Dilution Calculator [C1V1, Ratio, Serial & mg/mL]

This dilution calculator uses C₁V₁ = C₂V₂ to tell you how much stock to measure and how much diluent to add. It works with molarity (M, mM, µM, nM, pM), mass concentration (mg/mL, µg/mL, ng/mL, g/L), percent solutions (w/v, v/v and w/w), 10X-style stocks and cells/mL. Three more modes cover dilution ratios such as 1:10 under both common readings, serial dilutions with a tube-by-tube plan and chart, and a molarity calculator that finds the milligrams to weigh from a molar mass.

The dilution formula: C₁V₁ = C₂V₂ (M₁V₁ = M₂V₂)

When you dilute, you add solvent but no solute, so the amount of solute before and after is the same. OpenStax Chemistry writes this as C₁V₁ = C₂V₂, where C₁ and V₁ are the stock concentration and the volume you take, and C₂ and V₂ are the new concentration and the final total volume. With molarity it is often written M₁V₁ = M₂V₂. Weber State University's dilution notes show why it works: mol/L × L on each side is just moles, and moles do not change.

Stock volume: V₁ = C₂ × V₂ ÷ C₁
Final concentration: C₂ = C₁ × V₁ ÷ V₂
Diluent to add: about V₂ − V₁ (exact only when volumes add)
Dilution factor: V₂ ÷ V₁, which also equals C₁ ÷ C₂

OpenStax's worked example dilutes 0.850 L of 5.00 M copper nitrate to 1.80 L: C₂ = 5.00 × 0.850 ÷ 1.80 = 2.36 M. Weber's example prepares 500 mL of 0.10 N nitric acid from 12 N stock: V₁ = 0.10 × 500 ÷ 12 = 4.2 mL, mixed with enough water to make 500 mL. Both work with any concentration unit, provided the two C values use the same unit. The calculator converts M to mM, mg/mL to µg/mL and so on for you, and it will convert between molar and mass units if you give it the molar mass.

How to use the C₁V₁ mode

Enter the stock concentration and pick its unit.
Enter the target concentration. It can be in a different unit of the same kind, such as 1 M stock and 100 mM target.
Enter the final volume you want to end up with, not the volume of water to add.
Read the stock volume to measure. Add diluent until the total reaches the final volume.
Switch "Solve for" to find the concentration that results from a known stock volume.

The results also express the same dilution as a factor and as both kinds of ratio, which makes it easy to match what a protocol says.

Dilution ratio calculator: what 1:10 really means

Ratios cause more dilution errors than arithmetic does, because two readings are in common use:

Stock : total ("1 in 10"). 1 part stock in 10 parts of final solution, so 1 mL plus 9 mL. The number after the colon is the dilution factor. The FDA's Bacteriological Analytical Manual uses this sense: it makes decimal (tenfold) dilutions by transferring 10 mL into 90 mL of diluent and treats a "dilution ratio of 1:100" as one-hundredth, so 1 mL of that dilution carries 0.01 mL of the original sample.
Stock : diluent ("1 plus 10"). 1 part stock plus 10 parts diluent, 11 parts in all. Weber's notes use this reading for "diluted 1:2" (one volume of sample plus two of solvent), and describe 10 mL of soda plus 40 mL of water as diluted 1:4, which is also a 5x dilution.

The difference is small at 1:100 but large at 1:2, where one reading halves the concentration and the other cuts it to a third. When a protocol does not say, look for clues: a volumetric flask filled "to the mark" means stock : total; "add 4 volumes of water" means stock : diluent. In the ratio mode, choose the reading, enter the final volume, and the calculator gives both parts and the true dilution factor.

Stock needed per 100 mL and per 1 L under each ratio reading
Ratio	1 in N: stock per 100 mL	1 + N: stock per 100 mL	1 in N: per 1 L	1 + N: per 1 L
1:2	50 mL	33.33 mL	500 mL	333.3 mL
1:3	33.33 mL	25 mL	333.3 mL	250 mL
1:4	25 mL	20 mL	250 mL	200 mL
1:5	20 mL	16.67 mL	200 mL	166.7 mL
1:8	12.5 mL	11.11 mL	125 mL	111.1 mL
1:10	10 mL	9.09 mL	100 mL	90.9 mL
1:20	5 mL	4.76 mL	50 mL	47.6 mL
1:50	2 mL	1.96 mL	20 mL	19.6 mL
1:100	1 mL	0.99 mL	10 mL	9.9 mL

Percent dilutions: w/v, v/v and w/w

"Percent" alone is ambiguous. The IUPAC Green Book warns that % is often used as a unit of concentration without saying which fraction is meant, and that it should only be used where the quantity is clearly defined. OpenStax defines the three common kinds:

% w/v (mass-volume): grams of solute per 100 mL of solution. Physiological saline is 0.9% w/v, 0.9 g per 100 mL. So 1% w/v = 10 mg/mL = 10 g/L, and the calculator treats w/v as a mass concentration that can mix with mg/mL.
% v/v (volume): volume of solute per volume of solution, as in 70% v/v rubbing alcohol. Liquids can shrink or swell when mixed, so measure the stock and then make up to the final volume, rather than adding a calculated volume of water.
% w/w (mass): mass of solute per mass of solution. Dilute by weight: when both units are % w/w, the calculator switches the volume fields to grams, so you weigh the stock and bring the total to the final mass.

Example: to make 500 mL of 10% v/v from 70% v/v stock, V₁ = 10 × 500 ÷ 70 = 71.43 mL. The arithmetic difference is 428.57 mL, but because the volumes may not add exactly, fill to the 500 mL mark instead of measuring that amount. You can't convert % v/v to mg/mL or molarity without the liquid's density, so the calculator refuses to mix them.

Dilution in mg/mL and µg/mL

Mass concentrations follow the same formula. The prefixes are the SI ones NIST lists, so 1 mg/mL = 1,000 µg/mL = 1 g/L, and 1 µg/mL = 1 mg/L. Suppose an antibody or drug stock is 10 mg/mL and you need 10 mL at 50 µg/mL. Convert first: 50 µg/mL = 0.05 mg/mL. Then V₁ = 0.05 × 10 ÷ 10 = 0.05 mL, or 50 µL, plus 9.95 mL of buffer. That is a 200-fold dilution. Very small stock volumes are hard to pipette accurately, so for dilutions above a few hundred-fold consider making an intermediate dilution first (see serial dilution below).

Molarity dilution and mass-to-molarity

Molar dilutions are the classic case: 100 mL of 0.1 M from 1 M stock needs 0.1 × 100 ÷ 1 = 10 mL of stock. You can also mix units: a stock labeled 5 mg/mL and a target of 100 µM need the molar mass to connect them, because molarity = (g/L) ÷ (g/mol). Enter the molar mass and the calculator does the conversion inside the C₁V₁ step.

If you are starting from a powder, the molarity mode works like the molarity calculators from reagent suppliers: mass (g) = concentration (mol/L) × volume (L) × molar mass (g/mol). For 500 mL of 10 mM sodium chloride, with PubChem's molar mass of 58.44 g/mol, weigh 0.010 × 0.5 × 58.44 = 0.2922 g, or about 292 mg. Reverse it to find the molarity of a weighed sample. Use the molar mass of the exact form you have, including any water of hydration. For converting units without preparing anything, use the molarity unit converter, which also handles normality.

Cell dilution calculator

For cell culture, the concentration is a count per volume. After counting, set the unit to cells/mL. Example: your suspension is 2 × 10⁶ cells/mL and you want 10 mL at 2 × 10⁵ cells/mL. V₁ = 2 × 10⁵ × 10 ÷ (2 × 10⁶) = 1 mL of suspension, topped up with 9 mL of medium. Enter large counts as plain numbers (2000000), since the inputs do not accept the × symbol. Mix the suspension well before drawing V₁, because cells settle and a settled sample makes the count meaningless.

Serial dilution calculator

A serial dilution repeats the same step so that each tube is a fixed factor weaker than the one before. Weber's notes give the key rule: the total dilution is the product of the steps. Ten mL diluted to 100 mL (10x) and then 5 mL of that diluted to 100 mL (20x) is 10 × 20 = 200x overall. In microbiology, tubes with 9 mL of buffer each receive 1 mL from the previous tube; each transfer is a tenfold step, and a colony count from the sixth tube is multiplied by 10⁶ to get back to the original sample.

In the serial mode, enter the starting concentration, the step factor, how many tubes you want and the final volume in each tube. The calculator gives the transfer volume (tube volume ÷ factor), the diluent to pre-fill (the rest), each tube's concentration and total factor, and a bar chart of the fall-off. The table below shows a tenfold series from 1 mg/mL with 10 mL per tube.

Example tenfold serial dilution, 10 mL per tube
Tube	Transfer in	Diluent	Total factor	Concentration
1	1 mL	9 mL	1:10	100 µg/mL
2	1 mL	9 mL	1:100	10 µg/mL
3	1 mL	9 mL	1:1,000	1 µg/mL
4	1 mL	9 mL	1:10,000	100 ng/mL
5	1 mL	9 mL	1:100,000	10 ng/mL
6	1 mL	9 mL	1:1,000,000	1 ng/mL

Diluting 10X and other fold stocks

Buffers are often sold as 10X or 5X concentrates, meaning ten or five times the working strength. Pick "× stock" as the unit on both sides. For 1 L of 1X from 10X, V₁ = 1 × 1000 ÷ 10 = 100 mL of concentrate, made up to 1 L. For 1X from 5X, it is 200 mL per liter. The same logic works for any unit that scales linearly with the amount of solute, including enzyme units per mL.

Common mistakes

Adding V₂ of water instead of filling to V₂. V₂ is the final total. Adding 100 mL of water to 10 mL of stock gives 110 mL and the wrong concentration.
Mixing unit types. 1 M on one side and mg/mL on the other needs a molar mass; % v/v and mg/mL cannot be mixed at all without density.
Misreading the ratio. 1:4 can mean 4x or 5x. Confirm the convention before you pipette.
Pipetting tiny volumes. A 1:1000 dilution in one step means 1 µL per mL; three 1:10 steps are more accurate.
Diluting % w/w by volume. Weigh both parts when the stock is labeled by mass.

Related tools: the M, mM, µM and nM converter, the cylinder volume calculator for tanks and tubes, and Celsius to Fahrenheit for incubation and storage temperatures. Follow the safety data sheet and your lab's procedure when diluting concentrated acids and bases.

Frequently asked questions

What is the dilution formula C1V1 = C2V2?

C₁V₁ = C₂V₂ says the amount of solute in the stock you measure equals the amount in the final solution, because adding solvent adds no solute. Solve for the stock volume with V₁ = C₂V₂ ÷ C₁, or for the new concentration with C₂ = C₁V₁ ÷ V₂.

Is M1V1 = M2V2 the same as C1V1 = C2V2?

Yes. M₁V₁ = M₂V₂ is the same equation written with molarity (M). C stands for any concentration unit, as long as both sides use the same one: M, mg/mL, % w/v or cells/mL.

What does a 1:10 dilution mean?

In methods such as the FDA's plate-count procedure, 1:10 means 1 part stock in 10 parts total: 1 mL of stock plus 9 mL of diluent, a tenfold dilution. Other instructions, such as the sample-to-solvent convention in Weber State's lab notes, read 1:10 as 1 part stock plus 10 parts diluent, which is 11 parts total and an 11-fold dilution. Check which one your instructions mean; the ratio mode handles both.

How do I make a 1:10 dilution of 100 mL?

As 1 in 10 total: 10 mL stock and 90 mL diluent. As 1 part stock to 10 parts water: 9.09 mL stock and 90.91 mL water.

How do I dilute a percent solution?

Use C₁V₁ = C₂V₂ with percent on both sides. To make 500 mL of 10% from 70% v/v: 10 × 500 ÷ 70 = 71.43 mL of stock, then fill to 500 mL. Keep w/v, v/v and w/w separate; they are different quantities.

How do I use a dilution calculator in mg/mL?

Enter both concentrations in mass units. To make 10 mL of 50 µg/mL from a 10 mg/mL stock: 50 µg/mL is 0.05 mg/mL, so V₁ = 0.05 × 10 ÷ 10 = 0.05 mL, which is 50 µL of stock plus 9.95 mL of diluent.

How do I calculate a cell dilution?

Treat cells/mL as the concentration. To seed 10 mL at 2 × 10⁵ cells/mL from a suspension counted at 2 × 10⁶ cells/mL, V₁ = 2 × 10⁵ × 10 ÷ 2 × 10⁶ = 1 mL of cells plus 9 mL of medium.

How do I calculate a serial dilution?

Multiply the step factors. Ten tubes at 1:10 each give a total dilution of 10¹⁰. For each tube, the transfer volume is the tube's final volume divided by the step factor, and the diluent is the rest. Transferring 10 mL into 90 mL, as the FDA plate-count method does, is one tenfold step.

How much powder do I weigh to make a molar solution?

Mass (g) = molarity (mol/L) × volume (L) × molar mass (g/mol). For 500 mL of 10 mM NaCl (58.44 g/mol): 0.010 × 0.5 × 58.44 = 0.2922 g.

How do I dilute a 10X buffer to 1X?

Divide the final volume by 10. For 500 mL of 1X, measure 50 mL of 10X stock and bring it to 500 mL. In the calculator, choose × stock as the unit and enter 10 and 1.

Can the target be stronger than the stock?

No. Adding solvent can only lower the concentration, so C₂ must be less than or equal to C₁. To concentrate a solution you have to remove solvent or add more solute.

Sources & method

Results are estimates for general information. Found an error? It helps everyone — see our methodology.

Dilution Calculator: Percent & Molar