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What does this calculator estimate?
A serial dilution calculator computes concentrations across a dilution series. Enter the stock concentration, dilution factor, and number of steps to see each resulting concentration.
- Cₙ = C₀ × (1/d)^n
- 1:10 dilution → each step ×0.1
- Used in microbiology and assays
Why serial dilutions are used
Serial dilution produces a range of concentrations that span many orders of magnitude with a small number of steps — standard for microbial counting (plating dilutions), standard curves, and titration series. Each step is prepared from the previous one.
Limitations to watch for
Pipetting error compounds with each step, so later dilutions carry the error of all previous steps. The dilution factor must be > 1. Very dilute steps may fall below detection limits.
How to use it in practice
Choose a dilution factor (10 for most work) and number of steps to cover your range. Prepare each step by mixing 1 part previous solution with (factor − 1) parts diluent. Label carefully — steps are easy to confuse.
['Enter the stock concentration.', 'Enter the dilution factor (>1).', 'Enter the number of steps (1–20); the tool lists each resulting concentration.']
What serial dilution is
Serial dilution dilutes a stock repeatedly by a fixed factor: a 1:10 series reduces concentration ten-fold per step — 100 mM → 10 mM → 1 mM → 0.1 mM. Each step uses the previous solution, multiplying the total factor.
The multiplication rule
Total dilution = factor^steps: ten-fold three times is 1,000×; two-fold five times is 32×. The calculator returns the concentration after each step and the total factor.
Transfer volumes
A 1:10 step transfers 1 part stock plus 9 parts diluent: 1 mL stock + 9 mL buffer = 10 mL. The calculator lets you set the transfer and diluent volumes so the protocol is concrete.
A worked example
Starting at 50 mM with 1:10 steps: step 1 = 5 mM, step 2 = 0.5 mM, step 3 = 0.05 mM. After five steps: 0.0005 mM. The calculator returns each step's concentration.
Precision in practice
Serial dilution errors compound — a 5 percent pipetting error at each step becomes 23 percent after five steps. Using the calculator's volumes and fresh tips per step keeps the series accurate.
How this calculator works
Formula
After n steps of dilution factor d, concentration = C₀ × (1/d)^n. Each step dilutes the previous solution by the same factor — 1:10 dilution means each step is 1 part solution + 9 parts diluent.
Worked example
A 1.0 M stock diluted 1:10 three times: 0.10 M → 0.010 M → 0.0010 M. Each step multiplies by 0.1.
Assumptions to verify
- Each step is a perfect, well-mixed dilution.
- The dilution factor is constant across steps.
- Pipetting is accurate.
Frequently asked questions
What is a serial dilution?
A stepwise dilution where each step is made from the previous one at a constant factor — producing a logarithmic series of concentrations.
How do I calculate concentrations?
Cₙ = C₀ × (1/d)^n. A 1.0 M stock at 1:10 for 3 steps: 0.1, 0.01, 0.001 M.
How do I make a 1:10 dilution?
Mix 1 part solution with 9 parts diluent (water or buffer), then mix thoroughly.
Why is it used in microbiology?
Plating serial dilutions lets you count colony-forming units from plates with countable (30–300) colonies.
Does error accumulate?
Yes — pipetting error compounds with each step, which is why accuracy matters at every transfer.
What dilution factor should I use?
10 is standard; 2, 4, or 5 are common when finer steps are needed. Larger factors cover more range faster.
What is a dilution blank?
A tube of pure diluent used to make the next dilution — the reference for the series.
How do I calculate total dilution?
Factor^steps: ten-fold three times = 1,000× total.
What is a 1:10 dilution?
One part stock plus nine parts diluent — a ten-fold reduction.
Why do errors compound?
Each step multiplies the previous error, so precision matters at every step.
Cite this tool
BoringToolsKit. “Serial Dilution Calculator.” boringtoolskit.com/serial-dilution-calculator/ (reviewed 2026-08-25). Free to reference in articles, syllabi, and answer posts with a link.
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