Ratio calculator
Math & numbersHow do you simplify a ratio or find the missing number?
Simplify a ratio to its lowest terms, or find the missing number in an equal ratio, the rule of three.
What you enter stays on your device while you use this tool. Opening a shared link sends the settings in its address to HowToolbox to prepare the page.
Simplest form
16 : 9
1,920 : 1,080 simplifies to 16 : 9.
The working behind the answer
- Formula
- 1,920 : 1,080 ÷ 120 = 16 : 9
- First ÷ second
- 1.777778
- Share of the first term
- 64%
- Share of the second term
- 36%
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Simplify a ratio to its lowest terms, or find the missing number in an equal ratio, the rule of three.
How to use
- Choose Simplify to reduce a ratio, or Missing term to solve an equal ratio.
- Enter the two terms of the ratio. To find a missing term, say which term of the new ratio you know and enter it.
- Read the answer and the formula, and copy the link to share the same calculation.
How it works
A ratio compares two quantities: 1920 : 1080 says the first is 1920 for every 1080 of the second. You can multiply or divide both terms by the same number without changing the ratio. Dividing both by their greatest common divisor gives the simplest form, so 1920 : 1080 becomes 16 : 9, and 1.5 : 4.5 becomes 1 : 3.
Two ratios are equal when they have the same first ÷ second value. To find a missing term in a : b = c : x, scale by the same factor: x = b × c ÷ a. If a screen is 16 : 9 and 1280 wide, the height is 9 × 1280 ÷ 16 = 720. If you know the second term instead, x = a × c ÷ b. This is the rule of three, as described in Wikipedia’s “Ratio” and “Rule of three” articles.
Ratios here use positive numbers with up to six decimals. A ratio is not a percentage: 1 : 3 means one part to three parts, so the first is a quarter (25%) of the total, not a third.
Worked example
What is the missing term in 2 : 3 = 8 : x?
- Scale factor: 8 ÷ 2 = 4.
- x = 3 × 4 = 12.
The equal ratio is 8 : 12.
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Frequently asked questions
How do I simplify a ratio?
Divide both terms by their greatest common divisor. For 12 : 18 that is 6, so the ratio is 2 : 3.
How do I scale a recipe or a drawing?
Find the factor by dividing the new amount by the old one, then multiply the other terms by it. This tool does that when you enter the known number.
What is the difference between a ratio and a fraction?
A ratio 1 : 3 compares two parts, while the fraction of the whole is 1/4. The tool shows each term’s share of the total.
Can I use decimals?
Yes, up to six decimals. They are scaled to whole numbers first, so 0.5 : 1.5 simplifies to 1 : 3.
Can I compare measurements in different units?
Convert both measurements to the same unit first. For example, 1 metre to 50 centimetres is 100 : 50, or 2 : 1.
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