What is a ratio?
A ratio compares two quantities by showing how many times one contains the other, written A:B. A screen 1920 pixels wide and 1080 high has a ratio of 1920:1080, which simplifies to 16:9. This calculator does two things: it reduces a ratio to its lowest whole-number terms, and it solves a proportion A:B = C:D for the missing value D.
Mode 1: Simplify A:B
Enter A and B, and the calculator divides both by their greatest common divisor (GCD), the largest number that divides both exactly. It also shows the decimal equivalent, A ÷ B.
Example: 1920:1080
- Choose Simplify A:B.
- Enter 1920 as A and 1080 as B.
- The greatest common divisor of 1920 and 1080 is 120.
- 1920 ÷ 120 = 16 and 1080 ÷ 120 = 9, so the result is 16:9.
- Decimal equivalent: 1920 ÷ 1080 = 1.777778.
Decimal ratios. For inputs like 1.5:2.25, the calculator multiplies both numbers by 1,000,000 to make them whole, finds the GCD, and divides. The result is 2:3. If the two numbers share no common factor, such as 7:13, the ratio is already in its simplest form and comes back unchanged.
Mode 2: Solve a proportion A:B = C:D
A proportion says two ratios are equal. If you know three of the four values, you can find the fourth by cross-multiplying: A × D = B × C, so:
D = B × C ÷ A
Example: 3:4 = 9:?
- Choose Solve A:B = C:D.
- Enter 3 as A, 4 as B and 9 as C.
- D = 4 × 9 ÷ 3 = 12, and the calculator shows the full proportion, 3:4 = 9:12.
D doesn't have to be a whole number. 2:3 = 5:D gives 7.5. Results are rounded to six decimal places.
Everyday uses
| Situation | Inputs | Mode | Result |
|---|---|---|---|
| Screen aspect ratio | 1920, 1080 | Simplify | 16:9 |
| Recipe: 250 g flour for 4 people, how much for 6? | A 4, B 250, C 6 | Proportion | 375 |
| Mixing 1.5 parts to 2.25 parts | 1.5, 2.25 | Simplify | 2:3 |
| Scale a 3 × 4 photo so the short side is 9 | A 3, B 4, C 9 | Proportion | 12 |
The trick with proportions is to keep the same kind of quantity in the same position on both sides. In the recipe row, A and C are both numbers of people, and B and D are both grams of flour. Mixing them up (people on one side, grams first on the other) gives a wrong answer.
Ratios, fractions and percentages
A two-part ratio A:B can be read in two different ways, and it helps to be clear which you mean:
- Part to part. A ratio of 2:3 boys to girls means for every 2 boys there are 3 girls.
- Part to whole. The same group is 2 out of 5 boys, so boys are 2/5, or 40%, of the total.
To turn a part-to-part ratio into a percentage, add the parts to get the whole (2 + 3 = 5), then divide. The percentage calculator can do that last step: 2 is 40% of 5.
Limits
- A, B and C must be greater than zero. Ratios of negative numbers or zero aren't supported.
- Two-part ratios only. For a ratio like 1:2:4, simplify by hand or solve two proportions.
- Simplify range: 0.000001 to 9,000,000,000. Simplifying works to a precision of 0.000001, so digits past the sixth decimal place are rounded. A or B below 0.000001, or above 9,000,000,000, shows an error rather than a wrong ratio, because the scaled whole numbers would round to zero or grow past what the calculator can hold exactly. Scale very small or very large quantities to a convenient unit before entering them (grams instead of tonnes, for example). Solving a proportion doesn't have these bounds.
Related calculators
- Fraction calculator: add, subtract and simplify fractions.
- Percentage calculator: express one part as a percentage of a whole.
- Concrete calculator: material quantities for common concrete mix ratios.
- Scientific calculator: for any other arithmetic.
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