What is the formula for concentration at each step of a serial dilution?

Concentration at step n = Starting concentration × (1 / dilution factor)ⁿ. For a 10-fold serial dilution starting at 1000 µg/mL: Step 1 = 100, Step 2 = 10, Step 3 = 1 µg/mL, etc.

What dilution factor should I use for a serial dilution?

A 1:10 (10-fold) dilution is the most common in microbiology (e.g., for colony counts). A 1:2 (2-fold) dilution is common for dose-response curves and antibody titrations. Choose based on the concentration range you need to cover.

Can I use the serial dilution calculator for cell counting?

Yes. Enter your starting cell count (e.g., in cells/mL), choose your dilution factor, and the calculator generates the concentration at each step. Use this to count colonies on plates and back-calculate to the original sample concentration.

Serial Dilution Calculator (Free Tool)

Calculators › Lab Prep Tools › Serial Dilution

Serial Dilution Calculator

Generate a complete serial dilution table — exact transfer volumes, diluent volumes, and concentration at every step — for any starting concentration and dilution factor. Works for cells/mL, CFU/mL, µg/mL, µM, OD₆₀₀, or any custom unit.

Enter starting concentration (C₀), dilution factor (DF), number of steps, and tube volume.
Instantly get transfer volume (V_s), diluent volume (V_d), and concentration at each step.
Uses the formula Cn = C0 / DF^n — no manual calculation needed.

Common uses: 🦠 Colony counting 📈 qPCR curves 💊 MIC testing 🧫 ELISA assays ✓ Free · No login

What Is Serial Dilution?

A serial dilution is a stepwise process where each tube is diluted from the previous one by a constant dilution factor (DF) — unlike a single-step dilution (C₁V₁ = C₂V₂), which goes from one concentration to another in one step. The result is an exponential decrease in concentration: Cn = C0 / DF^n.

Why Is Serial Dilution Used?

Colony counting: Brings dense bacterial cultures into the countable 30–300 CFU/plate range.
Standard curves: Creates known-concentration series for qPCR, ELISA, and Bradford assays.
Dose–response: 2-fold dilutions vary drug/antibody concentration to find MIC, IC₅₀, or EC₅₀.
Matrix effects: Moves concentrated samples into the linear detection range of an assay.

Common Dilution Factors

1:10 — standard in clinical microbiology for urine/wound culture CFU counts.
1:2 — antibiotic MIC broth microdilution (EUCAST / CLSI guidelines).
1:5 or 1:10 — DNA quantification standard curves in qPCR experiments.

Serial Dilution Diagram

serial dilution stepwise dilution process diagram showing stock solution transferred through sequential tubes with decreasing concentration — Figure 1. A fixed transfer volume (Vs) moves from each tube into fresh diluent (Vd). Concentration decreases by DF at every step — formula: Cn = C0 / DF^n.

Generate Your Dilution Table

Enter your parameters below to instantly generate a complete serial dilution table with exact transfer and diluent volumes for every step.

Lab Prep C₂ = C₁ / DF

Dilution Parameters

Initial Concentration (C₀)

Starting concentration before any dilution. For bacteria, typically 10⁶–10⁹ cells/mL.

Dilution Factor (DF) per step

DF = 10: one part sample in nine parts diluent (1:10). Use 2 for dose–response assays.

Number of Dilution Steps tubes

5–7 steps for plate counts (10⁻⁵–10⁻⁷); 5–8 steps for qPCR standard curves.

Total Volume per Tube

1 mL (1000 µl) is standard for 1:10 dilutions — transfer 100 µl into 900 µl diluent.

Transfer per step

—

Diluent per step

—

Final DF

—

Final concentration

—

Tube Chain Visualisation

Colour depth decreases as concentration drops. Each arrow shows the transfer volume.

Enter values and click Generate Dilution Table to see the tube chain.

Serial Dilution Formulas updates as you type

C₀ Initial concentration (stock) —

DF Dilution factor per step —

V_total Total volume per tube —

V_s Transfer (sample) volume — µl

V_d Diluent volume — µl

n Number of steps —

Concentration After One Step

C₂ = C₁ ÷ DF

? ÷ ? = —

Each step divides concentration by DF. A 1:10 dilution = 10× less concentrated per step.

Concentration After n Steps

C_n = C₀ ÷ DFⁿ

After ? steps: —

Exponential decrease. After 5 steps of 1:10, cumulative dilution = 1:100,000 (10⁻⁵).

Transfer Volume

V_s = V_total ÷ DF

? µl ÷ ? = — µl

Volume pipetted from each tube into the next. Must be ≥ 0.5 µl for accurate delivery.

Diluent Volume

V_d = V_total − V_s

? − ? = — µl

Add diluent to each tube before transferring sample — prevents high-concentration carry-over.

How This Serial Dilution Calculator Works

Enter four parameters — C₀, DF, number of steps, and V_total — and the calculator applies the serial dilution formulas to every tube, producing a complete, error-free table.

Concentration Calculation

Applies Cn = C0 / DF^n at each step. After 5 steps of 1:10, total dilution = 10⁵ (five orders of magnitude).

Transfer & Diluent Volumes

Calculates Vs = Vtotal / DF and Vd = Vtotal − Vs. For 1:10 at 1,000 µL: Vs = 100 µL, Vd = 900 µL.

Complete Dilution Table

Repeats calculations per tube, outputting cumulative dilution ratio, concentration, transfer, and diluent volumes instantly.

Worked Example: 1:10 Serial Dilution (5 Steps)

Starting at 10⁶ cells/mL · DF = 10 · V_total = 1,000 µL · Vs = 100 µL · Vd = 900 µL. Formula: Cn = C0 / DF^n.

Tube 1: 1,000,000 / 10¹ = 100,000 cells/mL (10⁵)
Tube 2: 1,000,000 / 10² = 10,000 cells/mL (10⁴)
Tube 3: 1,000,000 / 10³ = 1,000 cells/mL (10³)
Tube 4: 1,000,000 / 10⁴ = 100 cells/mL (10²)
Tube 5: 1,000,000 / 10⁵ = 10 cells/mL (10¹)

Static Dilution Table — C0 = 10⁶ cells/mL · DF = 10 · Vtotal = 1,000 µL

Tube	Dilution	Concentration (cells/mL)	Transfer Volume (µL)	Diluent Volume (µL)
Stock	1:1 (undiluted)	1,000,000 (10⁶)	—	—
Tube 1	1:10 (10⁻¹)	100,000 (10⁵)	100 µL	900 µL
Tube 2	1:100 (10⁻²)	10,000 (10⁴)	100 µL	900 µL
Tube 3	1:1,000 (10⁻³)	1,000 (10³)	100 µL	900 µL
Tube 4	1:10,000 (10⁻⁴)	100 (10²)	100 µL	900 µL
Tube 5	1:100,000 (10⁻⁵)	10 (10¹)	100 µL	900 µL

Transfer volume (Vs) = 1,000 / 10 = 100 µL. Diluent (Vd) = 900 µL per tube. Use the calculator above to generate this table automatically for any inputs.

Common Applications of Serial Dilution

Each application has typical dilution factors and step counts.

🦠

Bacterial Colony Counting

Dilute to reach 30–300 CFU/plate — the statistically valid range.

1:10 × 5–7 steps

📈

qPCR Standard Curve

Known DNA concentration series for absolute quantification efficiency curves.

1:10 × 5–8 steps

💊

Antibiotic MIC Testing

Two-fold broth dilutions to determine the minimum inhibitory concentration.

1:2 × 8–12 steps

🧫

ELISA Dose–Response

Antigen/antibody series to generate a sigmoid curve and determine EC₅₀.

1:2 or 1:3 × 8–10 steps

🔬

Cell Viability Assays

Reach countable density for Trypan blue or fluorescent viability staining.

1:2–1:10 × 3–5 steps

🧪

Enzyme Activity Assay

Vary substrate concentration to determine enzyme kinetics (Km, Vmax).

1:2–1:5 × 6–10 steps

Step-by-Step Bench Procedure

Work on ice for live cells or thermolabile samples.

1
Label all tubes before starting
Label tubes sequentially (Stock, Tube 1, Tube 2 …) including the expected concentration. Labelling errors are the most common mistake in serial dilution.
2
Add diluent to each tube first
Pipette the diluent volume into all tubes before adding any sample. This prevents high-concentration carry-over.

💧 Add diluent first → 🧬 Then add sample → 🌀 Mix thoroughly → 🔄 Change tip
3
Transfer sequentially
Pipette Vs from the stock into Tube 1. Mix thoroughly (5–10 pipette strokes or 2–3 s vortex). Transfer Vs from Tube 1 into Tube 2, and so on.
4
Change tips between every transfer
Even a trace of concentrated solution on a reused tip will invalidate the dilution. Use a fresh tip for every single step — no exceptions.
5
Mix each tube before transferring
Vortex briefly or pipette 10× before taking an aliquot. For live cells, mix by aspiration — vortexing can damage cells.
6
Verify at a countable dilution
For colony counts, plate the last 3 steps (targeting 30–300 CFU). Back-calculate using: C0 = CFU_counted × DF^step / V_plated

Key Takeaways

📐 Each tube is diluted from the previous one — not from the original stock — by the same constant dilution factor (DF).
🔢 Core formula: Cn = C0 / DF^n — concentration drops exponentially, covering many orders of magnitude with just a few steps.
💧 Transfer volume is always Vs = Vtotal / DF. For 1:10 at 1 mL total, transfer exactly 100 µL tube to tube.
📊 5 steps of 1:10 cover 5 log units (10⁵-fold) — ideal for bacterial colony counting and qPCR standard curves.
✅ This calculator eliminates manual errors: enter C0, DF, steps, and volume once to get the full dilution table instantly.

Common Mistakes in Serial Dilution

🔴

Not Mixing Between Transfers

A non-uniform tube gives a non-representative aliquot — and the error compounds downstream. Always vortex briefly or pipette 10× before every transfer.

🔴

Using the Wrong Dilution Factor

Confusing 1:10 (1 part + 9 parts = 10-fold) with 1+10 (1 + 10 = 11-fold) is very common. Use this calculator to confirm volumes before going to the bench.

🟡

Pipetting Errors at Small Volumes

A 5% error at 10 µL compounds across 5 steps to ~28% deviation. Use 100 µL transfers where possible and forward-pipetting mode with calibrated micropipettes.

🟡

Reusing Pipette Tips

Even 1 µL of concentrated stock on a reused tip can invalidate downstream tubes. Use a fresh tip for every single transfer — no exceptions.

🔵

Diluting from the Wrong Tube

Serial dilution requires each transfer from the immediately preceding tube. Accidentally returning to the original stock collapses the entire series. Label tubes first and work sequentially.

Frequently Asked Questions

Click any question to expand the answer.

What is a serial dilution? ▼

A serial dilution is a stepwise dilution where each tube is diluted from the previous one by the same constant dilution factor (e.g., 1:10 or 1:2). Unlike a single-step dilution (C₁V₁ = C₂V₂), it chains multiple dilution steps together — allowing researchers to span many orders of magnitude from a single concentrated starting sample. Concentration formula: Cn = C0 / DF^n.

How do you calculate serial dilution volumes? ▼

For each step: transfer volume (Vs) = total volume / DF and diluent volume (Vd) = total volume − Vs. For a 1:10 dilution with 1 mL total volume: transfer 100 µL into 900 µL of diluent. Use this serial dilution calculator to generate the full table automatically.

What is the formula for concentration at each step? ▼

Cn = C0 / DF^n — where C0 is the starting concentration, DF is the dilution factor per step, and n is the step number. For a 10-fold serial dilution starting at 1,000 µg/mL: Step 1 = 100, Step 2 = 10, Step 3 = 1 µg/mL, and so on.

What dilution factor should I use? ▼

A 1:10 (10-fold) dilution factor is standard in microbiology (e.g., colony counts). A 1:2 (2-fold) dilution is used for dose–response curves and antibiotic MIC testing. A 1:5 dilution is common for qPCR standard curves. Choose based on the concentration range you need to cover and how many steps you want.

What is the difference between serial dilution and simple dilution? ▼

A simple dilution uses C₁V₁ = C₂V₂ to go from one concentration to another in a single step. A serial dilution chains multiple steps — each using the previous tube as its new stock — to cover a wide concentration range efficiently with smaller individual transfer volumes.

What is a 10-fold serial dilution? ▼

A 10-fold (1:10) serial dilution uses DF = 10 at every step. For 1 mL total volume: transfer 100 µL into 900 µL diluent. After 5 steps, the cumulative dilution is 1:100,000 (10⁻⁵). This is the most common serial dilution in microbiology for bacterial colony counting.

Can I use this calculator for cell counting? ▼

Yes. Enter your starting cell count (e.g., in cells/mL or CFU/mL), choose your dilution factor, and the calculator generates the concentration at each step. Count colonies on plates, then back-calculate to the original concentration using: C0 = CFU counted × DF^step / volume plated.

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