $\small \text{total}/\text{factor} = \text{stock}$.

There you have it – we hope this solves any of your issues regarding dilution factors. You can always check your results with our dilution factor calculator or just use it in the first place. It works either to find the dilution factor or the volume required to achieve a specific dilution factor. Just input the fields you know into our tool!

Jack Bowater
Initial volume
cm³
Dilutant volume
cm³
Final volume
cm³
Dilution Factors
Total to stock
:1
Dilutant to stock
:1
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