The rule of three: direct and inverse proportion
Two quantities are directly proportional when doubling one doubles the other: if 3 kg of apples cost 12, then 5 kg cost 12 × 5 ÷ 3 = 20. They are inversely proportional when doubling one halves the other: if 4 workers finish a job in 6 days, 3 workers take 4 × 6 ÷ 3 = 8 days. In the first tab, type the three numbers you know and choose the type of proportion.
How to solve a proportion a : b = c : d
In a proportion the product of the means (b and c) equals the product of the extremes (a and d): a × d = b × c. To find an extreme, multiply the means and divide by the other extreme; to find a mean, multiply the extremes and divide by the other mean. Example: 2 : 5 = 6 : x → x = 5 × 6 ÷ 2 = 15. In the second tab you can leave any box empty; if you fill all four, the calculator checks whether the proportion holds.
How to scale a recipe
To change the number of servings, multiply every ingredient by the ratio between the people: from 4 to 6 people the factor is 6 ÷ 4 = 1.5, so 250 g of flour becomes 375 g. To change the pan, what matters is the area, not the diameter: a 28 cm round pan has 1.36 times the area of a 24 cm one (28² ÷ 24²), so the quantities are multiplied by 1.36, not by 28 ÷ 24 = 1.17. The calculator also converts between round and rectangular pans, assuming the same batter depth.
Round eggs to the nearest whole egg or weigh them: a medium egg without its shell weighs about 50 grams. Baking powder, salt and spices follow the same factor. There is no fixed rule for baking time: in a bigger, shallower pan the cake bakes a little faster, in a deeper one a little slower, so check with a skewer.
Frequently asked questions
How do I solve a proportion with x?
Multiply the two numbers diagonally across and divide by the third: in 2 : 5 = 6 : x, x = 5 × 6 ÷ 2 = 15.
How do quantities change from a 24 cm to a 26 cm pan?
Multiply them by (26 ÷ 24)², about 1.17: 200 g of flour becomes about 235 g.
Can I type fractions like 1/2 or ½?
Yes: at the start of each line the calculator reads whole and decimal numbers (2.5), fractions (1/2, 1 1/2) and the symbols ½, ¼, ¾. Lines without a number, like "salt to taste", stay as they are.