Ratio Calculator
Simplify a two-part ratio by dividing both parts by their greatest common factor. The same reduced pair writes as a fraction and scales into equivalent ratios.
8 : 12 simplifies to 2 : 3
- Both parts are already whole numbers.
- The GCD of 8 and 12 is 4.
- Divide both parts: 8 ÷ 4 = 2 and 12 ÷ 4 = 3.
- The simplified ratio is 2 : 3, which is the fraction 2/3. Scaled by 2 it is 4 : 6.
All calculations run locally in your browser. Your entered values are not sent to an external service.
How to Use the Ratio Calculator
Enter the two parts of a ratio and an optional scale. Select Simplify the Ratio or press Enter. The page clears decimals if needed, finds the greatest common factor, divides both parts, and writes the reduced pair as a colon ratio and as a fraction.
- Type the first part, such as 8 in 8 : 12.
- Type the second part, such as 12.
- Type a scale if you want one equivalent pair. 2 turns 2 : 3 into 4 : 6.
The work stays in your browser. Whole numbers, decimals, and a zero in one part are allowed. Two zeros are rejected because there is no comparison left. Negatives are rejected: classroom ratios compare non-negative quantities. Solving “2/3 = x/18” for a missing term is a proportion, not this page.
What the scale does
The scale multiplies the already-simplified parts. It does not multiply the original 8 and 12 first. 8 : 12 simplifies to 2 : 3; scale 2 then gives 4 : 6. Scale 3 would give 6 : 9. Those pairs all describe the same relationship.
How to Simplify a Ratio
Divide both parts by the GCD
The greatest common factor is the largest whole number that divides both parts. For 8 and 12 that number is 4. 8 ÷ 4 = 2 and 12 ÷ 4 = 3, so 8 : 12 = 2 : 3. If the GCD is 1, the ratio is already in lowest terms.
Decimals first become whole numbers
1.5 : 2.5 is not ready for a whole-number GCD. Multiply both parts by 10 to clear one decimal place: 15 : 25. The GCD of 15 and 25 is 5, so the simplified ratio is 3 : 5. The extra factor of 10 cancels because it sits on both sides.
The fraction form
A two-part ratio A : B is the fraction A/B after you reduce. 2 : 3 is 2/3. The colon names two parts of a comparison. The slash names a single number, the quotient. Both describe the same relationship when the second part is not zero.
Part-to-whole shares
The two parts also split the whole. In 2 : 3 the whole is 5. The first part is 2/5 = 40%. The second part is 3/5 = 60%. Those two percents add to 100%. They are shares of the combined pile, not a percent change from one number to another.
Worked Ratio Examples
Eight to twelve
GCD(8, 12) = 4. 8 ÷ 4 = 2 and 12 ÷ 4 = 3. Simplified 2 : 3. Fraction 2/3. Scale 2 gives 4 : 6. First share 40%, second share 60%.
Fifteen to twenty-five
GCD(15, 25) = 5. 15 ÷ 5 = 3 and 25 ÷ 5 = 5. Simplified 3 : 5. That is the same relationship as 6 : 10 or 9 : 15.
Two to eight, scaled by three
GCD(2, 8) = 2. Simplified 1 : 4. Scale 3 gives 3 : 12. The first part is one fifth of the whole, or 20%.
A decimal pair: 1.5 to 2.5
Multiply by 10 to get 15 : 25. Reduce by 5 to 3 : 5. The decimals hid a 3-to-5 relationship.
Three to nine
GCD(3, 9) = 3. Simplified 1 : 3. The second part is three times the first. The first share is 25% of the whole 4.
Sixteen to twenty-four
GCD(16, 24) = 8. 16 ÷ 8 = 2 and 24 ÷ 8 = 3. Another 2 : 3, the same reduced ratio as 8 : 12.
Equal parts: 7 to 7
GCD(7, 7) = 7. Simplified 1 : 1. The fraction is 1/1. Each share is 50%.
A zero in one part
0 : 5 simplifies to 0 : 1. The first part contributes nothing. 5 : 0 simplifies to 1 : 0. That pair has no fraction form, because a denominator of 0 is undefined. The first share is 100% of the whole.
Ratio, Fraction, and Percent
The same comparison can wear three outfits. 2 : 3 is the ratio. 2/3 is the fraction. About 0.667 is the decimal. 40% and 60% are the part-to-whole shares. None of those is a percent change. A change from 2 to 3 would use a different formula and a different page.
| Original | Simplified | Fraction | Equivalent ×2 |
|---|---|---|---|
| 8 : 12 | 2 : 3 | 2/3 | 4 : 6 |
| 15 : 25 | 3 : 5 | 3/5 | 6 : 10 |
| 2 : 8 | 1 : 4 | 1/4 | 2 : 8 |
| 1.5 : 2.5 | 3 : 5 | 3/5 | 6 : 10 |
| 3 : 9 | 1 : 3 | 1/3 | 2 : 6 |
| 16 : 24 | 2 : 3 | 2/3 | 4 : 6 |
To reduce only a written fraction such as 8/12, use the Simplify Fraction Calculator. To find the GCD on its own, or the LCM of the same pair, use the GCD and LCM Calculator. Those two pages share the same Euclidean algorithm this tool uses on the cleared integers.
Common Ratio Mistakes
Subtracting instead of dividing
8 : 12 is not 8 − 4 : 12 − 4. You divide both parts by the GCD. Subtracting changes the relationship.
Reducing only one part
Dividing 8 by 4 and leaving 12 alone produces 2 : 12, which is a different ratio. Both parts must share the same divisor.
Treating 2 : 3 as 2.3
The colon is not a decimal point. 2 : 3 means two parts to three parts. The decimal of that ratio is 2 ÷ 3 ≈ 0.667.
Writing the fraction upside down
8 : 12 is 8/12, which reduces to 2/3, not 3/2. The first part is the numerator.
Calling every scaled pair a new ratio
4 : 6 and 2 : 3 are equivalent. They are not two different comparisons. If they do not reduce to the same pair, they are not equivalent.
Using this page to solve a proportion
If 2/3 = x/18, the missing x is 12. That is cross-multiplication. This calculator only simplifies and scales one ratio. It does not fill a blank term.
Entering two zeros or a negative part
0 : 0 has no GCD that produces a comparison. A negative part is outside the usual school meaning of a ratio of quantities.
How to Check a Simplified Ratio
Multiply the simplified parts by the GCD you used. You should recover the cleared whole-number pair. 2 × 4 = 8 and 3 × 4 = 12. Cross-check the fraction on the Simplify Fraction page: 8/12 should also become 2/3. If those disagree, a digit or a decimal place was dropped.
Equivalent ratios keep the same quotient. 2 ÷ 3, 4 ÷ 6, and 8 ÷ 12 are the same decimal. If a scaled pair drifts, the scale was applied to only one side. You can also add the two shares: 40% + 60% = 100% for 2 : 3.
Related learning path
Add or multiply the fraction form on the Fraction Calculator. Turn a finished decimal such as 0.4 into 40% on the Decimal to Percent Calculator if you want the first share written as a percent. Browse the rest of the live catalog on the Calculators hub or the Fractions cluster.
Ratio Calculator FAQs
How do I simplify a ratio?
Divide both parts by their greatest common factor. 8 : 12 has GCD 4, so it simplifies to 2 : 3.
What is 8 : 12 in simplest form?
2 : 3. The fraction form is 2/3, and one equivalent pair is 4 : 6.
How do I write a ratio as a fraction?
Write the first part over the second part, then reduce. 8 : 12 becomes 8/12, which reduces to 2/3.
What are equivalent ratios?
Pairs that reduce to the same simplified ratio. 2 : 3, 4 : 6, and 8 : 12 are equivalent.
Can a ratio have decimals?
Yes. Clear the decimals by multiplying both parts by 10, 100, or another power of ten, then reduce. 1.5 : 2.5 becomes 3 : 5.
How is a ratio different from a proportion?
A ratio compares two parts. A proportion says two ratios are equal and is used to find a missing term, such as 2/3 = x/18.
Are my numbers sent to a server?
No. The calculation runs locally in your browser.
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This page sits with the fraction tools. The full live catalog is on the Calculators hub.
Browse All CalculatorsBrowse Fraction ToolsReviewed by Prof. Dr. Khalil Mudassar (PhD) · Last updated: [mc_modified_date]
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Disclaimer
This calculator is intended for general educational and practical use. Review important results before relying on them in professional work.