Ratio Calculator

Name: Ratio Calculator
Author: True Calculator automated test suite

Simplify ratios or solve a:b = c:d for the missing value. Perfect for recipes, scale models and proportional problems.

Mode

First term (a)

Second term (b)

Simplified ratio

2 : 3

Original 6 : 9

Percentage split

40% / 60%

Share of first term / second term

Simplifying divides both terms by their greatest common factor, so 6:9 becomes 2:3.

How it works

Simplify: divide both parts by GCD. Solve a:b = c:d → d = (c × b) ÷ a.

Example: 6:9 → 2:3. If 2:3 = 4:d, then d = 6.

Last updated: February 2026

How this calculator is verified

Checked by True Calculator automated test suite on 23 August 2026

Formula verified against a published worked example in the automated test suite
Edge cases (zero, negative, boundary and unit-mismatch inputs) covered by unit tests

The full verification method is on our how we verify page. Found an error? Tell us and we will re-check it.

When to Use This Calculator

A caterer in Delhi mixes 150 grams of rice flour with 100 grams of gram flour for a snack. Entering 150 and 100 with simplify gives 3:2, since both terms divide by 50. To scale the recipe, the caterer uses solve mode with 3:2 = 9:x, so the missing term x is 6 grams. Cross-multiplication checks this: 3 times 6 equals 18, and 2 times 9 also equals 18. The same tool simplifies any two-term ratio and solves proportional problems for drawings, mixtures or splitting amounts in fixed shares.

How to Use This Calculator

Step 1: Enter the two terms of your ratio in the first pair of fields.
Step 2: Choose simplify to reduce the ratio to its lowest terms.
Step 3: For a missing value, pick the solve mode and enter the three known numbers from a:b = c:d.
Step 4: Read the simplified ratio or the solved missing term, and confirm it by cross-multiplication.

Worked Example

Tips and Common Mistakes

•Tip 1: Ratios reduce only when both terms share a common factor, so 3:2 cannot be simplified further.
•Tip 2: When a ratio mixes units such as grams and kilograms, convert everything to one unit before simplifying.
•Tip 3: For a:b = c:d, cross-multiply to find the missing term, then substitute it back to confirm the proportion.
✗Mistake 1: Converting the ratio into a rounded decimal and back, which loses the exact proportion that ratios express.
✗Mistake 2: Simplifying before checking units, since mixing grams with kilograms changes the ratio by a factor of 1000.

Frequently Asked Questions

How do I simplify a ratio?

Divide both parts by their greatest common factor. The ratio 6:9 simplifies to 2:3 because both divide by 3.

How do I solve a:b = c:d for the missing value?

Cross-multiply: d = (c × b) ÷ a. If 2:3 = 4:d, then d = (4 × 3) ÷ 2 = 6.

What does a ratio mean in everyday life?

A ratio compares quantities, like mixing paint 2:1 (two parts paint, one part thinner) or diluting juice concentrate 1:4.

How is a ratio different from a fraction?

A ratio compares two quantities (2:3), while a fraction is a single number. A ratio can be written as a fraction — in 2:3, the first part is 2/5 of the whole.

Compare these tools

Percentage Calculator — Calculate percentages, percentage difference and percentage change instantly
Rounding Calculator — Round any number to the nearest value, or up and down, to any decimal places
Standard Form Calculator — Convert numbers to and from standard form (scientific notation) with one click

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