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Equivalent Ratio Calculator

Enter ratio terms A and B and a new value for A to get the equivalent value for B.

How it is calculated

You give a ratio A : B and a new first term. The tool finds the scale factor k = new A ÷ A and applies it to the second term: new B = B × k. Both terms of the new ratio are shown rounded to two decimals, so a result like 7 : 11.67 is a rounded display of 11.666... The first term A cannot be zero, since the scale factor would be undefined. The inputs can be decimals or any units as long as A and new A are in the same unit and B keeps its own unit. The tool scales in one direction only (from the first term); to solve from the second term, swap the roles of A and B.

Worked example

A mix uses 3 parts concentrate to 5 parts water, and you want to use 12 parts concentrate. Step 1: scale factor = 12 ÷ 3 = 4. Step 2: new B = 5 × 4 = 20. Result: the equivalent ratio is 12.00 : 20.00. Check: 3 : 5 and 12 : 20 both equal 0.6 when you divide the first term by the second.

Try this example →

Common mistakes

  • Adding the same amount to both terms instead of multiplying; 3 : 5 becomes 6 : 8 by adding 3, which is a different ratio.
  • Entering the terms in the wrong order, so the new first term is applied to the wrong ingredient.
  • Mixing units between A and new A, such as millilitres against litres.
  • Putting the total amount into the new-A field when the ratio describes parts, so the second term comes out too large.
  • Expecting a whole number: 3 : 5 scaled to 7 gives 11.67, which may need rounding to something practical.

About this calculator

Two ratios are equivalent when one can be scaled to the other by multiplying (or dividing) both terms by the same factor — for example, 2:3 and 8:12 represent the same proportion. Given a ratio A:B and a new value for A, this calculator solves for the matching B using B_new = B × (A_new ÷ A), which preserves the original proportion exactly.

This cross-multiplication logic underlies everyday scaling tasks: doubling a recipe while keeping ingredient proportions intact, resizing a map or blueprint, or mixing paint, concrete or chemicals at the correct dilution.

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Comments (1)

  • Editorial team

    A fast way to confirm the answer is cross-multiplication: the original first term times the new second term must equal the original second term times the new first term. For 3 : 5 scaled to a first term of 7, the second term is 11.67, and 3 times 11.67 is about 35, the same as 5 times 7. Rounding up is safer for ingredients. What are you scaling, a recipe, a mix or a map?

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