Free account · save your work, full figure editorSign up free

C1V1 = C2V2 dilution calculator

Q: What does C1V1 = C2V2 mean?

It is the dilution equation, C₁ × V₁ = C₂ × V₂. C₁ and V₁ are the concentration and volume of the stock you take; C₂ and V₂ are the concentration and total volume after dilution. It holds because adding diluent does not change the amount of solute.

Q: How do you rearrange C1V1 = C2V2?

Divide by the term next to the unknown: V₁ = C₂V₂ / C₁ (the volume of stock), C₁ = C₂V₂ / V₁, C₂ = C₁V₁ / V₂ and V₂ = C₁V₁ / C₂. The calculator solves for whichever value you choose.

Q: Which units can I use in C1V1 = C2V2?

Any, as long as C₁ and C₂ are the same kind of unit (both molar, both mass per volume, both percent or both ×-fold) and V₁ and V₂ 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.

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.

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: $\begin{aligned} &C_1 \times V_1 = C_2 \times V_2 \\ &V_1 = C_2 \times V_2 \div C_1 \\ &\text{serial dilution tube } k = C_0 \div f^k \end{aligned}$
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.

Last updated 8 November 2026

FreeNo sign-upRuns in your browserLab calculators

Loading Dilution calculator…

At a glance

Dilution calculator 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
Runs in	Your web browser; nothing is uploaded
Price	Free, no account needed

What it does

How to use the dilution calculator

Choose single or serialUse $C_1V_1 = C_2V_2$ for one dilution, or the serial dilution planner for a series.
Enter the known valuesPick what to solve for and fill in the other three values with their units.
PipetteFollow the instruction: how much stock, how much diluent, or the volumes for each tube of the series.

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).

Frequently asked 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.

Make the whole figure in LabCanvas

Vector figure editor, slides, 3D models, protein structures and Prism-style graphs, in your browser.

Get started