Serial Dilution Calculator
Enter your stock concentration, choose a dilution factor or a target final concentration, set the number of steps and the volume per tube, and the calculator instantly outputs the transfer volume, diluent volume and resulting concentration for every step. Switch between dilution factor and concentration range modes, choose your preferred concentration unit, and export a complete pipetting protocol. Results update in real time as you type.
What is a serial dilution?
A serial dilution is a stepwise reduction in concentration produced by transferring a fixed volume from one tube to the next, each containing a set amount of diluent (buffer, water or solvent). Unlike a one-step dilution, the same fold reduction is applied repeatedly, so the concentration drops geometrically. For example, starting at 1000 µM and applying a 1:10 factor at every step gives 100 µM, 10 µM, 1 µM, 0.1 µM and so on. This geometric spacing is ideal for dose-response curves, antibiotic minimum inhibitory concentration (MIC) assays, colony-counting microbiology, ELISA standard curves, and virus or phage titrations where a wide concentration range must be covered with uniform spacing on a log scale.
How to perform a serial dilution - the key formulas
The fundamental relationship is C1V1 = C2V2, rearranged as V_transfer = V_total / dilution_factor, where V_total is the volume in each tube and the dilution factor is the fold reduction per step. The diluent volume is V_total minus V_transfer. For concentration range mode, the required dilution factor per step is (C_start / C_end)^(1/(n-1)), where n is the number of tubes. The concentration in tube i (counting from 1) is C_stock divided by df^(i-1). The cumulative dilution factor after n steps is df^(n-1). These formulas hold whether concentrations are in molar, mass-per-volume or any other linear unit.
Pipetting accuracy and practical tips
Accuracy in serial dilutions depends almost entirely on consistent pipetting. The most common errors are carry-over (residual solution on the outside of the tip) and volume inaccuracy at small volumes. As a rule of thumb, transfer volumes below 10 µL with a standard multichannel pipette introduce significant relative error, and below 1 µL the error can exceed 10 percent. To minimise this: use a calibrated pipette that is appropriate for the transfer volume (a P20 for volumes below 20 µL, not a P1000), pre-wet the tip by aspirating and expelling the solution twice before the actual transfer, always mix the tube thoroughly after each transfer, and change tips between every step. If the required transfer volume is below 1 µL, increase V_total or reduce the dilution factor, then adjust the number of steps.
Concentration range mode and log-scale spacing
When designing a dose-response curve, you usually know the concentration range you need to cover (for example, 1 nM to 10 µM for an IC50 assay) and the number of data points you can handle. Concentration range mode derives the correct per-step dilution factor automatically: df = (C_start / C_end)^(1/(n-1)). This guarantees even spacing on a logarithmic axis, which is what pharmacological and biochemical assays require for curve fitting. The resulting factor is often not a round number (for a 1000-fold range over 7 points, df = 10^(3/6) = 3.16, the classic half-log step). This calculator handles that case directly, so you do not need to work it out by hand.
Common serial dilution schemes
| Scheme | Dilution factor | Steps for 10^6 fold | Typical use |
|---|---|---|---|
| 1:2 | 2x | 20 | Antibody titrations, IC50 curves |
| 1:3 | 3x | 13 | MIC assays, dose-response |
| 1:5 | 5x | 9 | Rapid microbiology counts |
| 1:10 | 10x | 6 | Colony counts, ELISA, drug dilutions |
| Half-log (1:3.16) | 3.16x (10^0.5) | 12 | Pharmacology dose-response curves |
| 1:100 | 100x | 3 | Preparing working solutions from concentrated stocks |
Standard dilution series used in microbiology, pharmacology and biochemistry assays.
Frequently asked questions
What is the formula for serial dilution?
The concentration in tube n is C_n = C_stock / (df)^(n-1), where df is the dilution factor per step. The transfer volume is V_transfer = V_total / df and the diluent volume is V_total - V_transfer. For concentration range mode, the per-step factor is df = (C_start / C_end)^(1/(n-1)).
How do I calculate the volume to transfer?
Divide the total tube volume by the dilution factor: V_transfer = V_total / df. For example, if each tube holds 1 mL and you want a 1:10 dilution, transfer 0.1 mL (100 µL) and add 0.9 mL of diluent. The transfer volume stays the same for every step because the dilution factor is the same.
What dilution factor should I use for a dose-response curve?
Half-log steps (factor of about 3.16, or 10^0.5) are standard for pharmacological dose-response and IC50 assays because they give evenly spaced points on a log10 concentration axis. For colony counting in microbiology, 1:10 steps are conventional. For antibody titrations, 1:2 is common because a 2-fold difference in titer is the standard threshold for significance.
My transfer volume is less than 1 µL - what should I do?
A transfer volume below 1 µL is at the practical limit of standard micropipettes and introduces unacceptable error. You have two options: increase the total volume per tube (use a larger tube) so V_transfer = V_total / df is larger, or reduce the dilution factor and add more steps to cover the same range. For example, a 1:10 dilution in 100 µL tubes requires a 10 µL transfer (fine), but a 1:100 dilution in 100 µL tubes requires a 1 µL transfer (marginal). Splitting into two 1:10 steps avoids this.
What is the difference between a dilution factor and a dilution ratio?
A dilution factor is the fold reduction: a factor of 10 means the concentration is one-tenth of the original. A dilution ratio expresses the same thing as parts-transferred to parts-total: 1:10 means 1 part sample in 10 parts total (transfer + diluent = total volume). Both describe the same operation, but the notation differs. This calculator uses the dilution factor convention, where the factor equals the total tube volume divided by the transfer volume.
How many dilution steps do I need to reach a given concentration?
Rearrange the formula: n = log(C_stock / C_target) / log(df) + 1. For example, to go from 10 mg/mL to 1 ng/mL (a 10^7-fold range) with 1:10 steps, you need log(10^7) / log(10) + 1 = 7 + 1 = 8 tubes. Use the concentration range mode in this calculator and it derives both the factor and the number of steps for you.
Can I use serial dilution for anything other than concentration?
Yes. The same arithmetic applies to any quantity that halves (or reduces by a constant factor) at each step: cell counts for viability assays, virus plaque-forming units (PFU), radioactivity in tracer experiments, and even absorbance-based standard curves. The key requirement is that the relationship between the measured quantity and concentration (or amount) is linear, so that the geometric dilution series maps directly to evenly spaced values on a log axis.