Ratio and proportion formulas
Simplify: A : B = (A ÷ gcd) : (B ÷ gcd)
Proportion: A : B = C : D → D = B × C ÷ A
Proportion: A : B = C : D → D = B × C ÷ A
Example 1 — proportion: A recipe uses 3 cups of flour for 4 eggs. For 12 cups of flour you need 4 × 12 ÷ 3 = 16 eggs.
Example 2 — simplify: A 1920 × 1080 screen has a ratio of 1920 : 1080. The GCD is 120, so it simplifies to 16 : 9.
Example 2 — simplify: A 1920 × 1080 screen has a ratio of 1920 : 1080. The GCD is 120, so it simplifies to 16 : 9.
Common uses of ratios
- Scaling recipes up or down while keeping flavors balanced.
- Mixing concrete, fuel, fertilizer, paint or cleaning solutions.
- Maps and models — a 1:25,000 map means 1 cm equals 250 m.
- Aspect ratios for photos, video and displays (4:3, 16:9, 21:9).
How to use the calculator
- To solve a proportion, enter three of the four values in A : B = C : D and leave the unknown blank.
- To simplify a ratio, enter both parts; the calculator divides by their greatest common divisor.
- To scale or split a total, enter the ratio and the total amount.
Solving proportions: cross-multiplication
A proportion states that two ratios are equal: A/B = C/D. Cross-multiplying gives A × D = B × C, so any missing value can be found. If 3 cups of flour need 4 eggs, then for 12 cups: 3 × D = 4 × 12, so D = 48 ÷ 3 = 16 eggs.
Dividing an amount in a ratio
Example: Split $900 between three partners in the ratio 2 : 3 : 4. Add the parts: 2 + 3 + 4 = 9. Each part is $900 ÷ 9 = $100, so the shares are $200, $300 and $400.
Common ratios in everyday life
- Screens: 16:9 widescreen (1920 × 1080), 4:3 older monitors, 21:9 ultrawide. Keep the ratio when resizing images to avoid stretching.
- Cooking: rice to water about 1 : 1.5–2, vinaigrette oil to vinegar 3 : 1, coffee to water 1 : 15–17.
- Mixing: two-stroke fuel 50 : 1, concrete cement : sand : gravel 1 : 2 : 3, concentrated cleaners such as 1 : 10.
- Maps and models: 1 : 25,000 means 1 cm on the map is 250 m on the ground.
- Finance: debt-to-income and price-to-earnings ratios compare two amounts.
Ratios, fractions and percentages
A ratio of 3 : 1 means 3 parts of one thing for every 1 of another — 4 parts in total. As a fraction of the whole, the first part is 3/4 (75%) and the second 1/4 (25%). Mixing up “part to part” and “part to whole” is the most common ratio error: a 1 : 4 dilution can mean 1 part concentrate to 4 parts water (5 total) or 1 part in 4 total, so check the instructions.
Frequently asked questions
How do you simplify a ratio?
Divide both parts by their greatest common divisor. For 1920:1080 the GCD is 120, giving 16:9. If the ratio contains decimals, multiply both parts by 10, 100, etc. first to make them whole numbers.
How do you solve a proportion?
Cross-multiply. For A:B = C:D, D = B × C ÷ A. If 3 cups of flour need 4 eggs, 12 cups need 4 × 12 ÷ 3 = 16 eggs.
What is the difference between a ratio and a fraction?
A fraction compares a part with the whole (3 of 4 parts = 3/4). A ratio can compare any two quantities, including part to part: in a 3:1 mix, the paint is 3/4 of the total and the thinner 1/4.
How do I convert a ratio to a percentage?
Add the parts to get the total, then divide each part by the total. In a 3:2 ratio, the first part is 3 ÷ 5 = 60% and the second 40%.
How do I simplify a ratio with decimals?
Multiply both parts by 10, 100 or 1,000 until they are whole numbers, then divide by the greatest common divisor. 1.5 : 2.5 becomes 15 : 25, which simplifies to 3 : 5.
How do I find a ratio between two numbers?
Write them as A : B and simplify. 24 and 36 have a GCD of 12, so the ratio is 2 : 3.