In short
Reading a formula means knowing its unit, whether each line is diluted, and what it should total. These twelve problems drill those habits. Try each before reading the answer. They use invented formulas, only for arithmetic. If you want to compare a real one, the guide on how to read a perfume formula covers published layouts.
What you will learn
- Read an unfamiliar formula and find its total and shares
- Allow correctly for dilutions and stocks
- Find errors in someone else's calculation
Before this lesson: Percent to Grams: Study Guide and Batch Drill
Set A: totals and shares
1. Weights: A 3.2 g, B 1.6 g, C 0.8 g, D 0.4 g. What percent is B? Total 6.0 g. 1.6 ÷ 6.0 = 26.7%.
2. A formula in parts per 1,000 has a line of 35 parts. What weight is that in a 12 g batch? 35 × 12 ÷ 1,000 = 0.42 g.
3. Four lines total 100 parts, in the ratio 5:3:1:1. What is each? 50, 30, 10, 10.
Set B: dilutions
4. A line reads "2.5 g of a 10% dilution". How much pure material? 0.25 g.
5. You need 0.04 g of a material. Which is the best choice on a 0.01 g scale: neat, 10% or 1%? How much do you weigh? At 10%, 0.40 g. At 1%, 4.00 g, also fine, though that brings more solvent. Neat, 0.04 g is unreliable.
6. A blend has X 4 g neat, Y 2 g at 10% and Z 4 g at 1%. Find total weight, total pure material and X's share of pure material. Total weight 10 g. Pure: 4 + 0.2 + 0.04 = 4.24 g. X = 94.3%.
Set C: stocks and batches
7. You want 15 g of a 5% dilution from a 25% stock. 15 × 5 ÷ 25 = 3 g of stock + 12 g of solvent.
8. A batch of 30 g is to contain a line at 0.2%. Your stock is 10%. Pure needed: 0.06 g. Stock: 0.6 g.
9. You want 50 g of perfume at 15% concentrate. 7.5 g of concentrate + 42.5 g of alcohol.
Set D: find the mistake
10. A learner wants 20 g at 10% and weighs 2 g of material plus 20 g of solvent. What strength did they make? 2 ÷ 22 = 9.09%. They should have added 18 g.
11. A formula says "Musk 10%, 40 parts", and a learner weighs the musk as if it were 40 parts of pure material. By what factor have they overstated its active share? Ten. 40 parts of the 10% dilution is 4 parts of pure musk.
12. A learner scales a formula by doubling the top two lines, but none of the others, "because the batch is twice as big". What is wrong? Every line must be multiplied by the same factor, or the proportions change. See the batch calculation errors guide.
A method for any formula
- Find the unit: grams, percent, parts per 1,000, or a mixture.
- Mark every diluted line and its strength.
- Add the column, and compare with the stated total. Note any gap.
- Work out the pure material if you need true shares.
- Only then calculate your batch.
Published formulas sometimes carry mistakes or rounding, and old ones may mean something different by a "part". Check any total before you trust it.
Practical exercise: Work all twelve, then write your own
- Work all twelve problems without looking at the answers, on paper, and mark yourself.
- For each error, say which kind it was: unit, dilution, total, or plain arithmetic.
- Write one original problem like number 6, with the answer, and try it on a friend or try it yourself a week later.
You have done this well if you get at least ten right, can explain every miss, and your original problem has a correct answer. If you score lower, redo Set B, since dilutions cause most mistakes.
Common mistakes
- Doing it on a calculator without an estimate first. A rough idea catches a misplaced decimal.
- Assuming neat. If a line's strength is not stated, find out.
- Rounding too early. Keep extra digits until the last step.
Knowledge check
Written and reviewed by the RUŌOD Lab team. This is general education, not legal, regulatory, medical or safety advice. Example dilutions and exercises are for learning, are not validated products, and have not been safety-assessed. Completing a lesson confers no qualification. How we check these lessons.