Mathematics CalcyZone Calculator

Ratio Calculator

Solve ratio scales, scale up or down ratios, and find missing ratio terms A:B = C:D.

Ratio A

Ratio B

Calculation Solution

2:3

Greatest Common Divisor: 50

Mathematical Formula

A / B = C / D => D = (B * C) / A

Overview & Explanation

A ratio expresses the quantitative relationship between two amounts showing the number of times one value contains another.

How It Works

Set up the equivalent ratios A/B = C/D.
Cross multiply to solve for the unknown term D = (B * C) / A.

Practical Applications

Scaling cooking recipes.
Map scale calculations.
Mixing ingredients in chemistry.

What a ratio expresses

A ratio compares quantities of the same kind, such as 2:3 for the share of two partners or 1:4 for cement to sand. It says nothing about the actual amounts until you know the total or one of the parts.

Simplifying and sharing

Simplify a ratio by dividing all parts by their greatest common divisor: 24:36 becomes 2:3 after dividing by 12. Ratios with decimals or fractions are easier after scaling up: 1.5:2 becomes 3:4.

To share an amount in a ratio, add the parts and divide. Splitting ₹12,000 in the ratio 2:3 gives 5 parts of ₹2,400 each, so the shares are ₹4,800 and ₹7,200. The same method works for three or more parts: ₹9,000 in 1:2:3 gives ₹1,500, ₹3,000 and ₹4,500.

Ratios in everyday life

Recipes, concrete and mortar mixes, aspect ratios of screens (16:9), map scales (1:50,000), gear ratios and financial ratios such as debt-to-equity all use the same idea. To scale a ratio, multiply every part by the same number: a 16:9 screen 32 inches wide is 18 inches tall. A ratio can also be turned into a fraction of the whole: in 2:3, the first part is 2/5, or 40%, of the total.