Math
Ratio calculator
Three related jobs: reduce a ratio, find a missing term, or share a total out in proportion.
Ratios, fractions and rates
A ratio compares two quantities of the same kind — 3 : 2 means three of one thing for every two of another. A fraction expresses a part of a whole, so 3 : 2 corresponds to 3/5 and 2/5 of the total, not 3/2. Confusing the two is the most common error with ratio problems.
A rate compares quantities of different kinds, such as kilometres per hour or price per kilogram. Rates behave like ratios algebraically but carry units that do not cancel.
Solving proportions by cross-multiplication
This works because a proportion is two equal fractions, and multiplying both sides by both denominators clears them. It is the workhorse for scaling recipes, converting units, resizing images and reading maps.
A quick sanity check: identify the scale factor first. Going from 1280 to 1920 is a factor of 1.5, so the other term must also grow by 1.5. If your answer does not, something has been multiplied the wrong way round.
Aspect ratios
Screen and image dimensions are ratios in disguise. 1920 × 1080 simplifies to 16 : 9, the standard for video. Other common ones: 4 : 3 for older displays, 3 : 2 for most cameras, 21 : 9 for ultrawide monitors, and 1 : 1 for square social media posts.
To resize while preserving the ratio, solve the proportion. Fitting a 16 : 9 video into a 1280-pixel width gives 1280 × 9 ÷ 16 = 720 pixels of height. Getting this wrong is what produces stretched or letterboxed images.
Dividing a total in a ratio
Add the parts to get the total number of shares, then allocate proportionally. Splitting $1,000 in the ratio 2 : 3 : 5 gives ten shares, so each is worth $100, and the amounts are $200, $300 and $500.
This is how profit shares, inheritance splits and mixed-ingredient quantities are calculated. Concrete mixed 1 : 2 : 4 by volume means one part cement to two parts sand to four parts aggregate — seven parts in total, with cement making up a seventh of the mix rather than a quarter.
Common questions
How do I simplify a ratio with decimals?
Multiply both terms by a power of ten until they are whole numbers, then divide by their greatest common divisor. So 2.5 : 1.5 becomes 25 : 15, which reduces to 5 : 3.
What does a 1:n ratio mean?
It normalises the first term to one, which makes comparison easy. Map scales work this way — 1:25,000 means one unit on the map is 25,000 units on the ground. The calculator shows both the 1:n and n:1 forms.
Can a ratio have more than two terms?
Yes. Three-part ratios are common in mixtures and share splits. They simplify the same way — divide every term by the greatest common divisor of all of them. Use the divide-a-total mode above for these.
What is the golden ratio?
Approximately 1 : 1.618, the value where the ratio of the whole to the larger part equals the ratio of the larger part to the smaller. It appears in some natural growth patterns and has a long history in design, though claims about its universal aesthetic superiority are considerably overstated.