How do I solve a ratio?
Fill in three of the four numbers in A : B = C : D and get the fourth, with the ratio in its simplest form.
- D
- 8
3 : 4 = 6 : 8.
- Simplest form
- 3 : 4
- As a decimal
- 0.75
- Scale factor
- 2
D: 8. 3 : 4 = 6 : 8.
How to calculate
Solves A : B = C : D for any missing number, and shows the ratio in simplest form, as a decimal, and as a scale factor.
Example with the default inputs (A 3, B 4, C 6): 3 : 4 = 6 : 8.
Formula: A : B = C : D means A ÷ B = C ÷ D, so A × D = B × C.
- All four terms are more than 0.
- The simplest form is shown when it needs whole numbers of a billion or less; decimals are taken exactly as they print (0.1 is 1/10).
Worked examples
Each example is checked against the calculator on every build.
- A 3, B 4, C 6 gives D 8, Simplest form 3 : 4, As a decimal 0.75, Scale factor 2.Source: hand calculation in content.mdx: D = 4 × 6 ÷ 3 = 8
- A 5, C 15, D 21 gives B 7, Scale factor 3.Source: hand calculation in content.mdx: B = 5 × 21 ÷ 15 = 7
- A 1.5, B 2, C 4.5 gives D 6, Simplest form 3 : 4, As a decimal 0.75.Source: hand calculation in content.mdx: D = 2 × 4.5 ÷ 1.5 = 6; 1.5 : 2 = 15 : 20 = 3 : 4
- B 9, C 32, D 18 gives A 16, Simplest form 16 : 9.Source: hand calculation in content.mdx: A = 9 × 32 ÷ 18 = 16
- A 1,920, B 1,080, D 720 gives C 1,280, Simplest form 16 : 9.Source: hand calculation in content.mdx: C = 1920 × 720 ÷ 1080 = 1280; 1920 : 1080 = 16 : 9
How it works
Two ratios A : B and C : D are equal when their values are equal:
A ÷ B = C ÷ D, which is the same as A × D = B × C
Fill in any three of the four numbers and the calculator finds the fourth by cross-multiplying:
- D = B × C ÷ A
- C = A × D ÷ B
- B = A × D ÷ C
- A = B × C ÷ D
The multiplication comes first, so whole numbers give exact answers. When the product is too large (or too small) for the computer to hold, the division comes first instead.
It also shows:
- Simplest form: A : B in lowest whole-number terms. The calculator reads each number exactly as a decimal (1.5 is 15/10), divides A by B as an exact fraction, and writes the fraction in lowest terms as top : bottom. If A or B was worked out and has a long decimal, it uses C : D, which has the same simplest form.
- As a decimal: the value of the ratio, A ÷ B.
- Scale factor: C ÷ A, the number that turns A : B into C : D (C = A × scale and D = B × scale).
Assumptions
- All four numbers are more than 0.
- The simplest form is shown only when both of its whole numbers are at most 1,000,000,000.
Worked examples by hand
3 : 4 = 6 : ? D = 4 × 6 ÷ 3 = 8. The simplest form is 3 : 4, the decimal 3 ÷ 4 = 0.75, and the scale factor 6 ÷ 3 = 2.
5 : ? = 15 : 21. B = 5 × 21 ÷ 15 = 105 ÷ 15 = 7. The scale factor is 15 ÷ 5 = 3.
1.5 : 2 = 4.5 : ? D = 2 × 4.5 ÷ 1.5 = 9 ÷ 1.5 = 6. 1.5 : 2 = 15 : 20, and dividing both by 5 gives 3 : 4, with a decimal value of 0.75.
? : 9 = 32 : 18. A = 9 × 32 ÷ 18 = 288 ÷ 18 = 16, and 16 : 9 is already in simplest form (16 : 9).
1920 : 1080 = ? : 720. C = 1920 × 720 ÷ 1080 = 1280. 1920 and 1080 share the factor 120, so the simplest form is 16 : 9.
Other questions people ask
How do I solve a ratio with a missing number?
Write the two ratios as equal fractions and cross-multiply. For 3 : 4 = 6 : D, write 3 ÷ 4 = 6 ÷ D, so 3 × D = 4 × 6 = 24 and D = 8.
How do I simplify a ratio?
Divide both numbers by their greatest common factor. 1920 : 1080 has a greatest common factor of 120, so it simplifies to 16 : 9. For decimals, first multiply both numbers by the same power of 10 to make them whole: 1.5 : 2 becomes 15 : 20, which is 3 : 4.
What is the difference between a ratio and a proportion?
A ratio compares two amounts, such as 3 : 4. A proportion says that two ratios are equal, such as 3 : 4 = 6 : 8. This calculator solves proportions: it finds the number that makes the two ratios equal.
How do I scale a ratio up or down?
Multiply or divide both numbers by the same scale factor. 3 : 4 scaled by 2 is 6 : 8, and scaled by 0.5 is 1.5 : 2. The calculator shows the scale factor C ÷ A between the two ratios.
How are ratios used for screen sizes?
A screen's aspect ratio compares its width with its height. Full HD, 1920 × 1080 pixels, is 16 : 9. To find the width of a 16 : 9 picture that is 720 pixels tall, solve 1920 : 1080 = C : 720, which gives C = 1280.
Can a ratio be turned into a fraction or a percentage?
Yes, as a part of the whole. In a ratio of 3 : 4, the first part is 3 out of 3 + 4 = 7 parts, so it is 3/7 of the total, about 42.86%. The ratio's own value, 3 ÷ 4 = 0.75, compares the first part with the second part, not with the total.