A serial dilution is a chain of dilutions, where each new tube is made by diluting the previous one. It is the standard way to reach very low concentrations that you could never pipette directly: a single 1-in-100,000 dilution would need an impossibly small volume of stock, but five tenfold steps reach the same factor with comfortable volumes at every step. This planner takes a starting concentration, a dilution factor per step, and the number of steps, and returns the concentration at every step plus the total factor and the volume to transfer each time.
The maths is a repeated division. With a starting concentration of 100 units and a tenfold factor per step, step zero is the stock itself at 100, step one is 10, step two is 1, step three is 0.1, step four is 0.01, and step five is 0.001. Each step divides by the same factor, so after five steps the total factor is 10 to the power of 5, or 100,000. The tool lists every step so you can label tubes in advance and spot the step where your target concentration appears, instead of calculating under time pressure at the bench.
Here is a worked example with volumes. Each tube holds 10 mL, and the factor is 10, so each transfer is 10 divided by 10, which is 1 mL of the previous tube into 9 mL of solvent. You pipette 1 mL of stock into tube one, mix, then pipette 1 mL of tube one into tube two, and so on. The transfer volume is the same at every step when the factor and tube volume stay constant, which is why serial dilutions are easy to repeat but also easy to do on autopilot, so stay focused on which tube you are holding at each step.
Choosing the factor is a design decision, not a habit. Tenfold steps cover a huge range quickly, which suits finding an unknown concentration or testing a wide dose range, but they jump coarsely: nothing exists between 10 and 1. Twofold steps give finer resolution, doubling the work for the same range but showing a gentler curve, which suits dose-response work where the interesting change happens between tenfold points. Enter any factor above one, and the tool will plan it; the right factor depends on whether you need range or resolution more.
Error compounding is the serious warning for serial work. A single dilution has one pipetting error, but a serial chain carries every earlier error forward, because each tube is made from the one before it. A 5 percent error at step one becomes part of every later concentration, and a mislabelled tube ruins all the tubes after it. Mix each tube thoroughly before transferring, change tips between steps, and label every tube before you start pipetting, not after, when several similar tubes sit in a row and look identical.
Units and notation need care at low concentrations. After several tenfold steps, concentrations become small decimals or scientific notation, such as 1.0 times 10 to the minus 3, and it is easy to misread a zero. The tool shows steps in scientific notation for that reason, so the number of zeros is explicit. Keep the same concentration unit from start to finish, whether it is mg/mL, mol/L, or cells per mL, because mixing units mid-chain silently breaks the whole series, and the error will not show until your results make no sense.
This planner is an educational estimator only, and it differs from a single-step dilution tool in an important way: it plans a chain, not one dilution. A single-step tool answers one C1V1 = C2V2 question or one ratio question, while this tool answers the planning question for a whole series, including the total factor and the transfer volume at each step. Real lab work needs proper procedures, safety rules, protective equipment, and supervision. Planned in advance, labelled clearly, and pipetted carefully, a serial dilution is one of the most reliable techniques in the lab.