Ratio Calculator
Simplify ratios, solve proportions, scale, and convert. Results update instantly.
Simplify a Ratio
Enter a ratio A:B to reduce it to its simplest form.
Solve a Proportion (A:B = C:?)
Enter any three values to find the fourth.
Scale a Ratio
Multiply or divide both parts of a ratio by a scale factor.
Three-Part Ratio (A:B:C)
Simplify a three-part ratio and split a total into three shares.
Aspect Ratio Calculator
Find the missing dimension or the simplified aspect ratio for screens and images.
Scale to new width:
How to Use This Ratio Calculator
This ratio calculator provides five tools in one page: ratio simplification, proportion solving, ratio scaling, three-part ratios, and an aspect ratio calculator. All results update live as you type.
Simplifying Ratios
A ratio is in its simplest form when the two (or more) numbers share no common factor other than 1. To simplify a ratio, divide all parts by the greatest common divisor (GCD). For example, 12:8 has GCD = 4, so the simplified ratio is 3:2. Simplified ratios are easier to compare, visualize, and communicate.
The calculator also converts the ratio to a fraction (A/B), a decimal (A divided by B), and shows A as a percentage of the total (A + B). These conversions are useful in probability, cooking, finance, and many other contexts.
Solving Proportions
A proportion states that two ratios are equal: A:B = C:D. If one value is unknown, you can find it by cross-multiplication. The rule is: A x D = B x C. Rearranging gives D = (B x C) / A, or any other missing term. For example, if a recipe calls for 3 cups of flour for every 4 cups of water, and you want to use 9 cups of flour, how much water do you need? Solving 3:4 = 9:D gives D = (4 x 9) / 3 = 12 cups.
Proportions appear throughout everyday life: unit conversions, scaling recipes, map distances, similar triangles, and currency exchange rates all rely on proportion arithmetic.
Scaling Ratios
Scaling a ratio means multiplying or dividing both parts by the same number to produce an equivalent ratio. The ratio 3:2 scaled by 5 becomes 15:10, which still represents the same relationship. This is useful when you need specific whole-number quantities that maintain a given proportion, such as mixing paint colors in a specific ratio but for a larger batch.
Three-Part Ratios
Three-part ratios divide a quantity into three distinct portions. They appear in business (profit sharing, ingredient mixes), construction (concrete mixes like 1:2:3 cement:sand:aggregate), and finance (portfolio allocation). The calculator simplifies the three-part ratio and, if you enter a total, computes each share. Splitting $600 in the ratio 1:2:3 gives 6 total parts; each part is worth $100, so the shares are $100, $200, and $300.
Aspect Ratio Calculator
An aspect ratio is the proportional relationship between width and height, usually expressed as W:H. The most common aspect ratios are 16:9 (widescreen HD video, most monitors and televisions), 4:3 (classic television and computer monitors), 1:1 (square format, social media posts), 21:9 (ultra-wide cinema monitors), and 9:16 (vertical video for mobile). Knowing your aspect ratio lets you resize images and videos without distortion. If a 1920x1080 image needs to fit a 1280-pixel-wide container, the proportional height is 720 pixels (because 1280 / 1920 x 1080 = 720), preserving the 16:9 ratio.
Ratios vs. Fractions vs. Percentages
Ratios, fractions, and percentages are all ways of expressing the same relationship between two quantities. The ratio 3:2 is equivalent to the fraction 3/2 (or 1.5 as a decimal), and 3 represents 60% of the total (3 + 2 = 5; 3/5 = 60%). Choosing the right representation depends on context: ratios are natural for comparisons and mixing (paint, concrete, recipes), fractions for arithmetic, and percentages for communication and comparison at a glance.
Common Uses of Ratios
- Cooking and baking: Scaling recipes up or down while maintaining the correct ingredient ratios.
- Finance: Debt-to-income ratio, price-to-earnings ratio, asset allocation ratios.
- Maps and scale drawings: A map scale of 1:50,000 means 1 cm on the map equals 50,000 cm (500 m) in reality.
- Photography and video: Sensor and screen aspect ratios determine how images are cropped and displayed.
- Construction: Concrete mix ratios (cement:sand:aggregate), mortar ratios, and similar material formulas.
- Education: Student-to-teacher ratios, pass rate calculations, and statistics.