Ratio Calculator — Free Online Ratio and Proportion Tool

How to Use the Ratio Calculator

1. Select the mode: Choose one of three calculation modes from the dropdown. Simplify Ratio reduces your ratio to its lowest terms using the greatest common divisor. Scale Ratio multiplies both terms proportionally so the first term matches your target value. Find Missing Value solves the proportion A:B = C:? to find the unknown fourth term.
2. Enter the ratio terms: Type the first term (A) and second term (B) of your ratio into the input fields. These can be any positive integers. The ratio A:B represents the relationship between the two quantities. For example, if a recipe uses 3 cups of flour for every 2 cups of sugar, enter A = 3 and B = 2.
3. Enter additional values: In Scale mode, enter the target value you want the first term to be — the calculator will compute the proportional second term. In Find Missing Value mode, enter the known third term (C) and the calculator will determine what D must be so that A:B = C:D.
4. Read the results: The primary result is shown prominently based on your mode. Below it, you will always see the simplified ratio, the decimal ratio (A divided by B), and the percentage split showing what fraction of the total each term represents. These additional metrics provide context and make it easy to understand the ratio in different formats.

All results update in real time as you type. The calculator is useful for cooking, construction, design, finance, and any situation where proportional relationships matter.

Ratio and Proportion Formulas

Variables Explained

• A: The first term of the ratio. In a proportion A:B = C:D, this is the first known quantity that establishes the proportional relationship.
• B: The second term of the ratio. Together with A, it defines the proportional relationship that will be applied to other values.
• GCD: The Greatest Common Divisor of A and B. This is the largest integer that divides both terms evenly, used to reduce the ratio to its simplest form.
• T: The target value used in scaling. When you want the first term to equal a specific number, the second term is calculated proportionally.
• D: The unknown fourth term in a proportion. Calculated using cross-multiplication: D = (B x C) / A.

Step-by-Step Example

If a map uses a scale of 1:50,000 and you measure 3.5 cm on the map, find the real distance:

1. Set up the proportion: 1 : 50,000 = 3.5 : D
2. Cross multiply: D = 50,000 x 3.5 / 1
3. Calculate: D = 175,000 cm
4. Convert: 175,000 cm = 1,750 m = 1.75 km

The real-world distance is 1.75 kilometers. This proportion method works for any map scale and any measured distance on the map.

Practical Examples

Example 1: Laura's Recipe Scaling

Laura has a cookie recipe that serves 12 people with a flour-to-sugar ratio of 3:1 (3 cups flour, 1 cup sugar). She needs to serve 20 people. Using Scale mode with A = 12, B = 3 (cups flour), target = 20:

• Scale factor: 20 / 12 = 1.667
• Flour: 3 x 1.667 = 5 cups
• Sugar: 1 x 1.667 = 1.67 cups (about 1 and 2/3 cups)
• All ingredient quantities maintain the same 3:1 ratio

Laura can confidently scale her recipe knowing the proportions are preserved. The 3:1 flour-to-sugar ratio holds whether she makes a small batch or a party-size batch. For precise fractional measurements, she can use our fraction calculator.

Example 2: James's Investment Allocation

James wants to allocate his $10,000 investment portfolio in a 60:40 ratio between stocks and bonds. He simplifies the ratio and calculates the dollar amounts:

• Ratio: 60:40 simplifies to 3:2
• Total parts: 3 + 2 = 5
• Stocks: (3/5) x $10,000 = $6,000 (60%)
• Bonds: (2/5) x $10,000 = $4,000 (40%)

James allocates $6,000 to stocks and $4,000 to bonds. When he contributes an additional $5,000 next year, he simply applies the same 3:2 ratio: $3,000 more to stocks and $2,000 more to bonds to maintain his target allocation.

Example 3: Hannah's Concrete Mix

Hannah is pouring a concrete patio and the standard mix ratio is 1:2:3 (cement:sand:gravel). She needs 180 pounds of total material. Working with two-term ratios, she first calculates cement versus aggregate (sand + gravel):

• Cement : Aggregate = 1 : 5 (since 2+3=5)
• Total parts: 1 + 5 = 6
• Cement: (1/6) x 180 = 30 pounds
• Sand: (2/6) x 180 = 60 pounds
• Gravel: (3/6) x 180 = 90 pounds

Hannah needs 30 pounds of cement, 60 pounds of sand, and 90 pounds of gravel. The ratio ensures the concrete has the right proportions for strength and workability. She can verify: 30 + 60 + 90 = 180 pounds total.

Common Ratios Reference Table

Tips and Complete Guide

Understanding Proportional Relationships

A proportion is a statement that two ratios are equal: A:B = C:D. This means the relationship between A and B is the same as between C and D. Proportions are fundamental to scaling — whether you are resizing an image, converting units, or adjusting recipes. The key property is cross-multiplication: A x D = B x C. If any three values are known, the fourth can be found. This principle underlies similarity in geometry, unit conversion, map reading, and countless other applications across mathematics and daily life.

Ratios in Design and Photography

Aspect ratios define the width-to-height proportion of screens, images, and layouts. Common aspect ratios include 16:9 (HD/4K video), 4:3 (standard definition), 3:2 (35mm film and many digital cameras), 1:1 (square, Instagram), and 21:9 (cinema). When resizing images, maintaining the aspect ratio prevents distortion. If an image is 1920x1080 (16:9) and you want it 800 pixels wide, the height should be 800 x (9/16) = 450 pixels. Understanding ratios ensures your designs look professional without stretching or cropping artifacts.

Financial Ratios and Analysis

Financial analysts use ratios extensively to evaluate companies. The debt-to-equity ratio measures financial leverage (e.g., 0.5:1 means $0.50 of debt for every $1 of equity). The price-to-earnings ratio compares stock price to earnings per share. The current ratio (current assets : current liabilities) measures short-term liquidity. A healthy current ratio is typically above 1.5:1. These ratios allow comparison across companies of different sizes because they normalize values into proportional relationships. For financial calculations involving these ratios, explore our financial calculators.

Converting Between Ratios, Fractions, and Percentages

Ratios, fractions, and percentages are three ways to express proportional relationships. A ratio of 3:5 means 3 parts to 5 parts. As a fraction of the total, the first part is 3/8 and the second is 5/8. As percentages, that is 37.5% and 62.5%. To convert a ratio A:B to a fraction of the whole: first part = A/(A+B), second part = B/(A+B). Our calculator shows all three representations simultaneously, making conversions effortless. For more detailed percentage work, try our percentage calculator.

Common Mistakes to Avoid

• Confusing ratio order: 3:5 is not the same as 5:3. The order matters because each position represents a specific quantity. A mix ratio of 3 parts cement to 5 parts sand is very different from 5 parts cement to 3 parts sand.
• Adding ratios incorrectly: You cannot combine ratios by simply adding terms. If group A has a 2:1 success ratio and group B has a 3:1 ratio, the combined ratio is not 5:2. You need the actual counts to find the combined ratio (this is related to Simpson's paradox).
• Assuming ratios are absolute: A 3:2 ratio tells you the proportion but not the actual amounts. You need at least one absolute value (like the total) to determine specific quantities. Without knowing the total, 3:2 could mean 3 and 2, or 30 and 20, or 300 and 200.
• Not simplifying before comparing: To compare ratios, always simplify first. 8:12 and 6:9 look different but both simplify to 2:3, meaning they represent the same proportional relationship.
• Dividing by zero in proportions: In A:B = C:D, if A = 0 then D cannot be uniquely determined (any value of D satisfies 0 x D = B x C = 0). Always check for zero terms before solving proportions.

Frequently Asked Questions