Serial Dilution Calculator

Calculate concentrations in a serial dilution series. Each tube dilutes by the same dilution factor. Find concentration at any step, or determine steps needed to reach a target.

💧 Solutions📐 Cn = C0 × (V1/V2)^n🧪 Chemistry
Initial concentration C0
Dilution factor per step
Volume transferred V1 (mL)
Total volume V2 (mL)
Number of steps n
Please enter valid values.

Formula & Reference

VariableSymbolFormulaUnits
Serial Dilution Calculator—Cn = C0 × (V1/V2)^nmol/L

Step-by-Step Examples

Example 1
10x Serial Dilution

C0=1.00 M, dilution factor=10 per step. Find C at step 5.

  • C_n = C0 / 10^n = 1.00/10^5
  • C_5 = 1.00x10^-5 M
✓ C at step 5 = 1.00x10^-5 M
Example 2
5-fold Dilution

Transfer 1 mL into 4 mL (total 5 mL) each step. C0=100 mg/mL. C after 3 steps?

  • V2/V1 = 5/1 = 5x dilution per step
  • C_3 = 100/5^3 = 100/125 = 0.80 mg/mL
✓ C at step 3 = 0.80 mg/mL
Example 3
2-fold Series

ELISA: 2-fold serial dilution from 1/100 starting. C0=1/100. After 8 steps?

  • C = (1/100) x (1/2)^8 = 1/100 x 1/256 = 1/25600
  • = 3.9x10^-5 of original
✓ 1/25600 dilution after 8 steps of 1:2

Real-World Applications

🧬
ELISA Assay
Standard curves in ELISA made by serial 2-fold dilution of antibody or antigen.
🧪
Microbiology
Serial dilutions for bacterial counting: plate diluted samples to get countable colonies.
💊
Drug Testing
Serial dilution to find minimum inhibitory concentration (MIC) of antibiotics.
🧴
Titration
Serial dilutions prepare a range of concentrations for dose-response studies.

Common Mistakes to Avoid

⚠️
Factor is V_total/V_transferred, not V_total/V_solvent

Dilution factor = total volume / volume transferred. Transfer 1 mL into 9 mL: total 10 mL, factor=10 (not 9).

⚠️
Final concentration accumulates multiplicatively

After n steps: C_n = C0 / factor^n. After 5 steps of 10x: C = C0/100000.

⚠️
Pipetting errors accumulate

Each transfer has pipetting error. After 10 steps, errors multiply. Use dilution factors between 2 and 100 for manageable errors.

Frequently Asked Questions

What is a serial dilution? ▾
A sequence of dilutions where each step uses the same dilution factor, starting from the previous tube. Common in biology, microbiology, and analytical chemistry.
What is the difference between 1:10 and 10-fold dilution? ▾
Same thing. 1:10 means 1 part sample + 9 parts diluent = 10 total. Concentration becomes 1/10 of previous.
How many dilutions for a 10^-6 dilution? ▾
Six 10x dilutions (10^-6). Or ten 2x dilutions (2^10 = 1024 ~ 10^3; need 20 for 10^6). Or four 10x dilutions if you use 2 mL to 18 mL (10x, 4 steps = 10^-4 not 10^-6).
What is the sensitivity of serial dilution? ▾
Limited by pipetting precision (~1-2%) and contamination. For cell counting, colonies of 30-300 are most accurate.
How is serial dilution used for MIC testing? ▾
Prepare 2-fold serial dilutions of antibiotic (e.g., 1, 0.5, 0.25 ug/mL). Inoculate with bacteria. Lowest concentration inhibiting growth = MIC.

Related Chemistry Calculators

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Formula Explorer connections

Interpretation: This formula connects solute amount and solution volume, mass or particle count to concentration and colligative behavior. Assumption: Distinguish solution volume from solvent volume, use the stated temperature, and account for dissociation or nonideal activity when required.

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