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

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

> Canonical page: https://elysiatools.com/en/tools/dilution-factor-final

- **Category:** Health

- **Keywords:** serial dilution, dilution factor, final concentration, c1v1 c2v2, multi-step dilution, dilution scheme, concentration calculator, aliquot, diluent, log dilution, lab calculator, titration

## 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.

## Inputs

- **Initial concentration (C₀)** (number): Concentration of the starting solution before any dilution step.
- **Concentration unit** (select)
- **Dilution steps (aliquot : diluent)** (textarea): Each line: aliquot volume : diluent volume (any consistent unit). 1 : 9 = ten-fold.
- **Decimal places** (number)

## 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

- Enter the initial concentration C₀ and choose its unit (M, mg/mL, cells/mL, and others).
- List each step on its own line as aliquot volume : diluent volume (any consistent units; 1 : 9 is a 10-fold step).
- Optionally set how many decimal places to show.
- The 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

## Frequently asked questions

### 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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