Ratio Calculator

What this calculator does

This calculator handles the three most common questions you ask of a ratio:

1. Simplify — reduce a ratio to its smallest equivalent integers (e.g. 12:18 → 2:3) so it’s easier to read and compare.
2. Equivalent — solve for a missing term when two ratios are equal (e.g. 3:5 = ?:25 → 15:25).
3. Scale — resize one term of a ratio to a target value and compute the other to keep the proportion (e.g. 3:5 scaled so the first term is 30 → 30:50).

Each mode shows the working step by step. The three modes share one underlying idea — a ratio is a proportion, and proportional operations preserve the underlying decimal — so the simplified form and the scaled form always reduce to the same decimal value.

How ratios, fractions, decimals, and percentages relate

A ratio a:b is a comparison of two quantities. It can be re-expressed in four equivalent ways, and the calculator shows you all of them:

These are the same quantity in four costumes. Which one you use is a question of audience. Cookbooks use ratios and fractions (“3:1 sugar-to-water syrup”, “1⁄2 cup”). Engineers and lenders use decimals. Sales and marketing teams use percentages.

Simplifying a ratio

The simplification algorithm is the Euclidean GCD — the same greatest-common-divisor algorithm that simplifies fractions. Steps:

1. Find the GCD of the two terms.
2. Divide each term by the GCD.

Worked example: 12 : 18.

The simplified ratio is the canonical form. Two ratios are equal if and only if they simplify to the same canonical form, so simplifying is also how you check whether two ratios are equivalent without solving any equations.

Equivalent ratios — cross multiplication

Two ratios are equivalent when a/b = c/d. If you know three of the four terms, you can solve for the fourth by cross-multiplying:

a × d = b × c
→ c = (a × d) / b
→ d = (b × c) / a

Worked example: 3 : 5 = ? : 25 (find c).

So 3 : 5 = 15 : 25. This is the formula behind recipe scaling (“the recipe yields 5 portions and uses 3 cups of flour — how much flour for 25 portions?”), map scales, and ingredient dilutions.

Scaling a ratio

Scaling is the same arithmetic from a different angle: pick one term, decide what value it should become, and adjust the other term by the same multiplicative factor.

factor = target ÷ original value of the chosen axis
new pair = (a × factor, b × factor)

Worked example: 3 : 5 scaled so the first term is 30.

Final scaled ratio: 30 : 50. Its simplified form is still 3 : 5 — scaling preserves the proportion, it just expresses it at a different magnitude.

Where ratios show up in the real world

• Cooking. Recipe scaling is the canonical use case. Pancakes for 4 → pancakes for 10. Equivalent-ratio mode answers “how much flour do I need?”.
• Design. Aspect ratios — 16:9 for video, 4:3 for legacy display, 1:1 for social posts. Use the dedicated Aspect Ratio Calculator in our tool set when the question is specifically pixel dimensions; this generic calculator works for any proportional resize.
• Finance. The P/E ratio is price-to-earnings; the debt-to-income ratio is monthly debt payments divided by gross monthly income. Both are scaled ratios that get reported as decimals or percentages.
• Mixing and dilution. Stock solutions, paint, fertiliser, baby formula. A 1:4 dilution means 1 part concentrate to 4 parts water — total volume of 5 parts.
• Statistics. Odds (a:b for/against) and the odds ratio.
• Photography and cartography. Film aspect, scale of a map (1:25 000 means 1 cm on the map = 25 000 cm on the ground).

Common mistakes to avoid

Confusing the ratio with its decimal value. “3:1 odds in favour” means a 75 % chance, not a 30 % chance. A 4:1 mixture is 80 / 20, not 40 / 60. Always check whether the ratio adds to a whole — if it does, divide each part by the total to convert.

Adding ratios instead of finding a common scale. Two recipes calling for 2:1 and 3:1 sugar-to-flour don’t combine to 5:2 — you need a common base. If you want the average ratio for one of each recipe, you have to express both at the same total weight first.

Dropping the colon. The string “3 5” or “3, 5” is ambiguous — always write a ratio with a colon (3:5) or a slash with the words “to” between them. The calculator displays the colon form.

Privacy

This calculator runs as a few arithmetic operations in JavaScript on your device. There are no fetch calls, no analytics on the values you enter, no server-side logging.