1920 : 1080 is 16 : 9
Both numbers divide by 120, which is what makes a full-HD screen the same shape as a 16 : 9 one.
The ratio is what matters here, not the pixel count: 1280 : 720 and 3840 : 2160 reduce to exactly the same thing.
Ratio calculator
Reduce a ratio to its simplest form, divide a total between shares, or fill in the missing term of a proportion. Two terms or twenty — the calculator takes as many as you give it.
Result
Fill in the fields to see your result.
How it works
A ratio compares quantities of the same kind. Simplifying it means dividing every term by the largest number that goes into all of them, which is why 1920 : 1080 collapses to 16 : 9 — the same shape of screen, described with smaller numbers. The value never changes; only the writing gets easier.
Sharing a total works from the number of parts. Add the terms to find how many parts there are altogether, divide the total by that, and you have what one part is worth. Each share is then that figure multiplied by its own number of parts. Sharing 1 200 in 2 : 3 : 5 gives ten parts of 120, so 240, 360 and 600.
A proportion says two ratios are equal, and cross multiplication finds the term you are missing. It is the same manoeuvre used to scale a recipe, convert a map distance or price a different quantity of the same goods.
Formulas used
Simplifying
a : b = (a ÷ g) : (b ÷ g)
- g
- greatest common divisor of every term
Sharing a total
share = total × term ÷ (sum of terms)
Solving a proportion
a : b = c : d → d = b × c ÷ a
Multiply the two terms that are diagonally opposite, then divide by the one facing the unknown.
Worked examples
Sharing 1 200 in 2 : 3 : 5
The terms add up to ten parts, so one part is worth 120.
The three shares are 240, 360 and 600 — a fifth, just over a quarter, and half.
If 3 costs 4, what do 12 cost?
Cross multiplying gives 4 × 12 ÷ 3 = 16. The scale factor is 4, because 12 is four times 3.
The same arithmetic scales a recipe from three portions to twelve, or reads a distance off a map.
Assumptions and limits
- All terms are measured in the same unit.
- Terms are zero or positive.
- Shares are rounded for display only.
Frequently asked questions
What is the difference between a ratio and a fraction?
A fraction compares a part with the whole; a ratio compares parts with each other. In a class with 2 : 3 boys to girls, the fraction of boys is 2/5, not 2/3.
When a ratio has only two terms, the calculator shows both readings, because slipping between them is the most frequent error in ratio problems.
Does the order of the terms matter?
Very much. 3 : 1 and 1 : 3 describe opposite situations — three times as much versus a third as much.
Keep the order the same as the words: if you say "cement to sand", the cement figure comes first and stays first.
How do I scale a recipe?
Use the proportion mode. If three portions need 400 g of flour and you want seven portions, enter 3, 400 and 7 to get roughly 933 g.
Every ingredient scales by the same factor, so once you have that factor you can apply it to the whole list.
Can I use decimals in a ratio?
Yes. The calculator first converts the terms to whole numbers, then reduces: 1.5 : 2 becomes 3 : 4, which is the same relationship written more clearly.
You can also read a decimal ratio directly as a single number — 1.5 : 1 is simply 1.5 times as much.
Updated
Related calculators
Fractions Add, subtract, multiply and divide fractions, reduce them to lowest terms, and convert between fractions and decimals. Percentage Work out a percentage of a number, a share, a percentage change, or add and subtract a percentage — with every step shown. Discount Find the sale price, the percentage off, or the price before the discount — including stacked offers and sales tax.