How to use
- Enter the original ratio as two terms. A mix of 3 to 5 is first term 3 and second term 5.
- Enter the new first term, the amount you actually have of the first ingredient or the new width.
- Press Calculate. The hero is the matching second term.
- Swap the terms and run it again if you know the second amount instead of the first.
How it's calculated
New second term = original second × new first ÷ original first. The first term cannot be zero, because the proportion would be undefined.
The same relationship is new first ÷ original first = new second ÷ original second. Cross-multiplying gives the formula above.
Worked example
A 3:5 ratio scaled so the first term is 12: the second term is 5 × 12 ÷ 3 = 20. The new ratio is 12:20, which still reduces to 3:5. If you only have 5 of the second item and want the first, swap the boxes: original first 5, original second 3, new first 5, and the page returns 3.
Assumptions
One pair and one new first term. Units are yours to keep consistent. A zero first term is rejected.
FAQ
How is a ratio different from a fraction?
A fraction is one number divided by another. A ratio is the same idea written as a pair. 3:5 is the fraction 3/5 if you divide them.
Can a term be negative?
The arithmetic allows it. A negative scale flips the sign of the other term.
What about three-part ratios?
Split the job. Scale a:b first, then scale a:c with the same new first term.
Does this simplify the ratio?
It scales. It does not print a reduced pair. Divide both original terms by their greatest common divisor if you want 12:20 shown as 3:5.