Ratio Calculator
Simplify a ratio, solve a proportion, list equivalent ratios, scale one up or down, or turn it into a percentage or decimal. Two- and three-part ratios are supported, and every answer is worked out on your device.
Reduce a ratio to its lowest whole-number terms.
Leave blank for a two-part ratio.
16 : 9 in lowest terms
16 : 9
16 : 9 ÷ 1 = 16 : 9
Original
16 : 9
Greatest common divisor
1
Simplified
16 : 9
How is this calculated?
Formula
Divide every part by the greatest common divisor of all parts.
Calculation
16 : 9 ÷ 1 = 16 : 9
Result
16 : 9
- Each part was divided by their greatest common divisor, 1.
Example ratios
These are plain mathematical examples for trying the calculator.
Worked examples
Simplifying. 10 : 5 share a greatest common divisor of 5, so both parts divide by 5 to give 2 : 1. 6 : 9 : 12 share a divisor of 3 and reduce to 2 : 3 : 4.
Solving a proportion. In 2 : 3 = 10 : X, cross-multiplying gives X = (3 × 10) ÷ 2 = 15, so 10 : 15 is the same ratio as 2 : 3.
Percentage and decimal. 1 : 3 has a total of 4, so the shares are 25% and 75%. As a decimal, 3 : 5 is 3 ÷ 5 = 0.6.
Ratio change. The ratio value of 2 : 3 is 0.6667 and of 3 : 3 is 1, so the ratio value increased by 50%.
Ratio basics
- How do I read A : B?
- A ratio compares two amounts of the same kind. 2 : 3 means that for every 2 of the first thing there are 3 of the second — five parts in total.
- What does simplifying a ratio mean?
- Dividing every part by the largest whole number that divides them all, so the relationship stays identical but the numbers are as small as possible.
- When is a ratio written as a decimal?
- When you want one number instead of two. Dividing the first part by the second gives the ratio value — screen shapes are usually quoted this way, as 16 : 9 is about 1.78.
- Is a ratio the same as a fraction?
- They are related but not identical. 1 : 3 means one part to three parts — one quarter of the total — while the fraction 1/3 means one of three. The fraction calculator handles fraction arithmetic.
Related tools
- Fraction Calculator— Add, subtract, multiply and divide fractions and mixed numbers.
- Percentage Calculator— Calculate percentages, increases and decreases.
- Average Calculator— Average, sum, count, minimum and maximum of any list of numbers.
- Recipe Scaler— Scale ingredient quantities up or down for a new serving count.
Frequently asked questions
- How do I simplify a ratio?
- Divide every part by the greatest common divisor of all the parts. 10 : 5 both divide by 5, giving 2 : 1. Decimal ratios are multiplied by a power of ten first, so 1.5 : 2 becomes 15 : 20 and then 3 : 4.
- How do I solve A : B = C : X?
- Cross-multiply: X = (B × C) ÷ A. For 2 : 3 = 10 : X, X = (3 × 10) ÷ 2 = 15.
- How do I turn a ratio into a percentage?
- Divide each part by the total of all the parts, then multiply by 100. For 1 : 3 the total is 4, so the shares are 25% and 75%. The shares always add up to 100%.
- How do I turn a ratio into a decimal?
- Divide the first part by the second: 3 : 5 becomes 3 ÷ 5 = 0.6. This is the ratio value.
- What does 'ratio change' mean here?
- It compares the ratio value A ÷ B before and after. Going from 2 : 3 (0.6667) to 3 : 3 (1) is a 50% increase. It does not compare the individual parts separately — that is a different question and is not what this mode measures.
- Can a ratio contain zero or a negative number?
- Zero is fine wherever the maths stays defined — 0 : 5 simplifies to 0 : 1. Zero is only rejected when it would mean dividing by zero. Negatives work for simplifying, proportions, scaling and decimals, but not for percentage shares, since a negative share of a whole isn't meaningful.
- Can I use three-part ratios?
- Yes — simplifying, equivalent ratios, scaling and percentages all accept a third part such as 6 : 9 : 12. Proportions, decimals and ratio change are two-part operations.