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Serial Dilution Final Concentration (C_f = C₀ × ∏ Vᵢ/(Vᵢ+V_d))

· Last updated：2026-08-19

This tool is for informational purposes only and does not constitute medical, financial, or legal advice; consult a qualified professional for advice.

Compute the final concentration after multi-step serial dilutions, with per-step folds, cumulative folds, and total dilution factor.

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Written by the Elysia Tools team

Tool usage guide

Learn when to use this tool, what it supports, and how real users apply it.

Key facts

Category
Health
Input types
number, select, textarea
Output type
json
Sample coverage
4
API ready
Yes

Overview

Enter a starting concentration and each aliquot-to-diluent ratio to compute the final concentration after a serial dilution. The calculator returns every step fold, the cumulative dilution factor, and the concentration after each transfer in the unit you selected.

When to use

  • When you need the exact final concentration after several sequential transfers
  • When designing a multi-step dilution scheme with mixed or repeated folds
  • When converting a stock into a working concentration for assays or cell counts

How it works

  1. 1Enter the initial concentration C₀ and choose its unit (M, mg/mL, cells/mL, and others).
  2. 2List each step on its own line as aliquot volume : diluent volume (any consistent units; 1 : 9 is a 10-fold step).
  3. 3Optionally set how many decimal places to show.
  4. 4The tool multiplies C₀ by the product of each Vᵢ/(Vᵢ+V_d), then reports per-step folds, cumulative folds, total dilution factor, and final concentration.

Use cases

  • Prepare a 1000-fold series from a 5 mg/mL stock to a 5 µg/mL working solution
  • Dilute a cell suspension from 2×10⁶ cells/mL through 1:1 then 1:4 transfers
  • Build successive 10-fold steps for a log-scale standard curve

Examples

1. Three 1:9 steps from 5 mg/mL

Lab technician

Background

A 5 mg/mL stock must be diluted 1000-fold to a 5 µg/mL working solution using three identical transfers.

Problem

Confirm the concentration after each 10-fold step and the final value.

How to use

Set initial concentration to 5, unit to mg/mL, and enter three lines of 1 : 9.

initialConcentration: 5
concentrationUnit: mg/mL
dilutionSteps:
1 : 9
1 : 9
1 : 9
decimalPlaces: 6

Outcome

After 3 steps the total dilution is 1000× and the final concentration is 0.005 mg/mL (5 × 10⁻³).

2. Cell suspension 1:1 then 1:4

Cell-culture scientist

Background

A suspension at 2,000,000 cells/mL needs a 10-fold overall dilution before plating.

Problem

Calculate the count after a 2-fold step followed by a 5-fold step.

How to use

Enter 2000000 cells/mL and the two lines 1 : 1 and 1 : 4.

FAQ

What format do the dilution steps use?

One step per line as aliquot : diluent. Volumes may use any consistent unit. 1 : 9 equals a 10-fold dilution.

How is each step fold calculated?

Step fold equals (aliquot + diluent) divided by aliquot. A 1 : 9 line therefore has a fold of 10.

Does the tool convert between concentration units?

No. The selected unit is for display only. The numeric value of C₀ is scaled by the volume ratios you enter.

Can I mix different ratios in one series?

Yes. Enter any combination of ratios, one per line, such as 1 : 1 followed by 1 : 4.

What does the result contain?

A summary of total fold and final concentration, plus each step’s aliquot, diluent, step fold, cumulative fold, and concentration.

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initialConcentration: 2000000 concentrationUnit: cells/mL dilutionSteps: 1 : 1 1 : 4 decimalPlaces: 6

Outcome

After 2 steps the total dilution is 10× and the final concentration is 200000 cells/mL (2 × 10⁵).