Short answer
The dilution equation is C₁ × W₁ = C₂ × W₂: the strength of a solution times its weight equals the strength of the diluted solution times its weight, because the amount of material does not change when you add solvent. To make 20 g of a 1% solution from a 10% stock, you need 1 × 20 ÷ 10 = 2.00 g of the stock, made up to 20.00 g with solvent. The same idea, rearranged, tells you how to blend two strengths into a third, how much neat material strengthens a weak dilution, and how much concentrate makes a finished perfume stronger. In perfumery, every term is by weight.
The equation and its terms
C₁ × W₁ = C₂ × W₂
- C₁ — the strength of the solution you start from, in % w/w (grams of material per 100 g of solution);
- W₁ — the weight of that solution you take;
- C₂ — the strength you want;
- W₂ — the total weight of the new solution.
Both sides are the same quantity: grams of pure material. Chemists often write C₁V₁ = C₂V₂ with volumes, but volumes of different liquids do not add up neatly and drops vary, so perfumers use weights throughout — the reasons are in perfume weight vs volume.
Diluting a stock solution
Rearranged for the weight of stock to take:
W₁ = C₂ × W₂ ÷ C₁
For 20 g of a 1% solution from a 10% stock: 1 × 20 ÷ 10 = 2.00 g of stock, plus 18.00 g of solvent. For 10 g of 0.1% from the same 10% stock: 0.1 × 10 ÷ 10 = 0.10 g of stock — a weight many balances cannot measure well, which is why a 0.1% solution is usually made from a 1% one in a second step (1.00 g of 1% made up to 10.00 g). The routine for making and labeling dilutions is in how to dilute aroma chemicals.
Blending two strengths into a third
You have a 10% and a 1% solution of the same material in the same solvent, and you want 18 g of 5%. Each part of the 10% solution is 5 points above the target; each part of the 1% solution is 4 points below it. Take the strengths in the opposite proportion:
- parts of the stronger solution = target − weaker = 5 − 1 = 4;
- parts of the weaker solution = stronger − target = 10 − 5 = 5;
- 9 parts in all, so for 18 g: 8.00 g of the 10% and 10.00 g of the 1%.
Check: 8.00 × 0.10 + 10.00 × 0.01 = 0.80 + 0.10 = 0.90 g of material in 18.00 g, which is 5.00%. This "opposite proportion" shortcut is often taught as alligation or the Pearson square. It only works between the two strengths you have; you cannot blend a 10% and a 1% solution into 12%.
Strengthening a weak dilution with neat material
You have 30.00 g of a 5% solution and want 10%. Adding neat material (100%) raises both the material and the total, so the amount is:
neat to add = W × (C₂ − C₁) ÷ (100 − C₂)
30 × (10 − 5) ÷ (100 − 10) = 150 ÷ 90 = 1.667 g. Check: the solution held 1.50 g of material; with 1.667 g more it holds 3.167 g in 31.667 g, which is 10.0%. Weighing 1.667 g needs a balance reading to 0.001 g; on a 0.01 g balance, weigh 1.67 g and accept 10.01%.
Finished perfumes: the same equation
A finished perfume is a dilution of a concentrate in alcohol, so the equation applies with "concentrate" in place of "material".
Making it weaker
50 g of perfume at 20% contains 10 g of concentrate. At 15% that concentrate makes 10 ÷ 0.15 = 66.67 g, so add 16.67 g of alcohol. This case is worked in how to calculate perfume concentration.
Making it stronger
Strengthening needs concentrate, and the formula is the same as for neat material above. To take 50 g of a 15% perfume to 20%:
50 × (20 − 15) ÷ (100 − 20) = 3.125 g of concentrate
Check: 7.50 g of concentrate plus 3.125 g is 10.625 g in 53.125 g of perfume — 20.0%. Add it as a weighed amount of the same concentrate (same version, ideally the same batch), then rest the perfume again before judging it.
Things the equation does not handle
- Different solvents. Blending a 10% solution in DPG with a 1% solution in alcohol gives the right strength but a mixed solvent. Record both.
- Evaporation. An alcohol dilution left open loses solvent and grows stronger. The equation assumes the label is true; remake old alcohol dilutions rather than correcting them.
- Volume. Mixing 10 ml of ethanol with 10 ml of water does not give 20 ml. Weights add; volumes may not.
- What "strength" means in a finished perfume. If the concentrate itself contains solvent from diluted rows, "20% concentrate" is less than 20% fragrance material. See formula %, absolute % and relative %.
Quick reference
| Task | Formula | Example |
|---|---|---|
| Stock needed for a dilution | W₁ = C₂ × W₂ ÷ C₁ | 1% × 20 g ÷ 10% = 2.00 g |
| Solvent to add to a solution | W₁ × C₁ ÷ C₂ − W₁ | 2 g × 10 ÷ 1 − 2 = 18.00 g |
| Blend two strengths | Parts in opposite proportion | 10% and 1% → 5%: 4 parts and 5 parts |
| Strengthen with neat material or concentrate | W × (C₂ − C₁) ÷ (100 − C₂) | 30 g, 5% → 10%: 1.667 g |
The rest of the arithmetic of a formula — percentages, grams, scaling and cost — is gathered in the perfume dilution and calculations guide.
Frequently asked questions
Is a 10% dilution the same as 1 part in 10?
Yes, by weight: 1 g of material in 10 g of solution, which is 1 g of material plus 9 g of solvent. "1 part material to 10 parts solvent" is a different, weaker dilution (1 in 11, about 9.09%). Write dilutions as a percentage of the solution to avoid the ambiguity.
Can I use the equation with drops?
Not reliably. Drop size depends on the liquid and the dropper, so neither side of the equation is known. Weigh.
Written and reviewed by the RUŌOD Lab team. This article is general education about perfume formulation and record-keeping; it is not legal, regulatory or safety advice, and the examples are illustrations, not validated commercial formulas. How we write and check these guides.