Dilution cheat sheet

Everything you need to prepare a working solution from a stock, in one page.

The identity

$C_1 V_1 = C_2 V_2$

Moles conserved on both sides of the pipette: what you pull out of the stock is what ends up in the diluted solution. Rearranged for each variable:

V₁ — stock volume to pipette: $\;V_1 = \dfrac{C_2 V_2}{C_1}$
C₁ — stock concentration: $\;C_1 = \dfrac{C_2 V_2}{V_1}$
C₂ — final concentration: $\;C_2 = \dfrac{C_1 V_1}{V_2}$
V₂ — final total volume: $\;V_2 = \dfrac{C_1 V_1}{C_2}$

Units are your responsibility: C₁ and C₂ must share a unit, V₁ and V₂ must share a unit.

Dilution factor table

Dilution factor $\text{DF} = C_1 / C_2 = V_2 / V_1$ . “1:10” means the final is at 1/10 the stock.

DF	Stock (per 1 mL final)	Diluent	Notes
1:2	500 µL	500 µL	Half-strength
1:5	200 µL	800 µL
1:10	100 µL	900 µL
1:20	50 µL	950 µL
1:100	10 µL	990 µL	Below 10 µL is pipette-limited
1:1000	1 µL	999 µL	Serial-dilute in practice
1:10 000	0.1 µL	≈ 1 mL	Always serial

Common lab stocks

Stock	Concentration	Notes
Concentrated HCl	~12 M	37 % w/w, ρ 1.19 g/mL. Add acid to water.
Concentrated H₂SO₄	~18 M	98 % w/w, ρ 1.84 g/mL. Extremely exothermic.
Concentrated HNO₃	~16 M	70 % w/w, ρ 1.42 g/mL.
Glacial acetic acid	~17.4 M	99.7 % w/w, ρ 1.05 g/mL.
30 % H₂O₂	~9.8 M	Store 4 °C, dark. Add to water.
5 M NaCl	5 M	Common salt stock (292 g/L).
1 M Tris-HCl	1 M	Buffer stock; specify pH (6.8 / 7.4 / 8.0).
0.5 M EDTA (pH 8)	0.5 M	Chelator stock.
10× PBS	10× (1.37 M NaCl)	Dilute 1:10 for working 1× PBS.

Pipette accuracy floor

Every pipette has a lower bound below which the CV climbs quickly. Rough rules of thumb:

Pipette	Accurate to	Do not use below
P2 (0.1–2 µL)	~0.2 µL	0.1 µL
P20 (2–20 µL)	~2 µL	1 µL
P200 (20–200 µL)	~20 µL	10 µL
P1000 (100–1000 µL)	~100 µL	50 µL

If C₁V₁ = C₂V₂ tells you to pipette a volume below the floor of the smallest pipette in your reach, split the dilution into two or more steps (serial dilution).

Three most common mistakes

Water into acid. Adding water to concentrated acid can boil the surface and splash you with acid. Always place water first, then add acid.
Diluent vs. final volume. V₂ is the total final volume, not the volume of diluent added. “10 µL stock brought up to 1.0 mL” means 990 µL diluent + 10 µL stock.
Mismatched units. The identity requires C₁ and C₂ in the same unit and V₁ and V₂ in the same unit. Off-by-1000 answers usually trace back to mixing mM with M.

Sources

Harris, Quantitative Chemical Analysis, 10th ed. (2020), §1-3
IUPAC Gold Book — dilution
Merck Index, 15th ed. — HCl and H₂SO₄ concentrated-acid entries

Last updated: 2026-08-13 .