Ratio Calculator
Simplify a ratio to its lowest terms or solve a proportion A : B = C : D — with the fraction, decimal, percentage, and every step shown.
- 01Simplify any ratio (2 or 3 terms) to its lowest terms instantly.
- 02Solve a proportion A : B = C : D for the missing value.
- 03Convert a ratio to a fraction, decimal, and percentage in one click.
- 04See step-by-step working using the greatest common divisor and cross-multiplication.
- 05100% free and private — every calculation runs in your browser.
Ratio Calculator
Try an example ratio
Simplified Ratio
2:3
12:18 reduced to its lowest terms
Original Ratio
12:18
Greatest Common Divisor
6
As a Fraction
2/3
As a Decimal
0.666667
As a Percentage
66.666667%
Step-by-step calculation
- 01Read the ratio 12:18 as 2 terms.
- 02Find the greatest common divisor (GCD) of the terms of 12:18 = 6.
- 03Divide each term of 12:18 by 6 → 2:3.
- 04Write 2:3 as the fraction 2/3 = 0.666667.
Why Use This Ratio Calculator
Simplify Any Ratio
Reduce a ratio to its lowest terms by dividing every term by the greatest common divisor. Works with 2-term ratios like 12:18 and 3-term ratios like 12:18:24, so you can simplify ingredient ratios, screen aspect ratios, mixing ratios, and more in a single click.
Solve Proportions
Given three of the four numbers in a proportion A : B = C : D, the calculator solves for the missing value using cross-multiplication. Perfect for scaling recipes, converting units, resizing images, and any problem that involves equivalent ratios.
Ratio to Fraction, Decimal, Percentage
For a two-term ratio you instantly get the equivalent fraction, decimal, and percentage. Convert a ratio like 3:4 to the fraction 3/4, the decimal 0.75, and 75% without any extra steps.
Step-by-Step Working
Every result shows the working: how the greatest common divisor is found, how each term is divided, and how the proportion is cross-multiplied and solved. Ideal for homework, exam revision, and checking your own answers.
Instant and Private
Everything runs entirely in your browser with no server round-trips. Your numbers never leave your device, results appear instantly, and there is no signup or installation required.
Free with No Limits
Simplify ratios and solve as many proportions as you need — no daily limits, no account, and no paywall. The full ratio calculator is completely free.
What Is a Ratio?
A ratio compares two or more quantities, showing how much of one thing there is relative to another. It is written with a colon, such as 3:2, and tells you that for every 3 units of the first quantity there are 2 units of the second. Ratios are everywhere — in cooking, finance, maps, screen sizes, mixing solutions, and probability.
Whether you are a student learning ratio and proportion, a cook scaling a recipe, or a designer matching aspect ratios, this ratio calculator gives instant, step-by-step results for simplifying ratios and solving proportions.
- Simplifying a Ratio
- To simplify a ratio you divide every term by their greatest common divisor (GCD), the largest number that divides them all without a remainder. For example, 12:18 has a GCD of 6, so it simplifies to 2:3. A simplified ratio is in its lowest terms and is easier to read and compare.
- Equivalent Ratios
- Two ratios are equivalent if one can be obtained from the other by multiplying or dividing every term by the same number. 2:3, 4:6, and 12:18 are all equivalent ratios. Simplifying reveals the simplest equivalent ratio, while scaling up creates larger equivalent ratios.
- Ratios and Proportions
- A proportion is a statement that two ratios are equal, written A : B = C : D. If you know three of the four values you can solve for the fourth by cross-multiplication: A × D = B × C, so D = (B × C) ÷ A. Proportions are used to scale recipes, resize images, and convert between units.
- Ratio, Fraction, and Percentage
- A two-term ratio a:b is closely related to the fraction a/b. Dividing gives a decimal, and multiplying that decimal by 100 gives a percentage. So the ratio 3:4 is the fraction 3/4, the decimal 0.75, and 75% — different ways of expressing the same comparison.
How to Use the Ratio Calculator
- 01
Choose a mode
Pick Simplify ratio to reduce a ratio to its lowest terms, or Solve proportion to find a missing value in A : B = C : D. Switch between the two tabs at any time.
- 02
Enter your numbers
For Simplify, type a ratio such as 12:18 or 12:18:24. For Solve proportion, enter the three known values A, B, and C, and the calculator finds D. Whole numbers, decimals, and a colon, slash, or the word 'to' as separators are all accepted.
- 03
Click the button
Press Simplify or Solve. The tool reduces the ratio using the greatest common divisor, or solves the proportion by cross-multiplication, instantly in your browser.
- 04
Read the result and steps
The headline card shows the simplified ratio or the solved value. Below it you get the fraction, decimal, and percentage (for two-term ratios) or the completed proportion, plus a step-by-step breakdown of exactly how the answer was found.
Tips for Working With Ratios
Always Simplify to Lowest Terms
A ratio in its lowest terms is easier to read, compare, and use. Dividing by the greatest common divisor gives the simplest equivalent ratio — for example, prefer 2:3 over 12:18.
Keep the Order Consistent
A ratio is direction-sensitive: 3:2 is not the same as 2:3. When comparing or scaling ratios, make sure the quantities stay in the same order so the comparison remains meaningful.
Use Proportions to Scale
To scale a recipe or resize an image while keeping the same shape, set up a proportion and solve for the missing value. This preserves the original ratio exactly instead of guessing.
Match Units Before Comparing
Ratios only make sense when both quantities are in the same units. Convert to a common unit first — comparing 1 metre to 50 centimetres should be treated as 100:50, which simplifies to 2:1.
Convert When It Helps
Sometimes a fraction, decimal, or percentage communicates better than a ratio. Use the fraction and percentage outputs when you need to express a part of a whole rather than a comparison.
Watch for Zero Terms
A ratio term of zero cannot be simplified meaningfully, and a zero in the first position of a proportion would divide by zero. Enter non-zero values so the calculation stays valid.
Ratio Formulas and Definitions
Definition of a ratio
A ratio compares quantities of the same kind, written a:b. It shows how many units of the first quantity correspond to a number of units of the second, and can be scaled up or down without changing the relationship.
What simplifying a ratio means
- Dividing every term by their greatest common divisor (GCD).
- Producing the simplest equivalent ratio in lowest terms.
- Making ratios easier to read and compare (e.g. 12:18 → 2:3).
- Preserving the exact relationship between the quantities.
Ratios versus proportions
A ratio compares two quantities; a proportion states that two ratios are equal (A : B = C : D). Use simplification to reduce a single ratio, and cross-multiplication to solve a proportion for a missing value.
Key Ratio Formulas
Simplified ratio
a:b = (a ÷ g):(b ÷ g), where g = GCD(a, b)
Example: 12:18, g = 6 → 2:3.
Ratio as a fraction
a:b = a / b
Example: 3:4 = 3/4.
Ratio as a decimal
a:b → a ÷ b
Example: 3:4 = 0.75.
Ratio as a percentage
a:b → (a ÷ b) × 100%
Example: 3:4 = 75%.
Proportion
A : B = C : D ⇒ A × D = B × C
Cross-multiply to relate the two ratios.
Solving a proportion
D = (B × C) ÷ A
Example: 2:3 = 8:D → D = (3 × 8) ÷ 2 = 12.
Ratio Calculator FAQ
Q01How do I simplify a ratio?
To simplify a ratio, find the greatest common divisor (GCD) of all its terms — the largest number that divides each term exactly — then divide every term by it. For example, 12:18 has a GCD of 6, so dividing both terms by 6 gives the simplified ratio 2:3. This calculator does it automatically and shows the working, including for three-term ratios like 12:18:24.
Q02How do I solve a proportion?
A proportion A : B = C : D is solved by cross-multiplication. Since A × D = B × C, the missing value is D = (B × C) ÷ A. Enter the three known numbers in the Solve proportion tab and the calculator finds the fourth value and shows the completed proportion.
Q03How do I convert a ratio to a fraction?
A two-term ratio a:b is the same as the fraction a/b. So the ratio 3:4 becomes the fraction 3/4. Simplifying the ratio first gives the fraction in its lowest terms. This calculator shows the fraction, decimal, and percentage for every two-term ratio.
Q04How do I convert a ratio to a percentage?
For a two-term ratio a:b, divide a by b to get a decimal, then multiply by 100 to get a percentage. For example, 3:4 = 3 ÷ 4 = 0.75 = 75%. The calculator displays the decimal and percentage automatically.
Q05What are equivalent ratios?
Equivalent ratios represent the same comparison even though the numbers differ. You get an equivalent ratio by multiplying or dividing every term by the same non-zero number. For example, 2:3, 4:6, and 12:18 are all equivalent. Simplifying finds the simplest equivalent ratio.
Q06Can I simplify a ratio with three terms?
Yes. Enter a ratio like 12:18:24 and the calculator divides all three terms by their greatest common divisor to give 2:3:4. Three-term ratios are common in recipes and mixing problems, and the same GCD method applies.
Q07Is my data sent to a server?
No. The calculator runs entirely in your browser using JavaScript. Your numbers are never uploaded or stored anywhere, so it is safe to use with private or sensitive data.
Q08Is this ratio calculator free?
Yes, it is completely free with no limits, no signup, and no premium tier. Simplify ratios and solve as many proportions as you like.