Ratio calculator
A ratio of 1.5 : 2 is not stuck as a decimal; scaling both sides by ten gives 15 : 20, which reduces to 3 : 4. This tool does that automatically by working in whole numbers behind the scenes, so entering measured values with decimal places still produces a clean ratio rather than an unhelpful 0.75 : 1.
A ratio simplifies by dividing both sides by their greatest common divisor: 6 : 8 becomes 3 : 4. To solve a proportion A : B = C : x, multiply B by C and divide by A. To split by shares, divide the total by the sum of the parts.
How to work with ratios
The three modes cover almost everything ratios are used for. Simplifying puts a measured relationship into its clearest form. Solving a proportion is the scaling operation behind recipes, map scales, mixing paint and converting units. Splitting by shares is how profit, rent and inheritance get divided, and it is the one where the arithmetic most often goes wrong, because people divide by the number of shares rather than by their sum.
Simplifying a decimal ratio works by counting the decimal places you typed and scaling both sides by that power of ten before reducing, so 1.5 : 2 becomes 15 : 20 and then 3 : 4. Two consequences follow from that. Write the decimal point as a full stop, because a comma is not counted as one and 1,5 : 2 comes back as 1 : 1 rather than 3 : 4, even though the decimal row beneath it still reads 0.75. And a rounded measurement reduces to exactly what you typed rather than to what you meant: 0.333 : 1 gives 333 : 1000, not 1 : 3, because 0.333 genuinely is not a third.
The three rows under a simplified ratio answer three different questions and are easy to read as one. The decimal is the first divided by the second. The share is the first as a percentage of both together, so 6 : 8 gives 42.857 per cent rather than 75. Per one restates the whole thing against a first term of 1, which is the form a mixing instruction usually wants.
What people use it for
- Reducing a measured ratio to its simplest form
- Scaling a recipe or a mix by proportion
- Splitting a bill or a profit by agreed shares
- Converting a ratio into a percentage
- Reading a map or model scale as a plain multiplier
- Getting a two-part mix down to something per one unit of the first
Questions
Divide both sides by their greatest common divisor. 6 : 8 divided by 2 is 3 : 4.
Cross-multiply. For 2 : 3 = 10 : x, x is 3 × 10 ÷ 2 = 15.
Yes, and it still reduces. 1.5 : 2 is the same as 3 : 4, because both sides are scaled to whole numbers before the common factor is taken out.
A comma was used as the decimal point. The reducer counts places after a full stop, so 1,5 : 2 loses its decimal place: the 1.5 rounds to 2, that gives 2 : 2, and 2 : 2 reduces to the 1 : 1 you saw. The decimal row underneath still reads 0.75, which is the giveaway. Type 1.5 and the ratio comes back as 3 : 4.
Because it reduces exactly what you typed, and 0.333 is not a third. Type the ratio you actually mean, 1 : 3, if a third is what you want.
The first number as a percentage of both added together, not as a percentage of the second. For 6 : 8 that is 6 out of 14, or 42.857 per cent.
Restating the ratio with 1 on the left. 6 : 8 becomes 1 : 1.3333, which is the form to use when a mix is quoted per unit of the first ingredient.
How many times the first pair fits into the second, C divided by A. For 2 : 3 = 10 : x that is 5, so the whole ratio has been scaled up fivefold.
Add the parts, divide the total by that sum, then multiply by each part. For 2:3:5 out of 1000, one part is 100, so the shares are 200, 300 and 500.
The sum of the shares you entered, not how many of them there are. For 2, 3 and 5 the number of shares is 3 and the total parts is 10, and it is the 10 that the total gets divided by.
Rounding to two decimals. Splitting 100 three ways shows 33.33 each, which comes to 99.99. Give the last penny to somebody rather than letting it vanish.
Yes. The share box takes one number per line with no limit, so a seven-way split is seven lines.
Use the solve tab. Put the ratio in A and B, put the new first term in C, and x is the matching second term.
A ratio compares two quantities; a fraction is one quantity divided by a whole. 3 : 4 means 3 parts to 4, which is 3/7 of the total.