Ratio Calculator

Solve a : b = c : x, simplify any ratio, and get the scale factor — the number you actually need when doubling a recipe or reading a plan.

Reference table

A	Result	Simplified ratio	As a decimal
0.5	30	1 : 6	6
1	15	1 : 3	3
1.5	10	1 : 2	2
2	7.5	2 : 3	1.5
2.5	6	5 : 6	1.2
3	5	1 : 1	1
4	3.75	4 : 3	0.75
5	3	5 : 3	0.6
6	2.5	2 : 1	0.5
7	2.1429	7 : 3	0.4286
8	1.875	8 : 3	0.375
9	1.6667	3 : 1	0.3333
10	1.5	10 : 3	0.3
12	1.25	4 : 1	0.25
15	1	5 : 1	0.2

📺 Ratios You Meet Daily

1920 × 1080 (Full HD)16:9
3840 × 2160 (4K UHD)16:9
1080 × 1080 (square post)1:1
1080 × 1920 (story / reel)9:16
A4 paper, any size1:√2
Rice to water, long grain1:1.5

Where Ratios Go Wrong

A ratio has no units of its own. 2:3 is the same relationship whether it's cups, litres or tonnes — but both sides must be in the SAME unit before you compare.
3:1 and 1:3 are opposites, not the same thing. Order matters, and mixing paint the wrong way round is an expensive way to learn it.
A ratio is not a fraction of the whole. In a 2:3 mix, the first part is 2/5 of the total, not 2/3.
1920×1080 reduces to 16:9 because the greatest common divisor is 120. Divide both by 120 and there it is.

A Ratio Compares, It Doesn't Measure

Two to three tells you how two quantities relate, not how big either one is. That is the whole idea, and it is why a ratio survives scaling: two cups to three cups, two litres to three litres and two tonnes to three tonnes are all 2:3, and all describe the same mixture. It also means a ratio is meaningless until both sides use the same unit. Comparing 2 kilograms to 3 grams is not 2:3, it is 2000:3, and that mistake shows up constantly in recipes copied between metric and imperial. Reduce both sides by their greatest common divisor and you get the ratio in lowest terms — the form everyone quotes.

Cross-Multiplication, and Why It Works

If 2 cups of rice need 3 cups of water, how much water do 5 cups of rice need? Write it as 2 : 3 = 5 : x. Cross-multiply — 2 times x equals 3 times 5 — so 2x = 15 and x = 7.5. The reason this works is that both sides represent the same fraction: 2/3 and 5/x must be equal, and multiplying both sides of that equation by 3x clears the denominators. The scale factor is the shortcut: 5 divided by 2 is 2.5, so multiply the other side by 2.5 as well. Once you see the scale factor, most proportion problems stop needing algebra at all.

Aspect Ratios, Demystified

1920 × 1080 is 16:9 because the greatest common divisor of the two numbers is 120. Divide both and you get 16 and 9.
3840 × 2160 is also 16:9 — 4K has four times the pixels of Full HD, but exactly the same shape.
A vertical video at 1080 × 1920 is 9:16, the same ratio flipped. Uploading one where the other is expected is what causes the black bars.
Cinema uses 2.39:1, far wider than any TV, which is why letterboxing exists on a 16:9 screen.
A4 paper is 1:√2, about 1:1.414. Folding it in half gives exactly the same ratio again — the only shape that does.
Cropping changes the ratio, resizing does not. A 16:9 image scaled to any size stays 16:9; cropping to a square makes it 1:1 and loses content.

Ratios in Real Life

Recipes: rice to water at 1:1.5, bread at 100:65 flour to water — baker's percentages are ratios in disguise.
Two-stroke fuel: 50:1 petrol to oil means 100 ml of oil in 5 litres of petrol. Getting it backwards destroys the engine.
Map scales: 1:25,000 means one centimetre on paper is 25,000 centimetres — 250 metres — on the ground.
Gear ratios: a 3:1 gear turns the output once for every three turns of the input, trading speed for torque.
Concrete: a 1:2:3 mix is one part cement, two sand, three aggregate — a three-term ratio, and the order is never optional.
Screen and print: 300 dpi means the ratio of pixels to inches, which is why a 1200-pixel image prints well at 4 inches and badly at 12.

Worked Examples

Solving and simplifying

Scaling a rice recipe

2 cups rice : 3 cups water = 5 cups rice : x
Scale factor = 5 ÷ 2 = 2.5
x = 3 × 2.5 = 7.5 cups of water

7.5 cups of water

Why 1920 × 1080 is 16:9

Greatest common divisor of 1920 and 1080 is 120
1920 ÷ 120 = 16
1080 ÷ 120 = 9

16:9, the same shape at any size

Frequently Asked Questions

How do I solve a ratio problem?

Write it as a : b = c : x and cross-multiply: a × x = b × c, so x = (b × c) ÷ a. For 2 : 3 = 5 : x that gives x = (3 × 5) ÷ 2 = 7.5. The shortcut is the scale factor: 5 ÷ 2 = 2.5, so multiply the other side by 2.5.

How do I simplify a ratio?

Divide both terms by their greatest common divisor. For 1920:1080 that divisor is 120, giving 16:9. If the only number dividing both is 1, the ratio is already in lowest terms.

What is a scale factor?

How many times bigger the new quantity is than the old one. Going from 2 cups to 5 cups is a scale factor of 2.5, and every other ingredient must be multiplied by that same 2.5 for the recipe to hold.

Is a ratio the same as a fraction?

Not quite. 2:3 compares two parts to each other; the fraction 2/3 compares one part to another. But in a 2:3 mixture the first part is 2/5 of the whole, not 2/3 — the total is five parts, and confusing the two is the most common ratio error.

Why is 1920 × 1080 called 16:9?

Because both numbers divide by 120: 1920 ÷ 120 = 16 and 1080 ÷ 120 = 9. Any resolution with that same shape — 1280 × 720, 3840 × 2160 — reduces to 16:9 as well.

Does the order of a ratio matter?

Always. 4:1 and 1:4 describe opposite mixtures. With paint, fuel or concrete, reversing the order is not a rounding error — it produces something that does not work and often cannot be fixed.