Free · Ratios and proportions

Proportion Solver with Worked Steps

Solve an unknown ratio term with signed numbers and see the cross-multiplication steps for the value the calculator actually found.

  • Formula & worked example
  • Private in your browser
  • No signup
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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

Private by default

Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

The proportion 2/3 = c/9 gives c = 6.

a/b = c/d; a*d = b*c, with b and d nonzero.

Worked example

Enter these known values and leave the other values blank.

A
2
B
3
D
9
C
6

Assumptions and limitations

  • This model compares two ratios a/b = c/d. Both denominator terms b and d must be nonzero. Signed values and zero numerators are allowed.
  • Supply three terms and leave the unknown blank. Some zero-input combinations have no unique solution: the calculator must not invent a value when an inverse divides by zero.
  • Worked steps follow the currently calculated field. Manually entered or locked values are not automatically labeled as calculated; clearing or editing a field may change which worked solution appears.

Common questions

How do I solve a proportion?

Cross multiply a*d = b*c, then divide by the coefficient of the unknown when that coefficient is nonzero.

Can a denominator be zero?

No. A ratio with denominator zero is undefined. Some zero-numerator inverse requests are underdetermined and require another independent known quantity.

References

Bind calculated-state display predicates to the exact proportion source and spec; preserve actual state semantics. Exclude undefined ratio denominators, retaining meaningful signed and zero numerators.

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