Dilution Calculator

A dilution calculator uses C₁V₁ = C₂V₂: the stock concentration times the stock volume equals the final concentration times the final volume. To make 100 mL of 50 mM solution from a 1 M stock, V₁ = (0.050 M × 100 mL) ÷ 1 M = 5 mL. Add 95 mL of diluent for a 20-fold dilution.

How to use the dilution calculator

1. On the C₁V₁ = C₂V₂ tab, pick the value to solve for (usually V₁, the stock volume) and enter the other three with their units.
2. Mix units freely: M with mM or µM, mg/mL with µg/mL, % w/v, % v/v or X for buffers. To go between molar units and mass units (for example M to g/L), type the molar mass or the formula.
3. Use the Dilution ratio tab for label instructions such as 1:4 or 1:10, and the Serial dilution tab for a series of tubes.

You get the answer, the diluent to add, the dilution factor, the ratio written both ways, a bar showing stock versus diluent, and the steps with units shown.

The dilution formula C₁V₁ = C₂V₂

Diluting adds solvent but no solute, so the amount of solute is the same before and after. Amount = concentration × volume, which gives C₁V₁ = C₂V₂, where

• C₁ = concentration of the stock solution
• V₁ = volume of stock you take
• C₂ = concentration you want
• V₂ = final total volume (stock plus diluent)

Rearranged: V₁ = C₂V₂ / C₁, C₁ = C₂V₂ / V₁, C₂ = C₁V₁ / V₂ and V₂ = C₁V₁ / C₂. The two concentrations must be in the same unit, and so must the two volumes; the calculator converts them for you. With molar units the same equation is often written M₁V₁ = M₂V₂.

Dilution factor and dilution ratio

The dilution factor is DF = V₂ / V₁ = C₁ / C₂. Taking 5 mL of stock to 100 mL is a 20-fold dilution, and the concentration falls to 1/20 of the stock.

Ratios are written two ways, and mixing them up is the most common dilution error:

• Stock : diluent. 1:4 means 1 part concentrate plus 4 parts water, 5 parts in total, so DF = 5. Cleaning products and garden concentrates usually mean this.
• Stock : total. A “1:10 dilution” in many lab protocols means 1 part stock in 10 parts of final solution (1 + 9), so DF = 10.

Worked examples

Molar stock to millimolar working solution

Stock 1 M, target 50 mM, final volume 100 mL. First match units: 50 mM = 0.050 M. V₁ = (0.050 M × 100 mL) ÷ 1 M = 5.0 mL. Diluent = 100 − 5 = 95 mL. DF = 100 / 5 = 20.

10X buffer to 1X

To make 500 mL of 1X buffer from a 10X concentrate: V₁ = (1X × 500 mL) ÷ 10X = 50 mL of concentrate plus 450 mL of water.

mg/mL to µg/mL

A 1 mg/mL standard must become 5 mL at 20 µg/mL. Convert: 20 µg/mL = 0.020 mg/mL. V₁ = (0.020 × 5 mL) ÷ 1 = 0.1 mL = 100 µL, plus 4.9 mL of diluent.

Molar stock to a g/L target

You want 500 mL at 5 g/L NaCl from a 2 M stock. With molar mass 58.44 g/mol, 5 g/L ÷ 58.44 g/mol = 0.08556 M. V₁ = (0.08556 M × 500 mL) ÷ 2 M = 21.39 mL. In the calculator, pick g/L for C₂ and type NaCl in the molar mass box.

A label ratio

A concentrate says “dilute 1:4” and your spray bottle holds 32 fl oz. Total parts = 1 + 4 = 5, so one part is 32 ÷ 5 = 6.4 fl oz: 6.4 fl oz of concentrate and 25.6 fl oz of water.

Serial dilutions

A serial dilution repeats the same dilution several times, which is more accurate than one huge step. For a 10-fold series in 1 mL tubes, put 900 µL of diluent in each tube, move 100 µL of stock into tube 1, mix, then move 100 µL from tube 1 into tube 2, and so on. After n steps the concentration is C₀ / Fⁿ: starting from 1 mg/mL, tube 3 holds 1 µg/mL and tube 6 holds 1 ng/mL. The transfer volume is V / F and the diluent is V − V / F.

Common dilution mistakes

• Using V₂ as the diluent volume. V₂ is the final total. Add V₂ − V₁ of diluent, or better, fill up to the V₂ mark.
• Mismatched units. 50 mM with a 1 M stock is a 20-fold dilution, not 50-fold. Convert before you divide.
• Reading 1:10 the wrong way. Check whether the source means stock : diluent or stock : total; the stock volumes differ by about 10%.
• Pipetting tiny volumes. If V₁ is below about 1% of V₂, use two steps instead of one.
• Expecting volumes to add exactly. Mixing ethanol and water, or concentrated acid and water, gives slightly less volume than the sum. C₁V₁ = C₂V₂ is exact for the amount of solute, so fill to the final mark. Always add concentrated acid to water, not water to acid.

Need the stock concentration itself, or the grams to weigh for it? The molarity calculator works out molarity from a mass, finds the molar mass from a formula, and converts a % w/w label to molarity. Every number on this page was re-checked with a script.

Dilution practice quiz: 10 questions

Test yourself with 10 multiple-choice questions. Choose an answer and press Submit to see if you are right and why. Your score appears at the end.

Frequently asked questions

How do you calculate a dilution?

Use C₁V₁ = C₂V₂. Multiply the concentration you want by the final volume, then divide by the stock concentration to get the stock volume. Make it up to the final volume with solvent.

What does a 1:10 dilution mean?

In most lab settings it means 1 part stock in 10 parts total (1 mL stock + 9 mL diluent), a dilution factor of 10. On many product labels, 1:10 means 1 part concentrate to 10 parts water, which is 11 parts total.

How do I calculate the dilution factor?

Divide the final volume by the stock volume, or the stock concentration by the final concentration. 2 mL made up to 50 mL is a dilution factor of 25.

How much water do I add to dilute a solution?

Find V₁ with C₁V₁ = C₂V₂, then the water is V₂ − V₁. To halve the concentration of 200 mL you add 200 mL of water, making 400 mL.

Does C₁V₁ = C₂V₂ work with mg/mL and percent?

Yes, as long as both concentrations are in the same unit. It works for M, mg/mL, % w/v, % v/v and X. To go between molar and mass units you need the molar mass.

Related calculators

• Molarity calculator: make the stock, with molar mass from a formula
• Density calculator: mass, volume and density with units
• Ratio and proportion calculator: scale any ratio
• Scientific notation converter: very small serial-dilution concentrations
• Unit converter: liters, milliliters and fluid ounces