What is the dilution equation?

The dilution equation is C1 × V1 = C2 × V2, where C1 and V1 are the stock (concentrated) solution's concentration and volume, and C2 and V2 are the final (diluted) solution's concentration and volume. It holds because diluting adds only solvent, so the amount of solute is conserved.

How do I work out the stock volume I need?

Rearrange to V1 = (C2 × V2) ÷ C1. For example, to make 100 mL of 2 M solution from a 10 M stock, V1 = (2 × 100) ÷ 10 = 20 mL of stock, then top up to 100 mL with solvent.

Can I mix different units like mM and µM, or mg/mL and g/L?

Yes, within the same family. The calculator converts every value to a common base (mol/L for molar units, g/L for mass units) before solving, so you can enter C1 in M and C2 in mM. It will not mix molar and mass units together, because converting between them needs a molar mass.

How much solvent do I add?

Solvent to add equals the final volume minus the stock volume, V2 − V1. The tool shows this automatically whenever both volumes are known or solved, in your chosen final-volume unit.

What is a dilution factor?

The dilution factor is the ratio of final volume to stock volume, V2 ÷ V1, which equals C1 ÷ C2 for a valid dilution. A factor of 10 (a 1:10 dilution) means one part stock plus nine parts solvent, reducing the concentration tenfold.

Does the % unit mean weight/volume?

Yes. The % option is percent weight/volume (w/v), defined as grams of solute per 100 mL of solution, so 1 percent w/v equals 10 g/L. It sits in the mass family alongside g/L, mg/mL, mg/L (ppm) and µg/mL.

Can I use this for serial dilutions?

Yes. Apply the equation one step at a time: each diluted solution becomes the stock for the next step. Chaining several modest dilution factors (for example three 1:10 steps for a 1:1000 result) is more accurate than one huge step because pipetting tiny volumes carries more error.

Dilution Calculator (C1V1 = C2V2)

A precise dilution calculator built on the relationship C1 × V1 = C2 × V2. Give it any three of the four quantities and it solves for the fourth, handling real laboratory units on each side — molar units (M, mM, µM, nM) and mass-based units (g/L, mg/mL, mg/L as ppm, µg/mL and % w/v) — and showing the full working. It is for anyone preparing solutions: bench chemists, biologists making buffers and media, students, pharmacists and water-treatment technicians.

How it works

When you dilute a concentrated stock, you add only solvent, so the amount of solute does not change. Amount equals concentration multiplied by volume, and because that product is identical before and after, you get the dilution equation:

C1 · V1 = C2 · V2

Here C1 and V1 are the stock concentration and volume, and C2 and V2 are the final, diluted concentration and volume. The tool rearranges the equation to isolate whichever variable you choose to solve for:

Solve for	Rearranged formula
Stock concentration C1	C1 = (C2 · V2) ÷ V1
Stock volume V1	V1 = (C2 · V2) ÷ C1
Final concentration C2	C2 = (C1 · V1) ÷ V2
Final volume V2	V2 = (C1 · V1) ÷ C2

Before the algebra runs, every input is converted to a common base — concentration to mol/L (molar family) or g/L (mass family), and volume to litres — then the answer is converted back to the unit you picked for the unknown. This lets you mix, say, a stock entered in M with a target written in mM without doing any conversions by hand. The calculator also reports the dilution factor (V2 ÷ V1, equal to C1 ÷ C2) and the solvent to add (V2 − V1), and an expandable panel reveals the exact substitution it used.

Worked example

Suppose you need 100 mL of a 2 M working solution from a 10 M stock. Choose to solve for V1:

V1 = (C2 · V2) ÷ C1 = (2 M × 100 mL) ÷ 10 M = 20 mL of stock

So measure 20 mL of the 10 M stock and add 100 − 20 = 80 mL of solvent to reach 100 mL total. The dilution factor is 100 ÷ 20 = 5×, which matches C1 ÷ C2 = 10 ÷ 2 = 5, confirming the result. To instead express the answer in microlitres, just switch the answer unit and read 20,000 µL.

Formula note

The equation assumes ideal mixing, where volumes are additive and the solute amount is exactly conserved — an excellent approximation for the dilute aqueous solutions used in most lab work. For very concentrated stocks (for example strong acids), real volumes can contract slightly on mixing, so prepare to a final volume in a volumetric flask rather than relying on adding a calculated solvent volume. The % unit here is weight/volume (g per 100 mL); for weight/weight or volume/volume percentages, convert to a common unit first. Everything is computed locally in your browser — no values are uploaded or stored.