Ratio Calculator - Solve, Simplify, and Scale Ratios

Solve proportions like A:B = C:D with one unknown, reduce any ratio to lowest terms, or scale a ratio up and down for recipes and mixes. Free, instant, and browser-based.

Enter three values and leave the unknown field empty. The calculator uses cross-multiplication: A x D = B x C.

:=:

D =

12

3 : 4 = 9 : 12

Working with Ratios and Proportions

A ratio expresses how two quantities relate: 3:4 means for every 3 units of the first there are 4 of the second. A proportion states that two ratios are equal, written A:B = C:D, and the cross-multiplication rule (A x D = B x C) lets you solve for any single unknown. If 3:4 = 9:D, then 3D = 36 and D = 12. This one rule powers unit pricing, map scales, currency conversion checks, and most homework problems labeled "solve the proportion".

Simplifying a ratio means dividing both parts by their greatest common divisor. A screen resolution of 1920:1080 divides by 120 to give 16:9, the standard widescreen aspect ratio. The calculator also handles decimals by scaling them to whole numbers first, so 2.5:1.5 simplifies to 5:3. The "n : 1" form shown below the result is useful for comparing ratios directly: 16:9 is 1.78:1 while 4:3 is 1.33:1, which tells you at a glance the first is wider.

Scaling keeps a ratio constant while changing the absolute amounts. Cooking is the everyday case: classic vinaigrette holds a 3:1 oil to vinegar ratio whether you make 40 ml or 400 ml, and rice cooks at about 1:1.5 rice to water by volume. Concrete mixing (1:2:3 cement to sand to gravel), paint tinting, fuel mixes for two-stroke engines (typically 1:50 oil to petrol), and photo enlargements all work the same way: multiply every part by the same factor and the mix or shape stays true.

For screen and image work specifically, the aspect presets cover 16:9, 4:3, 21:9, 1:1, 3:2, and vertical 9:16. If you need to calculate pixel dimensions at a given aspect ratio, the Aspect Ratio Calculator on ToolForte does exactly that, and the Percentage Calculator and Fraction Calculator handle the adjacent math. All tools are free and run in your browser with nothing uploaded.

How the Ratio Calculator Works

  1. 01Pick a mode: solve a proportion, simplify a ratio, or scale a ratio.
  2. 02For proportions, fill three of the four A:B = C:D fields and leave the unknown empty.
  3. 03For simplifying, enter any two numbers or tap an aspect-ratio preset like 1920:1080.
  4. 04For scaling, enter the ratio and a factor, such as 1.5 to take a recipe from 4 to 6 servings.

Solving, Simplifying, and Scaling Ratios

A proportion A:B = C:D holds when the cross products are equal: A x D = B x C. Leave any one value empty and the calculator solves it instantly, so 3:4 = 9:? gives 12. Simplify mode divides both parts by their greatest common divisor (1920:1080 becomes 16:9) and also shows the n:1 decimal form for easy comparison. Scale mode multiplies both parts by your factor, keeping the relationship intact while the absolute amounts change.

When to Use This Tool

Use it for recipe scaling, mixing ratios (concrete, paint, two-stroke fuel, cleaning solutions), map scales, unit pricing comparisons, screen and image aspect ratios, and proportion homework. Any problem shaped like 'if X goes with Y, what goes with Z?' is a proportion this tool solves in one step.

Common Use Cases

Tips

  • In solve mode, leave exactly one field empty; that is the one being solved.
  • Use the aspect presets to jump straight to common screen ratios.
  • For recipes, scale weights (grams) rather than cups for better precision.

Frequently Asked Questions

How do I solve a proportion with one unknown?→
Use cross-multiplication: in A:B = C:D, the products A x D and B x C are equal. To find D in 3:4 = 9:D, compute 4 x 9 = 36 and divide by 3 to get 12. The calculator does this automatically for whichever field you leave empty.
How do you simplify a ratio like 1920:1080?→
Divide both numbers by their greatest common divisor. For 1920 and 1080 that is 120, giving 16:9. The calculator also handles decimals by scaling first, so 2.5:1.5 becomes 5:3.
How do I scale a recipe from 4 to 6 servings?→
The factor is 6 divided by 4, which is 1.5. Multiply every ingredient by 1.5: 200 g flour becomes 300 g, 2 eggs become 3. Enter any ingredient pair as a ratio and apply the factor in scale mode, or convert everything to grams first for the least error.
What is the difference between a ratio and a fraction?→
A fraction is a part of a whole; a ratio compares two parts to each other. In a class with 12 boys and 18 girls the ratio of boys to girls is 12:18 = 2:3, while the fraction of boys is 12 out of 30, which is 2/5. Confusing the two is the most common ratio mistake.
What does 16:9 mean for screens?→
For every 16 units of width there are 9 of height. A 1920x1080 monitor, a 1280x720 video, and a 3840x2160 TV are all 16:9. The n:1 form, 1.78:1, makes comparisons easy: cinema 21:9 is 2.33:1, so visibly wider.

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