ClearQuip · Everyday math

Ratio calculator

Keep a:b when the first term changes

A ratio calculator keeps two numbers in proportion. You enter the original pair and a new value for the first term. The page returns the second term that preserves the same relationship. Recipes, map scales, and paint mixes all use that one step.

Inputs

Result

Fill in the fields and press Calculate.

Disclaimer: Proportion of the two terms you enter. It does not convert units.

How to use

  1. Enter the original ratio as two terms. A mix of 3 to 5 is first term 3 and second term 5.
  2. Enter the new first term, the amount you actually have of the first ingredient or the new width.
  3. Press Calculate. The hero is the matching second term.
  4. 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.

Related tools