Need to simplify or compare ratios? This ratio calculator helps you reduce ratios to their simplest form, check if two ratios are equivalent, or find a missing value in a ratio equation.
Ratios are used in math, finance, recipes, construction, and statistics to compare two or more numbers. Instead of working them out manually, this calculator gives instant answers with step-by-step clarity.
What is a Ratio?
A ratio is a way of comparing two quantities by showing how many times one value contains or is contained within the other. For example, the ratio 2:3 means for every 2 parts of one quantity, there are 3 parts of another.
How Does the Ratio Calculator Work?
The calculator offers three main functions:
- Simplify a ratio (e.g., 12:16 becomes 3:4)
- Compare two ratios (e.g., check if 4:6 is equal to 10:15)
- Find a missing value (solve a:b = c:x)
By covering simplification, comparison, and proportion solving, it works as an all-in-one tool for ratio calculations.
Ratio Calculator
This free ratio calculator simplifies ratios, compares two ratios, or finds the missing value in a ratio equation.
How to Simplify a Ratio
To simplify a ratio, divide both numbers by their greatest common divisor (GCD). For example, 12:16 can be simplified by dividing both numbers by 4, resulting in 3:4.
| Original Ratio | Divisor | Simplified Ratio |
|---|---|---|
| 12:16 | ÷4 | 3:4 |
| 18:24 | ÷6 | 3:4 |
| 50:100 | ÷50 | 1:2 |
How to Compare Two Ratios
Two ratios are equal if they simplify to the same value. For example, 4:6 and 10:15 are equivalent because both reduce to 2:3.
| Ratio 1 | Ratio 2 | Are They Equal? |
|---|---|---|
| 4:6 | 10:15 | Yes |
| 5:7 | 15:21 | Yes |
| 8:12 | 6:10 | No |
How to Find a Missing Value in a Ratio
To solve for a missing value in a ratio equation a:b = c:x, use cross multiplication. The formula is x = (b × c) ÷ a.
| Equation | Calculation | Result |
|---|---|---|
| 4:6 = 10:x | (6 × 10) ÷ 4 | x = 15 |
| 3:5 = 12:x | (5 × 12) ÷ 3 | x = 20 |
| 7:9 = 21:x | (9 × 21) ÷ 7 | x = 27 |
Common Uses of Ratios
Ratios are used in many real-world scenarios, such as:
- Cooking – Adjusting recipe quantities (e.g., 2:1 flour to sugar)
- Finance – Debt-to-income or profit ratios
- Education – Student-to-teacher ratios
- Construction – Cement-to-sand mixing ratios
- Statistics – Probability and odds ratios
Ratio Calculator FAQs
To simplify a ratio, divide both numbers by their greatest common divisor. For example, 12:16 simplifies to 3:4.
Two ratios are equal if they reduce to the same simplified form. For example, 4:6 and 10:15 are equal because both reduce to 2:3.
Use cross multiplication. If a:b = c:x, then x = (b × c) ÷ a.
Ratios are used in recipes, finance, statistics, construction, and education. They help compare quantities in simple proportional terms.
A ratio compares two quantities, while a proportion states that two ratios are equal.