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DailyCalc

Ratio Calculator

Simplify ratios, scale them, and solve proportions for a missing term.

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Your details

Bar split into two parts showing a ratio A horizontal bar divided into two unequal segments labelled A and B, showing how a ratio splits a total into parts. AB1 part3 partsthe total — 4 parts

Result

Simplified ratio
1 : 3
As a decimal
0.333333
As a fraction of the total
25.00% : 75.00%
Scaled to 100
25.00 : 75.00

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Formula — written step by step

Simplifying 16 : 48…

Divide both terms by their greatest common divisor

GCD of 16 and 48 = 16

16 ÷ 16 = 1

48 ÷ 16 = 3

16 : 48 = 1 : 3

The two terms are parts of a total of four, so A is one quarter of the whole — 25% — not one third. A ratio compares the parts to each other; a fraction compares a part to the total.

The formula for each shape

  • Simplify a ratio

    Bar split into two parts showing a ratio A horizontal bar divided into two unequal segments labelled A and B, showing how a ratio splits a total into parts. AB1 part3 partsthe total — 4 parts

    a : b → (a ÷ g) : (b ÷ g)

    Needs both terms, where g is their greatest common divisor

  • Solve a proportion

    A : B = C : D ⟹ A × D = B × C

    Needs any three of the four terms

A worked example

Solve 3 : 4 = 9 : D

A
3
B
4
C
9
D
unknown
  1. A × D = B × C
  2. 3 × D = 4 × 9
  3. 3 × D = 36
  4. D = 36 ÷ 3

D = 12

Cross-multiplying works whichever term is missing — the two products are always equal, so rearranging for the unknown is a single division.

How to use this calculator

  1. Choose "Simplify a ratio" to reduce a ratio to its lowest terms, or "Solve A : B = C : D" to find a missing term.
  2. In simplify mode, enter both terms. Decimals are fine — they are scaled to whole numbers first, so 2.5 : 5 reduces to 1 : 2.
  3. In proportion mode, leave exactly one of the four boxes empty and it will be solved for.
  4. Fill all four instead and the calculator tells you whether the proportion is true, showing both cross-products.

Simplifying and cross-multiplying

A ratio simplifies by dividing both terms by their greatest common divisor: 16:48 becomes 1:3. Decimal ratios are scaled to whole numbers first, so 2.5:5 also reduces to 1:2.

Proportions are solved by cross-multiplication. In A:B = C:D, the products A×D and B×C are always equal, so any one missing term follows from the other three.

Ratios with more than two terms

A three-part ratio like 2:3:5 works the same way — divide all terms by their greatest common divisor to simplify, and the parts sum to the whole. Here the total is ten parts, so the shares are 20%, 30% and 50%.

This is how profit-sharing, inheritance splits and concrete mixes are specified. To apply a ratio to a quantity, divide the quantity by the total number of parts, then multiply by each term.

Scaling recipes and mixtures

Ratios are what make recipes scalable. A 1:2 rice-to-water ratio holds whether you cook one cup or five, which is why professional kitchens work in ratios rather than fixed quantities.

The same logic applies to fuel mixes, fertiliser blends and mortar. Keep the ratio and change the total, and the properties of the mixture stay the same.

Frequently asked questions

What is the difference between a ratio and a fraction?

A ratio compares two parts to each other (1:3 means one part to three parts, four parts total). A fraction compares a part to the whole (1/4 of the total). The same situation gives 1:3 as a ratio and 1/4 as a fraction.

How do I scale a ratio to a specific total?

Add the parts to get the total number of shares, divide your quantity by that, then multiply by each part. For 2:3 across 100 units: 100 ÷ 5 = 20, giving 40 and 60.

Can a ratio have decimals?

Yes, though it is conventionally converted to whole numbers. 1.5:2 is usually written 3:4 after multiplying both sides by two.