Serial Dilution Calculator
Calculate serial dilution with our free science calculator. Uses standard scientific formulas with unit conversions and explanations.
Reviewed by Daniel Agrici, Founder & Lead Developer
Formula
C(n) = C(0) / DF^n, where DF = (Sample Vol + Diluent Vol) / Sample Vol
Where C(n) is the concentration at dilution step n, C(0) is the initial concentration, DF is the dilution factor per step, and n is the number of dilution steps performed. The dilution factor is calculated from the ratio of total volume to sample volume transferred.
Worked Examples
Example 1: Bacterial Plate Count Dilution
Problem:A bacterial culture at 2 x 10^9 CFU/mL needs to be diluted for plate counting. Perform 1:10 serial dilutions (1 mL into 9 mL) for 6 steps. What concentration is at each step?
Solution:Step 0: 2 x 10^9 CFU/mL (undiluted)\nStep 1: 2 x 10^9 / 10^1 = 2 x 10^8 CFU/mL\nStep 2: 2 x 10^9 / 10^2 = 2 x 10^7 CFU/mL\nStep 3: 2 x 10^9 / 10^3 = 2 x 10^6 CFU/mL\nStep 4: 2 x 10^9 / 10^4 = 2 x 10^5 CFU/mL\nStep 5: 2 x 10^9 / 10^5 = 2 x 10^4 CFU/mL\nStep 6: 2 x 10^9 / 10^6 = 2 x 10^3 CFU/mL\nPlate steps 4-6 for countable colonies (30-300 CFU/plate)
Result:Final concentration: 2 x 10^3 CFU/mL, Overall dilution: 1:1,000,000
Example 2: Antibody Titer Twofold Dilution
Problem:Determine antibody titer using 1:2 serial dilutions of serum. Start at 1:2 and perform 8 dilution steps. If positive reaction stops at step 5, what is the titer?
Solution:Step 1: 1:2\nStep 2: 1:4\nStep 3: 1:8\nStep 4: 1:16\nStep 5: 1:32 (last positive)\nStep 6: 1:64 (negative)\nStep 7: 1:128\nStep 8: 1:256\nTiter = reciprocal of last positive dilution = 32
Result:Antibody titer = 1:32 (last dilution showing positive reaction)
Frequently Asked Questions
What is a serial dilution and why is it used?
A serial dilution is a stepwise dilution of a substance in solution, where the dilution factor remains constant at each step. Starting from a stock solution, a fixed volume is transferred to a tube of diluent, mixed, and then a fixed volume from that tube is transferred to the next. Serial dilutions are fundamental in microbiology for plating to count colony-forming units, in immunology for antibody titer determination, in pharmacology for dose-response curves, and in analytical chemistry for preparing calibration standards. They allow researchers to cover a wide range of concentrations efficiently using minimal reagents.
How do I choose the correct dilution factor?
The dilution factor depends on your experiment needs. A 1:10 (tenfold) dilution is the most common in microbiology because it creates simple logarithmic concentration steps and is easy to calculate (1 mL into 9 mL). A 1:2 (twofold) dilution is standard for MIC testing and antibody titers because it provides higher resolution between steps. A 1:5 dilution offers a middle ground. Choose based on your expected concentration range: if you need to span 6 orders of magnitude, use 1:10 with 6 steps. If you need finer resolution across 2-3 orders of magnitude, use 1:2 with 10 steps.
What are common errors in serial dilution technique?
The most critical errors include inadequate mixing between transfers, which causes carryover of concentrated solution and skewed results. Always vortex or pipet mix at least 5-10 times per transfer. Using the same pipette tip without changing can cause contamination. Inaccurate pipetting volumes compound at each step, so use calibrated pipettes and proper technique. Air bubbles in pipette tips cause volume errors. Temperature changes can affect solution viscosity and thus pipetting accuracy. Finally, failure to change tips between dilution steps can carry over microorganisms and cause falsely elevated counts.
How do I calculate the concentration at any dilution step?
The concentration at step n equals the initial concentration divided by the dilution factor raised to the power of n: C(n) = C(0) / DF^n. For example, starting with 10^9 CFU/mL and doing 1:10 dilutions, step 3 gives: 10^9 / 10^3 = 10^6 CFU/mL. The cumulative dilution factor at any step is simply DF^n. For a 1:10 series, step 1 = 1:10, step 2 = 1:100, step 3 = 1:1000, and so on. Each step multiplies the previous dilution by the dilution factor. This geometric progression is what makes serial dilutions so efficient for spanning large concentration ranges.
References
Reviewed by Daniel Agrici, Founder & Lead Developer · Editorial policy