Arithmetic
Ratio Calculator
Simplify a ratio to lowest terms, solve a proportion for a missing number, or split a total by a ratio. Every answer updates as you type, with the GCD and cross-multiplication shown.
Enter a ratio
Use a colon, slash, or “to”. Two or more parts, decimals allowed.
Simplified ratio
2 : 3
Divided both sides by 4
fraction
2/3
decimal
0.6667
percent
66.6667%
Try an example
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The basics
What is a ratio?
A ratio compares quantities — how much of one thing there is relative to another. Written A:B and read “A to B”, it tells you the proportion without fixing the totals, so the same ratio describes a recipe for two people or for two hundred. Two ideas do most of the work.
A : B → lowest terms
Lowest terms
A ratio is simplest when its terms share no common factor beyond one. Dividing both by their greatest common divisor gives the cleanest way to write the same comparison.
8 : 12 → 2 : 3
A : B = C : D
Proportion
A proportion sets two ratios equal. When three of the four terms are known, the fourth is fixed — and cross-multiplication recovers it.
3 : 4 = 9 : 12
Method
How to simplify a ratio by hand
Three steps reduce any ratio to its lowest whole-number terms.
- 1
Write the ratio as whole numbers
If A or B has decimals, multiply both by a power of ten to clear them. The comparison is unchanged because both sides scale together.
0.5 : 1.5 → 5 : 15 - 2
Find the greatest common divisor
Find the largest number that divides both A and B exactly. The Euclidean algorithm does it fast for big numbers.
gcd(8, 12) = 4 - 3
Divide every term by the GCD
Divide each side by that common factor. What remains shares no factor but one — the ratio in lowest terms.
8 ÷ 4 : 12 ÷ 4 = 2 : 3
Worked examples
See it across ratio types
The same thinking covers reducing, solving for an unknown, three-part ratios, and sharing a total.
Given Reduce 18 : 24 to lowest terms
gcd(18, 24) = 6
18 ÷ 6 : 24 ÷ 6
3 : 4
Where it shows up
Why ratios matter
A ratio is the quiet engine behind recipes, maps, money, and screens — anywhere a proportion has to hold as the totals change.
flour : water
Cooking & mixing
Recipes, paint, and concrete are written as ratios so you can scale the batch up or down while the result stays the same.
map : ground
Maps & scale models
A scale like 1:25,000 is a ratio: one unit on the map stands for that many of the same units on the ground.
width : height
Screens & images
Aspect ratios such as 16:9 fix the shape of a screen or photo no matter how many pixels wide it is.
Reference
Ratio, fraction, decimal, percent
A two-part ratio can be read four equivalent ways. Converting between them is often what a “ratio” question is really asking.
| Ratio | Fraction | Decimal | Percent of B |
|---|---|---|---|
| 1 : 2 | 1/2 | 0.5 | 50% |
| 1 : 4 | 1/4 | 0.25 | 25% |
| 3 : 4 | 3/4 | 0.75 | 75% |
| 2 : 5 | 2/5 | 0.4 | 40% |
| 1 : 1 | 1/1 | 1 | 100% |
| 5 : 4 | 5/4 | 1.25 | 125% |
Worth knowing
Rules worth remembering
A few facts keep ratio work fast and mistake-free.
A : B = kA : kB
Scaling keeps it equal
Multiplying or dividing every term by the same non-zero number gives an equivalent ratio. This is how you scale a recipe or reduce to lowest terms.
A : B ≠ B : A
Order matters
A ratio is directional. Boys to girls is not the same as girls to boys unless the counts happen to be equal, so keep the order the question gives.
A · D = B · C
Cross-products are equal
In any true proportion the outer and inner products match. It is both the test for equality and the way to solve for a missing term.
A : B : C
Ratios extend past two parts
A ratio can compare three or more quantities at once. Simplify it by dividing every part by the GCD of all the parts together.
A : 0
A zero term is special
A term of zero means none of that quantity. It cannot be a denominator, so a zero can sit in a ratio but not where you would divide by it.
part : whole
Part-to-part vs part-to-whole
Decide which you mean. In 2:3 there are 5 parts total, so the first is 2 parts of every 5 (40%) — a part-to-whole reading, not 2 of 3.
Quick chart
What does N : M simplify to?
The ratios people look up most, plus a grid you can resize. Reduced ratios are highlighted; the rest are already in lowest terms.
2 : 4
1 : 2
= 1/2 = 0.5
3 : 6
1 : 2
= 1/2 = 0.5
4 : 8
1 : 2
= 1/2 = 0.5
6 : 8
3 : 4
= 3/4 = 0.75
8 : 12
2 : 3
= 2/3 = 0.6667
9 : 12
3 : 4
= 3/4 = 0.75
10 : 15
2 : 3
= 2/3 = 0.6667
12 : 16
3 : 4
= 3/4 = 0.75
15 : 20
3 : 4
= 3/4 = 0.75
16 : 24
2 : 3
= 2/3 = 0.6667
20 : 30
2 : 3
= 2/3 = 0.6667
25 : 100
1 : 4
= 1/4 = 0.25
16 : 9
16 : 9
= 16/9 = 1.7778
4 : 3
4 : 3
= 4/3 = 1.3333
3 : 2
3 : 2
= 3/2 = 1.5
21 : 9
7 : 3
= 7/3 = 2.3333
1920 : 1080
16 : 9
= 16/9 = 1.7778
1280 : 720
16 : 9
= 16/9 = 1.7778
Pitfalls
Common mistakes
The errors that quietly turn a right method into a wrong answer.
2 : 3 → 2 of 3 ✗
Confusing part with whole
In 2:3 the total is five parts. Reading the first term as “2 out of 3” instead of 2 out of 5 is the most common ratio slip.
add, don't cross-add
Adding instead of scaling
To go from 2:3 to an equivalent ratio you multiply both terms, not add to them. Adding 1 to each gives 3:4, a different ratio entirely.
flip C and D
Mismatching the proportion
When you set up A:B = C:D, the matching quantities must line up on the same side. Swapping C and D solves a different problem.
2 : 3 ≠ 0.66
Forgetting to simplify
Leaving an answer as 6:8 when the question wants lowest terms loses marks. Always divide out the common factor at the end.
FAQ
Common questions
Find the greatest common divisor (GCD) of the terms, then divide every term by it. For 8:12 the GCD is 4, so 8 ÷ 4 = 2 and 12 ÷ 4 = 3, giving 2:3 — the same comparison written with the smallest whole numbers.
Cross-multiply. In A:B = C:D the products A·D and B·C are always equal, so to find a missing D you rearrange to D = B·C ÷ A. For 3:4 = 9:?, D = (4 × 9) ÷ 3 = 12. The same trick recovers any one missing term.
A ratio compares two or more quantities (A to B), while a fraction names a part of a single whole. A two-part ratio A:B has the same value as the fraction A/B, but a ratio can also compare three or more parts (like 2:3:5), which a single fraction cannot.
Multiply or divide every term by the same number. To scale 2:3 up by 5 you multiply each term to get 10:15; to scale 10:15 down you divide both by 5 back to 2:3. The comparison stays the same because both sides change equally.
Add the ratio parts to get the total number of shares, divide the amount by that total to find the value of one share, then multiply by each part. Splitting $100 by 3:2 gives 3 + 2 = 5 shares, $100 ÷ 5 = $20 per share, so $60 and $40.
Yes, but it usually reads more clearly as whole numbers. Multiply every term by a power of ten to clear the decimals, then simplify. The ratio 0.5:1.5 becomes 5:15, which reduces to 1:3.
A 1:1 ratio means the two quantities are equal — for every one of the first there is exactly one of the second. Mixed 1:1, two ingredients are used in equal amounts. Any ratio where both terms are the same number, like 5:5, simplifies to 1:1.
Cross-multiply and compare. Two ratios A:B and C:D are equivalent when A·D = B·C. For 2:3 and 8:12, 2 × 12 = 24 and 3 × 8 = 24, so they are equal. Equivalently, simplify both — equal ratios reduce to the same lowest terms.
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Author
Ugo CharlesBuilt and fact-checked against our editorial standards · Last updated June 2026
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