# C1V1 = C2V2 dilution calculator

> C1V1 = C2V2 with a worked example: V1 = C2 × V2 / C1. Solve for any of the four values with unit conversion, or plan a serial dilution tube by tube. Free.

URL: https://www.labcanvas.com/tools/dilution-calculator

C1V1 = C2V2 is the dilution formula: stock concentration × stock volume = final concentration × final volume. To find how much stock to use, V1 = C2 × V2 / C1, then add diluent up to V2. Example: for 1 mL of 1 mM from a 10 mM stock, V1 = 1 mM × 1 mL / 10 mM = 0.1 mL, so 100 µL of stock plus 900 µL of diluent. Enter any three values to get the fourth, with molar, mass, percent or ×-fold units, or plan a serial dilution tube by tube.

## Quick answer

- **What it does:** Solves C₁V₁ = C₂V₂ for whichever of the four values is missing, with molar, mass, % and ×-fold units, and plans serial dilutions tube by tube.
- **Formula:** C₁ × V₁ = C₂ × V₂, so V₁ = C₂ × V₂ ÷ C₁; serial dilution tube k = C₀ ÷ fᵏ.
- **Example:** To make 1 mL of 1 mM from a 10 mM stock: V₁ = 1 mM × 1 mL ÷ 10 mM = 0.1 mL, so 100 µL of stock plus 900 µL of diluent.

Free, in the browser, no account needed. Updated 2026-11-08.

## Features

- Solve for \(C_1\), \(V_1\), \(C_2\) or \(V_2\)
- Molar, mass/volume, % and × units
- Diluent volume and dilution factor
- Serial dilution table with CSV export

## How to use it

1. **Choose single or serial**: Use \(C_1V_1 = C_2V_2\) for one dilution, or the serial dilution planner for a series.
2. **Enter the known values**: Pick what to solve for and fill in the other three values with their units.
3. **Pipette**: Follow the instruction: how much stock, how much diluent, or the volumes for each tube of the series.

## At a glance

| | |
| --- | --- |
| Formula | \(C_1 \times V_1 = C_2 \times V_2\) |
| Solves for | \(C_1\), \(V_1\), \(C_2\) or \(V_2\), with the diluent volume and dilution factor |
| Units | Molar, mass/volume, % and × |
| Serial dilutions | Table of tubes, tube \(k\) at \(C_0 / f^k\); CSV export |

## How it works

$$C_1 \times V_1 = C_2 \times V_2$$

The amount of solute is the same before and after dilution. Concentrations must be in the same kind of unit (molar with molar, mass/volume with mass/volume). For a serial dilution with factor \(f\) and final volume \(V\) per tube, each tube holds \(V\) of diluent and receives \(V/(f - 1)\) from the previous tube; tube \(k\) has concentration \(C_0 / f^k\).

## Worked example

To make 1 mL of 1 mM from a 10 mM stock: \(V_1 = 1\ \mathrm{mM} \times 1\ \mathrm{mL} / 10\ \mathrm{mM} = \mathbf{100\ \upmu L}\) of stock plus 900 µL of diluent (a 1:10 dilution). Check: \(C_1V_1 = 10\ \mathrm{mM} \times 0.1\ \mathrm{mL}\) \(= 1\ \mathrm{mM} \times 1\ \mathrm{mL} = C_2V_2\).

Percentages work the same way: for 50 mL of 70 % ethanol from 95 % ethanol, \(V_1 = 70\,\% \times 50\ \mathrm{mL} / 95\,\% = \mathbf{36.8\ mL}\), made up to 50 mL with water.

### Antibody dilutions (1:500, 1:1000, 1:5000)

A datasheet ratio such as 1:1000 means 1 part antibody in 1000 parts of final solution, a dilution factor of 1000. Set \(C_1\) to 1000 × and \(C_2\) to 1 ×, or simply divide: \(V_1 = V_2 / \text{dilution factor}\).

- **Western blot, 1:1000 in 10 mL** of blocking buffer: \(10\ \mathrm{mL} / 1000 = \mathbf{10\ \upmu L}\) of antibody in 9.99 mL of buffer.
- **Secondary antibody, 1:5000 in 15 mL**: \(15\ \mathrm{mL} / 5000 = \mathbf{3\ \upmu L}\) in 14.997 mL. Volumes under about 2 µL are hard to pipette accurately; make a 1:100 intermediate dilution first, then dilute that 1:50.
- **From a concentration instead of a ratio**: for 2 µg/mL in 5 mL from a 1 mg/mL stock, \(V_1 = 2\ \upmu\mathrm{g/mL} \times 5\ \mathrm{mL} / 1000\ \upmu\mathrm{g/mL}\) \(= \mathbf{10\ \upmu L}\) (a 1:500 dilution).

## Questions

### How do I calculate an antibody dilution such as 1:1000?

Divide the final volume by the dilution factor: for 1:1000 in 10 mL, \(10\ \mathrm{mL} / 1000 = 10\ \upmu\mathrm{L}\) of antibody plus 9.99 mL of buffer. In the calculator, enter \(C_1 = 1000\times\), \(C_2 = 1\times\) and \(V_2 = 10\ \mathrm{mL}\). If the datasheet gives a concentration (for example 1 µg/mL) instead, use the stock concentration as \(C_1\).

### What does C1V1 = C2V2 mean?

It is the dilution equation, \(C_1 \times V_1 = C_2 \times V_2\). \(C_1\) and \(V_1\) are the concentration and volume of the stock you take; \(C_2\) and \(V_2\) are the concentration and total volume after dilution. It holds because adding diluent does not change the amount of solute.

### How do you rearrange C1V1 = C2V2?

Divide by the term next to the unknown: \(V_1 = C_2V_2 / C_1\) (the volume of stock), \(C_1 = C_2V_2 / V_1\), \(C_2 = C_1V_1 / V_2\) and \(V_2 = C_1V_1 / C_2\). The calculator solves for whichever value you choose.

### Which units can I use in C1V1 = C2V2?

Any, as long as \(C_1\) and \(C_2\) are the same kind of unit (both molar, both mass per volume, both percent or both ×-fold) and \(V_1\) and \(V_2\) are both volumes. The calculator converts within a kind, for example mM to µM or mg/mL to µg/mL, and warns if you mix kinds.

### Is a 1:10 dilution 1 part in 10 or 1 part plus 10?

In most lab usage 1:10 means 1 part sample in 10 parts total (1 + 9 diluent). Some fields use 1:10 for 1 part plus 10; check your protocol.

### Can I convert between mM and mg/mL?

Only with the molar mass. Use the molarity calculator to convert, then dilute in one kind of unit.

### How do I make a 2-fold serial dilution?

Choose serial dilution, factor 2: each tube gets the final volume of diluent and the same volume transferred from the previous tube, mixing at every step.