Ratio calculator

Use this calculator to solve problems related to ratios

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Ratio simplifier and converter calculator

This calculator performs operations to solve problems that involve ratios. You may do the following:

  • Simplify a known ratio (like simplifying a fraction).
  • Convert a ratio to 1:n form (like you often see in maps).
  • Convert a ratio to n:1 form.
  • Find equivalent ratios.

To simplify a ratio enter the terms (antecedent and consequent) of the ratio in the cells marked respectively A and B, and and press 'Simplify'. This will reduce the ratio to its simplest form.

To convert a ratio to 1:n form or to n:1 form enter the terms of the ratio, also in A and B, and press '1:n' or 'n:1'

If you wish to find an equivalent ratio use the fields in the second line to enter any three of the known values, then click 'Calculate'.

How does the ratio simplifier and converter work

To simplify the ratio, this calculator uses the same procedure as the one used to simplify fractions.

To convert the ratio to 1:n form, the calculator divides both numbers by the antecedent term (A). To convert to n:1 form, it divides both numbers by the consequent number (B).

To calculate the missing value in equivalent ratios it applies one of the following formulas depending on which one is the missing value:

  • If the missing value is A: $ A = C / D \times B $
  • If the missing value is B: $ B = D / C \times A $
  • If the missing value is C: $ C = A / B \times D $
  • If the missing value is D: $ D = B / A \times C $

What is a ratio

Ratio is a way to describe the relationship between two related numbers. Ratios are used in many diverse activities of our life: In maps they express the scale of the map (1:63360 means that one inch on the map represents 63360 inches or 1 mile in the real world). In recipes they can be used to describe the proportions of each ingredient (2 cups of water for every cup of rice).

Ratios can be also expressed as fractions and can be calculated following the same rules.