# How do I calulcate the amount of concentrated stock solution to add to get the correct dilution?

For example, how much loading buffer (6X) do I need for my PCR reaction with a volume of 25 μl? What is the general way to calculate it?

For any question regarding volume and concentration, you should consider the equation $$C_1V_1=C_2V_2$$. We can use it to derive a general equation for the addition of concentrated stock solutions. We want to find the volume of stock solution ($$V_1$$) to add so that its final concentration is 1X. Here's what we know:

• The initial concentration of stock solution, $$C_1=X$$
• The final concentration of the solution, $$C_2=1$$
• The volume of solution we are diluting the stock into, $$V_s$$

So the equation becomes:

$$XV_1=V_2$$

We don't know $$V_2$$, but we do that $$V_2=V_1+V_s$$. Subbing that in:

$$XV_1=V_1+V_s$$

Solving for $$V_1$$:

$$XV_1-V_1=V_s$$ $$V_1(X-1)=V_s$$ $$V_1=\frac{V_s}{X-1}$$

Then you simply need to sub in your values:

$$V_1=\frac{25μL}{6-1}$$ $$V_1=5μL$$

• @biologist You’re welcome! Oct 11 '18 at 8:41
• Absolutely correct. I leave this comment only as an aside for people who may find it unhelpful to think and visualize mathematically: a 6X buffer simply means it should make up one part in six. You add 1μl of it to 5μl of your solvent. Or add 2μl to 10μl. Or add 5μl to 25μl. Or 1 teaspoon of honey added to 5 teaspoonfuls of tea. Now that's some 6X honey.
– S Pr
Oct 11 '18 at 10:24

Candianer's answer is a generally correct way of solving these problems but, in my opinion, overkill for this situation.

All Nx buffers are mixed to make your life easier, and you will generally encounter 10x, 6x, and 5x buffers. 10x and 5x seem obvious, you just put them in so they make up a tenth or a fifth of your solution, but 6x seems to confuse people. The reason it's x6 is because you are adding it to an existing solution, so as well as you're solution you're going to have one lot of whatever you're adding. This makes it (1+N)x and you can then clearly see that 6x is (1+5)x, so you need to add an amount equal to one fifth of your volume.

One fifth of 25 μL is 5 μL so that is what you need to add.

• Certainly one doesn’t need to derive the equation every time; I was just showing how it’s done. It really is as simple as dividing the volume by 1-N. Oct 11 '18 at 9:46