Ratio Calculator
Solve a proportion for the missing value, simplify a ratio to lowest terms, or divide an amount in a ratio, with every step shown.
Fill in three values and leave one box empty. Fill all four to check whether the ratios are equal.
Both ratios simplify to 3 : 4.
Check by cross multiplication
In a true proportion the diagonal products are equal.
The second ratio is the first one multiplied by 3.
Your calculation
The same steps the calculator runs, with your numbers.
Equivalent ratios
Multiplying every term by the same number keeps the ratio equal. Your ratios are highlighted.
Results are rounded for display. Decimal terms are scaled to whole numbers (up to 6 decimal places) before simplifying.
What Is a Ratio?
A ratio compares two or more quantities of the same kind by showing how many times one contains the other. A recipe with 3 cups of flour for every 5 cups of water has a flour to water ratio of 3 : 5, read as "3 to 5". The same ratio can be written as 3 to 5, 3 : 5 or the fraction 3/5.
Ratios describe relative size, not actual amounts. A batch with 6 cups of flour and 10 cups of water has the same 3 : 5 ratio, because both quantities doubled. Multiplying or dividing every term by the same nonzero number always produces an equivalent ratio.
A proportion is a statement that two ratios are equal, such as 3 : 4 = 9 : 12. Proportions let you find an unknown quantity from a known relationship, which is how recipes are scaled, maps are read and images are resized without stretching.
How to Use the Ratio Calculator
- Proportion: enter three of the four values in A : B = C : D and leave the unknown box empty. The calculator finds the missing value by cross multiplication. Fill in all four boxes to check whether two ratios are equal.
- Simplify: enter two terms, or three for a ratio such as 12 : 18 : 30. You get the ratio in lowest terms, the greatest common factor, the 1 : n and n : 1 forms and each term as a share of the whole. Decimals such as 0.75 : 1.5 and screen sizes such as 1920 × 1080 both work.
- Divide: enter an amount and the ratio terms. You get each share, the value of one part and a check that the shares add up to the amount.
Results update as you type, and each mode shows the working step by step, a bar showing how the parts split and a table of equivalent ratios or shares.
Proportion Formula and Cross Multiplication
The two products across the equals sign, called cross products, are equal only when the proportion is true. For 5 : x = 20 : 32, the cross products give 20 × x = 5 × 32 = 160, so x = 8. The term you divide by must not be zero.
Dividing an Amount in a Ratio
Always check that the shares add back to the amount: 45 + 75 = 120. When the amount does not divide evenly, such as 100 in 1 : 2, the exact shares are 33.33 and 66.67 after rounding, and the rounded values may need a one cent adjustment.
How to Simplify a Ratio Step by Step
- Make every term a whole number. Multiply all terms by the same power of 10 to clear decimals, or by the least common denominator to clear fractions.
- Find the greatest common factor (GCF) of all the terms.
- Divide every term by the GCF. The result is the ratio in lowest terms.
A ratio can also be written in unit form by dividing by one term. 16 : 9 becomes 1.7778 : 1 when divided by 9, and 1 : 0.5625 when divided by 16. Unit forms make ratios easy to compare: a 4 : 3 screen is 1.3333 : 1, so a 16 : 9 screen is wider for the same height.
Common Aspect Ratios Reference Table
An aspect ratio is width : height in lowest terms. The decimal is width ÷ height, rounded to four places.
| Ratio | Width ÷ height | Example sizes (pixels) |
|---|---|---|
| 16 : 9 | 1.7778 | 1280 × 720, 1920 × 1080, 3840 × 2160 |
| 4 : 3 | 1.3333 | 640 × 480, 1024 × 768 |
| 3 : 2 | 1.5 | 1080 × 720 |
| 1 : 1 | 1 | 1080 × 1080 |
| 9 : 16 | 0.5625 | 1080 × 1920 (vertical video) |
| 64 : 27 | 2.3704 | 2560 × 1080 (sold as 21 : 9) |
| 43 : 18 | 2.3889 | 3440 × 1440 (sold as 21 : 9) |
The label 21 : 9 is a rounded marketing name. Simplifying the real pixel counts shows that 2560 × 1080 is 64 : 27 and 3440 × 1440 is 43 : 18. The HDTV standard ITU BT.709 uses a 16 : 9 picture with 1920 × 1080 pixels.
Scaling with Ratios
Recipes
A recipe for 4 servings scaled to 10 servings uses a factor of 10 ÷ 4 = 2.5, so 300 g of flour becomes 300 × 2.5 = 750 g. Every ingredient uses the same factor.
Maps and models
On a 1 : 50,000 map, 2 cm on paper is 2 × 50,000 = 100,000 cm, which is 1 km on the ground. A 1 : 24 model car is 24 times smaller than the real car in every length.
Resizing images
To keep a 16 : 9 image undistorted at a width of 1280 pixels, solve 16 : 9 = 1280 : h. The height is 1280 × 9 ÷ 16 = 720 pixels.
Ratio, Fraction, Percent and Rate
A ratio of 3 : 5 compares two parts. The whole has 3 + 5 = 8 parts, so the first part is the fraction 3/8 of the whole, which is 37.5%, and the second part is 5/8, which is 62.5%.
Comparing the terms directly gives a different number: 3 ÷ 5 = 0.6, so the first quantity is 60% of the second. Say which comparison you mean.
A rate is a ratio of quantities with different units, such as 150 km in 2 hours, which is 75 km per hour. A unit rate always has 1 as the second term.
Common Mistakes
- Reversing the order. 3 : 5 and 5 : 3 are different ratios. Keep the terms in the order the question names them.
- Mixing units. Convert first. 2 m : 50 cm is 200 cm : 50 cm, which simplifies to 4 : 1, not 1 : 25.
- Adding instead of multiplying. Adding 1 to each term of 3 : 4 gives 4 : 5, which is a different ratio (0.75 versus 0.8). Only multiplying or dividing all terms keeps a ratio equal.
- Confusing part to part with part to whole. In a 3 : 5 split the first share is 3/8 of the total, not 3/5.
- Rounding shares too early. Divide the exact amount first, then round, and check that the rounded shares still add up to the total.
Related Calculations
Ratios connect closely to other calculations. The Fraction Calculator adds, multiplies and simplifies fractions such as the 3/8 share above. The Percentage Calculator converts shares to percentages and finds the percent change between two values.
For geometry, similar triangles have equal ratios of corresponding sides, which the Triangle Calculator uses. The Slope Calculator treats slope as the ratio of rise to run.
Frequently Asked Questions
How do you solve a ratio with a missing value?
Write the two ratios as equal fractions and cross multiply. For 3 : 4 = 9 : x, write 3/4 = 9/x, so 3 × x = 4 × 9 = 36 and x = 36 ÷ 3 = 12. The same method works wherever the unknown sits: for 5 : x = 20 : 32, 20 × x = 5 × 32 = 160, so x = 8. Check the answer by multiplying diagonally, because the two cross products of a true proportion are always equal. The known term you divide by cannot be zero.
How do you simplify a ratio?
Divide every term by their greatest common factor. For 1920 : 1080, the greatest common factor is 120, so the ratio simplifies to 16 : 9. If the terms contain decimals, first multiply every term by the same power of 10 to make whole numbers: 0.75 : 1.5 becomes 75 : 150, which simplifies to 1 : 2. For fractions, multiply by the least common denominator: 2/3 : 5/6 times 6 gives 4 : 5. Three part ratios work the same way, so 12 : 18 : 30 becomes 2 : 3 : 5.
How do you divide an amount in a given ratio?
Add the ratio terms to get the total number of parts, divide the amount by that total to find the value of one part, then multiply each term by the value of one part. To divide 120 in the ratio 3 : 5, there are 3 + 5 = 8 parts, one part is 120 ÷ 8 = 15, and the shares are 3 × 15 = 45 and 5 × 15 = 75. Check that the shares add back to the amount: 45 + 75 = 120. For 900 in the ratio 2 : 3 : 4, one part is 100 and the shares are 200, 300 and 400.
How do you convert a ratio to a percentage?
A ratio compares parts, while a percentage compares a part with the whole, so first add the terms. In a ratio of 3 : 5 there are 8 parts in total, so the first part is 3 ÷ 8 = 0.375 = 37.5 percent and the second is 5 ÷ 8 = 62.5 percent. To express the first term as a percentage of the second instead, divide the terms directly: 3 ÷ 5 = 0.6 = 60 percent. State which comparison you mean, because the two answers differ.
What is the difference between a ratio and a fraction?
A fraction compares a part with the whole, while a ratio can compare one part with another part. In a class of 12 girls and 18 boys, the ratio of girls to boys is 12 : 18 = 2 : 3, but the fraction of the class that is girls is 12 ÷ 30 = 2/5. A ratio a : b can be written as the fraction a/b when you compare the two quantities directly. Ratios with three or more terms, such as 2 : 3 : 5, have no single fraction form.
Sources & References
- OpenStax. Prealgebra 2e, 5.6 Ratios and Rate (ratio notation a to b, a/b, a : b). openstax.org
- OpenStax. Prealgebra 2e, 6.5 Solve Proportions and their Applications (cross products of a proportion). openstax.org
- International Telecommunication Union. Recommendation ITU R BT.709, Parameter values for the HDTV standards. itu.int
Results are for educational purposes. Every worked number on this page was recomputed with the same functions the calculator uses. Methodology reviewed: 2026.