How to use the ratio Calculator
- Enter the two known terms of the ratio as A and B, for example 3 and 4 for 3 : 4.
- Enter C, the term you are scaling to. The calculator finds the matching fourth term so that A : B = C : ?. Leave C empty if you only want to simplify A : B.
- The result updates instantly as you type. There is no button to press.
- Use Copy result to copy the figures, or Copy link to share a link that reopens the ratio Calculator with the same inputs.
How it works
A ratio compares two quantities by division. A recipe that uses 3 cups of flour to 4 cups of water has a flour-to-water ratio of 3 : 4. Ratios stay the same when both sides are multiplied or divided by the same number, so 3 : 4, 6 : 8 and 15 : 20 all describe the same mix. A statement that two ratios are equal is called a proportion.
The most common ratio problem is scaling: you know one full ratio and one part of a second, and you need the missing part. This calculator solves A : B = C : ? by cross-multiplication. The same method resizes recipes, scales maps and drawings, converts currency at a fixed rate, mixes concrete, fertiliser or paint, and resizes images while keeping their aspect ratio.
It also simplifies A : B to lowest whole-number terms by dividing both sides by their greatest common divisor, converting decimals to whole numbers first. And it shows each side's share of the total. A 3 : 4 split means A gets 3 of every 7 parts (42.9%) and B gets 4 (57.1%), which is how you divide a sum of money or a quantity in a given ratio.
Formula
To simplify, divide both terms by their greatest common divisor: 18 : 24 → (18 ÷ 6) : (24 ÷ 6) = 3 : 4.
Example
If 3 : 4 = 15 : ?, then ? = 4 × 15 ÷ 3 = 20, because both sides were multiplied by 5. To split $700 in the ratio 3 : 4, the shares are 3/7 and 4/7: $300 and $400. To resize a 1920 × 1080 image to 1280 pixels wide, solve 1920 : 1080 = 1280 : ?, giving a height of 720.
Frequently asked questions
How do I simplify a ratio with decimals?
Multiply both sides by 10, 100 or more until both are whole numbers, then divide by their greatest common divisor. 1.5 : 2.5 becomes 15 : 25, which simplifies to 3 : 5.
What is the difference between a ratio and a fraction?
A ratio compares two parts with each other, while a fraction compares a part with the whole. In a 3 : 4 ratio, the first part is 3/7 of the total.
How do I divide an amount in a ratio?
Add the ratio terms to find the total number of parts, divide the amount by that total, then multiply by each term. For 5 : 3 of 400: 400 ÷ 8 = 50, so the shares are 250 and 150.