Ratio Calculator

What is a ratio calculator?

A ratio calculator is a tool that reduces a ratio to its lowest terms and solves a proportion A:B = C:? for the missing value. You type two numbers to simplify the ratio, and an optional third number to find what completes an equivalent proportion. A ratio compares two quantities — like 2 parts to 3 parts, written 2:3 — and is the same idea as the fraction 2/3. This calculator handles whole numbers and decimals, making it useful for recipes, maps, mixing ratios, aspect ratios, and any “for every X, how many Y” question.

How does the ratio calculator work?

It uses two classic methods. To simplify, it divides both numbers by their greatest common divisor (GCD). To solve a proportion, it cross-multiplies: the missing term equals B times C divided by A.

The exact steps the widget follows are:

1. Simplify. Compute the GCD of A and B, then divide each by it. The formula is:

   Simplified = (A / GCD) : (B / GCD)

2. Handle decimals. If A or B is not a whole number, multiply both by a power of 10 (10 raised to the most decimal places present) so they become integers, then simplify. For 1.5:3, both are multiplied by 10 to get 15:30, which reduces to 1:2.

3. Solve the proportion. Given A:B = C:?, the missing fourth term d is found by cross-multiplication:

   d = (B × C) / A

   The result is shown as C : d (rounded to four decimals).

How do you simplify a ratio with the GCD?

Find the largest number that divides both terms evenly, then divide. For 12:18, the largest common factor is 6, so 12 ÷ 6 = 2 and 18 ÷ 6 = 3, giving the simplified ratio 2:3.

Worked example 1 — whole numbers. Take 200:150 (say, 200 ml water to 150 ml concentrate).

• GCD of 200 and 150 is 50.
• 200 ÷ 50 = 4 and 150 ÷ 50 = 3.
• Simplified ratio = 4:3.

Worked example 2 — decimals. Take 0.75:1.5.

• Most decimal places is 2, so multiply both by 100 → 75:150.
• GCD of 75 and 150 is 75.
• 75 ÷ 75 = 1 and 150 ÷ 75 = 2.
• Simplified ratio = 1:2.

A ratio that shares no factor other than 1 is already in lowest terms. For example, 16:9 (a common screen aspect ratio) cannot be reduced, so the calculator returns it unchanged.

How do you solve a proportion A:B = C:?

Use cross-multiplication: the unknown term equals B times C divided by A. For 12:18 = 4:?, the answer is 18 × 4 ÷ 12 = 6, so the full proportion is 12:18 = 4:6.

Worked example 3 — scaling up. A salad dressing uses oil to vinegar of 2:3. You pour 10 spoons of oil and want to keep the ratio.

• Proportion: 2:3 = 10:?
• Missing term = (3 × 10) ÷ 2 = 15 spoons of vinegar.

Worked example 4 — a map scale. A map is drawn at 1:4 (1 cm represents 4 km in this simplified example). A road measures 250 cm on the map.

• Proportion: 1:4 = 250:?
• Missing term = (4 × 250) ÷ 1 = 1000 km represented.

What does an equivalent-ratios table look like?

Equivalent ratios are different number pairs that reduce to the same lowest terms. Multiplying both sides of a ratio by the same factor keeps it equivalent. The table below shows the simplified ratio 2:3 (from the default 12:18) scaled across common multipliers.

Multiplier	A side	B side	Ratio
×1	2	3	2:3
×2	4	6	4:6
×3	6	9	6:9
×4	8	12	8:12
×5	10	15	10:15
×6	12	18	12:18

Every row reduces back to 2:3, which is exactly what the calculator confirms when you enter any of these pairs. Reading down the table is the same as solving a series of proportions such as 2:3 = 4:? or 2:3 = 10:?.

What are common uses for a ratio calculator?

Ratios appear anywhere quantities are compared or scaled. The most frequent uses are:

• Recipes and cooking. Scale ingredients up or down while keeping flavour balanced — for example, a 1:2 rice-to-water ratio for any pot size.
• Maps and models. Convert map distances to real distances, or scale a model to full size.
• Mixing and dilutions. Fuel-to-oil mixes, paint tints, fertiliser and cleaning concentrates, or cocktail builds.
• Finance and business. Split costs, profit, or shares between people, and compare quantities like debt-to-income.
• Design and screens. Aspect ratios such as 16:9 or 4:3, and keeping images proportional when resizing.

For percentage-style comparisons you may prefer the percentage calculator, and for reducing fractions specifically, the mixed number calculator is a close companion. Browse more tools on the math calculators page.

What mistakes and limitations should I watch for?

The most common error is mixing up the order of the terms — A:B is not the same as B:A. Keep your units consistent and always put the matching quantities in the same positions.

Tips and limitations to keep in mind:

• Use the same units. Compare cm to cm or ml to ml, not cm to metres. Convert first if needed.
• Order matters. In A:B = C:?, the value C must correspond to A’s position, and the answer corresponds to B’s position.
• Two terms only. This calculator simplifies and solves two-part ratios. For a three-part ratio like 2:3:5, divide all parts by the GCD of all three numbers manually.
• Rounding. Proportion answers are rounded to four decimals, so a long repeating result may be displayed slightly shortened.
• Non-zero inputs. A and B must both be non-zero numbers; a zero makes the ratio or division undefined, and the tool will prompt you to fix it.

A ratio expresses proportion, not absolute amounts: 2:3 and 200:300 describe the same balance at very different scales. Use the simplified form to understand the relationship, and use the proportion solver to convert it to the exact quantities you need.