How to Calculate a Dilution: Ratios, Factors & Worked Examples

A dilution lowers the concentration of a solution by adding solvent without adding more solute. Every dilution question is really the same equation, C1V1 = C2V2, solved for whichever value you do not know. This guide works through the four directions, gives a ready-reckoner table for the ratios you will actually meet, shows how to handle percentage dilutions and mg/mL concentrations, and lists the mistakes that quietly ruin a batch. The dilution calculator runs all of it and shows the stock and diluent volumes you need to pipette.

What is a dilution factor?

The dilution factor (DF) says how many times the original solution has been spread out. It is the ratio of the final volume to the volume of stock you started with:

DF = V2 / V1 = C1 / C2

A DF of 10 means one part of stock in ten parts of total volume — written as a 1:10 dilution. Note that the second number in a ratio is the total volume, not the solvent. A 1:10 dilution is 1 part stock plus 9 parts diluent, because 1 + 9 = 10. Treating 1:10 as “1 plus 10” is the single most common way a dilution ends up slightly too weak.

How do I calculate a dilution step by step?

Start from C1V1 = C2V2 and decide what you are solving for:

Stock volume to pipette: V1 = (C2 × V2) / C1
Final concentration: C2 = (C1 × V1) / V2
Diluent to add: V_diluent = V2 − V1
Dilution factor: DF = C1 / C2

For the everyday case — dilute a 1 M stock to 100 mM in a final volume of 50 mL:

V1 = (0.100 M × 50 mL) / 1.0 M = 5 mL of stock
V_diluent = 50 mL − 5 mL = 45 mL of solvent
DF = 1.0 / 0.100 = 10 (a 1:10 dilution)

Pipette 5 mL of the 1 M stock into a vessel and bring the total to 50 mL. The C1V1 calculator solves the same relation when you prefer to think directly in concentrations and volumes.

Common dilution ratios: a ready-reckoner table

Most bench dilutions use a handful of round ratios. For each, the table shows how much stock to take and how much diluent to add to reach exactly 10 mL final — scale linearly for any other volume.

Ratio (1:n)	Dilution factor	Stock for 10 mL	Diluent for 10 mL
1:2	2	5.0 mL	5.0 mL
1:5	5	2.0 mL	8.0 mL
1:10	10	1.0 mL	9.0 mL
1:20	20	0.5 mL	9.5 mL
1:50	50	0.2 mL	9.8 mL
1:100	100	0.1 mL (100 µL)	9.9 mL
1:200	200	0.05 mL (50 µL)	9.95 mL
1:1000	1000	0.01 mL (10 µL)	9.99 mL

The stock volume is always final volume ÷ DF, and the diluent is whatever is left over. If a single step would need you to pipette less than about 2 µL, the measurement is unreliable — split it into a serial dilution instead.

How do I make a 1/200 dilution?

A 1/200 dilution means one part stock in 200 parts total volume (DF = 200). Two practical routes:

Single step, larger volume: 50 µL stock + 9,950 µL (9.95 mL) diluent = 10 mL total.
Two steps, when you cannot pipette 50 µL accurately into a large volume: first make 1:20 (50 µL + 950 µL = 1 mL), then take 50 µL of that into 950 µL for another 1:20. The overall factor is 20 × 20 = 400, so adjust to hit exactly 200 — for example 1:20 then 1:10 gives 200.

The general rule for combining steps is that factors multiply: DF_total = DF1 × DF2 × … This is why serial dilutions can reach huge factors with comfortable pipetting volumes.

How do I calculate a percentage dilution?

Percentage dilutions come up two ways. The first is diluting a solution that is already expressed in percent. A 10% stock diluted 1:5 becomes 10% ÷ 5 = 2% — the same C1V1 = C2V2 math, with percent as the concentration unit.

The second is expressing the dilution itself as a percentage. The fraction of the final volume that is stock equals 1/DF, and as a percentage that is (1/DF) × 100:

1:10 → 1/10 = 10% stock
1:100 → 1/100 = 1% stock
1:200 → 0.5% stock

So “a 5% dilution of the concentrate” means take stock equal to 5% of the final volume — a 1:20 dilution. Be careful: a “% v/v dilution” of a concentrated reagent is a ratio statement, not a final mass-per-volume concentration; if you need the latter, use the percent solution calculator.

Dilutions expressed in mg/mL

Concentration does not have to be molar. Antibody and protein work is usually in mg/mL or µg/mL, and the dilution equation is unit-agnostic — as long as C1 and C2 share the same unit. To make 2 mL of a 0.05 mg/mL working solution from a 1 mg/mL stock:

V1 = (0.05 mg/mL × 2 mL) / 1 mg/mL = 0.1 mL = 100 µL
V_diluent = 2 mL − 0.1 mL = 1.9 mL
DF = 1 / 0.05 = 20 (a 1:20 dilution)

Because mg/mL, µg/mL and g/L are numerically related (1 mg/mL = 1 g/L = 1000 µg/mL), you can dilute in whichever unit your stock is labelled in and convert at the end.

Worked example: from molar stock to working solution

You have a 5 M NaCl stock and need 250 mL of 0.15 M saline:

V1 = (0.15 M × 250 mL) / 5 M = 7.5 mL of stock
V_diluent = 250 mL − 7.5 mL = 242.5 mL of water
DF = 5 / 0.15 ≈ 33.3

Pipette 7.5 mL of the 5 M stock and bring to 250 mL. If you also need to know how many grams of NaCl that stock contains per litre, the stock solution calculator converts between molar and mass terms.

What mistakes should I watch for?

Ratio read as parts-of-solvent. 1:10 means 1 stock + 9 diluent, not 1 + 10.
Mixing units between C1 and C2. Both must be molar, or both mg/mL; do not divide mM by M.
V2 as the diluent, not the total. In C1V1 = C2V2, V2 is the final volume.
Pipetting volumes too small to be accurate. Below ~2 µL, use a serial dilution.
Forgetting to mix. An unmixed dilution has a gradient; the concentration you calculate is not the concentration you have.

If a final concentration comes out higher than the stock, or a stock volume larger than the final volume, a unit or a ratio has been swapped — the calculator flags these rather than returning a silent impossible number.

Where does this fit in the wider workflow?

Dilution sits between making a stock and running an experiment. You prepare the concentrated stock with the stock solution calculator, dilute it to a working strength here, and reach large factors with the serial dilution calculator. The underlying equation is explained in the C1V1 guide, and all of these tools live together in the laboratory calculators collection.