All three modes expect whole numbers. A blank field is only allowed for the term you marked as unknown, or for the boxes a mode does not use.
How to use
- Choose simplify, find the missing term, or split a total.
- Enter the whole numbers that mode asks for. In the missing-term mode, pick which of A, B, C or D is unknown.
- Press Calculate and read the reduced ratio, the unknown, or the two shares.
Formula / how it works
Simplify. A ratio 18:12 describes the same relationship as 3:2, because both parts can be divided by 6. The calculator finds the greatest common divisor by Euclid’s algorithm: replace the larger number by the remainder of the division until the remainder is zero. The last non-zero remainder is the divisor. 18 and 12 give 6, so the simplified ratio is 3:2. The decimal line is A divided by B, here 1.5, which is useful when you are comparing the ratio with a percentage. The percentage calculator answers “what percent is A of B”; this page keeps both parts visible. Signs are preserved as a single leading minus when the two parts have opposite signs. Both parts zero is rejected because there is nothing to compare.
The missing term. A proportion says the two ratios are equal: A/B = C/D. Cross-multiplying gives A×D = B×C. If D is the unknown, D = B×C / A, provided A is not zero. The sample 2:5 = 8:D is 2×D = 5×8, so D = 20. The result prints the finished proportion and the cross-product check so you can see both products match. If the division does not land on a whole number, the unknown is shown with up to six decimal places. Zero is rejected when it would require dividing by zero: you cannot solve for A when D is zero, for B when C is zero, for C when B is zero, or for D when A is zero.
Splitting a total. If paint, money or seats must follow 1:3, the shares are 1/(1+3) and 3/(1+3) of the total. A total of 100 becomes 25 and 75. The check line adds the shares and should return the total. Parts must be zero or positive in this mode; a negative share of a pile of objects is not a meaningful split. If both parts are zero there is no way to weight the total. Whole shares stay whole. A split that cannot be even, such as 100 in the ratio 1:2, is shown with the necessary decimals rather than quietly rounded to money.
How this differs from fractions. A ratio 3:2 is not the fraction 3/2 unless you decide that the first part is being compared with the second as a quotient. The fraction calculator adds and multiplies fractions. Use it when you already have numerators and denominators and you need a sum. Use the ratio page when the problem is still worded as “for every”.
Scale in words. “Scale a recipe from 2 to 5” is the missing-term mode: 2:5 = original amount : new amount, or the reverse if you know the new amount. Write down which number is A before you type. The labels on the form are the only thing that keeps the cross-multiplication pointed the right way.
Size. Each whole number must fit in a plain integer up to one billion. Decimals are rejected in every box so a ratio is not silently treated as already simplified. Type 2 and 1, not 2.5 and 1.25; simplify 5:2 if those were tenths you have already scaled.
Worked examples
Reducing 18 to 12
Inputs: Mode: simplify | A: 18 | B: 12
Choose simplify and enter A 18 and B 12. Both parts divide by 6.
Result: Mode: simplify
Input ratio: 18:12
Greatest common divisor: 6
Simplified ratio: 3:2
As a decimal (A ÷ B): 1.5
The decimal A ÷ B is 1.5.
Sharing 100 in the ratio 1:3
Inputs: Mode: split | A: 1 | B: 3 | Total: 100
Choose split and enter A 1, B 3 and total 100. The first share is one quarter of the total because 1 is one part out of 4.
Result: Mode: split
Ratio: 1:3
Total: 100
Share for A: 25
Share for B: 75
Check: 25 + 75 = 100
Use cases
- Reducing a map scale or a mixing instruction to smaller whole numbers.
- Filling the fourth term of a proportion in a homework problem.
- Splitting a bill or a pile of materials in a stated ratio.
- Checking that two recipes stay in proportion when you change the yield.
Tips & limitations
- Mark the unknown before you fill the other three terms.
- Do not type decimals. Scale to whole numbers first.
- Read the cross-product line. Equal products mean the proportion holds.
- Use fractions when the problem is already a sum of parts of a whole.
FAQ
Why is 18:12 the same as 3:2?
Both sides divide by 6, the greatest common divisor. The relationship does not change.
How is the missing term found?
From A×D = B×C. The unknown is the one value that makes those products equal.
Can I split a total three ways?
This form splits into two shares, A and B. Combine steps or rewrite the problem as two ratios if you have a third part.
What if the share is not a whole number?
It is shown in decimals. The page does not round to currency.
Why are decimals rejected?
Simplifying and the greatest common divisor are defined here on whole numbers. Multiply through by 10 or 100 first if you started from tenths.
Is a ratio uploaded for calculation?
No. The arithmetic stays in the browser.
Results are calculated from the values you enter. Double-check measurements and allow a margin before buying materials or making decisions.