Ratio Calculator

How this is calculated

simplified = (a ÷ gcd) : (b ÷ gcd) · scaled right = new-left × b ÷ a

Worked example: 1920:1080 has GCD 120, so it simplifies to 16:9 — the video standard. Scaling that to 1280 on the left gives 720 on the right: the familiar 1280×720. Ratios are unitless, so the same page settles screens, print sizes, map scales, and two-part mixes alike.

A ratio is not a fraction

This is the error that spoils more mixtures than any other. A 1:3 ratio means one part of the first thing to three parts of the second — four parts in total, so the first thing is one quarter of the mixture, not one third. Concentrate mixed "one to three" with water is 25% concentrate. Read as a fraction it becomes 33%, and the drink is a third too strong.

The reliable habit is to add the parts first. 2:3:5 is ten parts, so the shares are 20%, 30% and 50%. Once you have the total, every question about the mixture becomes a single multiplication.

Sharing an amount in a given ratio

To split R4,500 in the ratio 4:5, add the parts (9), divide the amount by the total to get one part (R500), then multiply out: R2,000 and R2,500. Checking that the shares add back to the original is worth the two seconds — it catches almost every arithmetic slip in this kind of problem.

Simplifying, and when not to

Ratios simplify like fractions, by dividing every part by a common factor: 12:18 is 2:3. That is usually what you want, because 2:3 is easier to scale. There is one situation where it is not — when the original numbers carry information. Telling someone a recipe is 250:375 grams of flour to water is more useful in a kitchen than telling them it is 2:3, even though the second is tidier. Simplify to reason, keep the original to work from.

Ratios with decimals or fractions can be cleared by multiplying every part by the same number: 0.5:1.5 becomes 1:3 when both sides are doubled. Ratios in different units must be converted to the same unit first, and forgetting that is why "300 g to 1 kg" is 3:10 rather than 3:1.

Where ratios are used in earnest

Mixing is the obvious one — concrete at 1:2:4 cement, sand and stone; two-stroke fuel at 50:1; screen aspect ratios of 16:9. Finance uses them constantly: a debt-to-income ratio, a price-to-earnings ratio, a current ratio. Maps and drawings use scale ratios, where 1:50,000 means one unit on the paper is 50,000 of the same unit on the ground, which is why a scale has no units attached.

Aspect ratios have a quirk worth knowing: they describe shape, not size, so 1920×1080 and 1280×720 are both 16:9. Fitting 4:3 content into a 16:9 frame means either bars at the sides or cropping the top and bottom, and there is no third option that preserves both the whole image and the shape.