Ratio Solver

The Ratio Solver is an excellent calculator for solving related ratio values between a pair of ratios (for example to calculate the ratio 1:r). Simply change the ratio denominator and numerator values in ratio a or ratio b to instantly calculate the corresponding values within the paired ratio. The ratio calculator can solve complex ratio pairs upto 16 decimal places.

Ratio Solver Calculator

Ratio Solver Results (detailed calculations and formula below)

Please note that the formula for each calculation along with detailed rato calculations is shown further below this page. As you enter the specific factors of each ratio solver calculation, the Ratio Solver Calculator will automatically calculate the results and update the formula elements with each element of the ratio solver calculation. You can then email or print this ratio solver calculation as required for later use.

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Ratio Solver. This image shows the properties and ratio solver formula for the Ratio Solver

What is a paired ratio?

A "paired ratio" or "ratio pair" is a set of two ratios which are proportionally related to each other. For example the ratio 1:10 is the same as the ratio 10:100, the second ratio is simply 10 times the value of the first ratio. Ratio pairing is important in math and quite common in engineering for gearing engines, managing torque and transmitting power. The key point to understand is that when you change the value in the numerator or denominator in one ratio, its corresponding value must be adjusted to ensure its relationship with the partner ratio remains the same. This relationship is in fact a third ratio, that ratio can be expressed as ratio a : ratio b or a:b in shorthand. by defining a = 1 we can state that b = x where x = ratio a numerator/ratio b numerator or x = ratio a denominator/ratio b denominator.

How to calculate and answer ratio questions using the Ratio Solver

This ratio calculator is called the ratio solver because it allows you to adjust the denominator and numerator of two paired ratios (see below for additional information on what a paired ratio is). The ratio solver adjusts the corresponding value within the ratio when adjustments are made to ensure sustained relationship ("Paired Ratio") to the corresponding paired value, in simple words, When you:

  • Change the value of ratio a numerator an, the value of ratio a denominator ad is recalculated to maintain the "Paired Ratio" relationship with ratio b
  • Change the value of ratio a denominator ad, the value of ratio a numerator an is recalculated to maintain the "Paired Ratio" relationship with ratio b
  • Change the value of ratio b numerator bn, the value of ratio b denominator bd is recalculated to maintain the "Paired Ratio" relationship with ratio a
  • Change the value of ratio b denominator bd, the value of ratio b numerator bn is recalculated to maintain the "Paired Ratio" relationship with ratio a

Note that you can change the "Paired Ratio" value as required.

How do I change the Paired Ratio value

The "Paired Ratio" value (the proportional relationship or ratio a to ratio b) can be changed by updating the "Paired Ratio" value in the ratio solver.

How are paired ratios calculated?

Paired ratios are calculated by adjusting the relating value within the ratio adjusted to ensure that the calculated amount sustains is relational value both within the ratio adjusted and to the related ratio by the "Paired Ratio" factor. The ratio formulas below define the formula for the calculation of each corresponding ratio as computed by the Ratio Solver calculator

Ratio a Numerator Formula and Calculation

an = ad/bd × bn
an = a/ ×
an =

Ratio a Denominator Formula and Calculation

ad = bd × an/bn
ad = × /
ad =

Ratio b Numerator Formula and Calculation

bn = bd/ad × an
bn = / ×
bn =

Ratio b Denominator Formula and Calculation

bd = ad × bn/an
bd = × /
bd =

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