Free · Algebra and geometric models

Signed Percentage Change and Reverse Values

Measure change relative to the absolute starting value and solve supported reverse-value branches.

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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.

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

Formula and method

For the worked inputs, Percent change = 20, difference = 20.

r=(final−initial)/|initial|; final=initial+r|initial|

Worked example

Enter these known values and leave the other values blank.

Initial value
100
Final value
120
Percent change
20 %

Assumptions and limitations

  • The starting value is nonzero. Signed starting and ending values are supported.
  • A reverse starting-value calculation can have two sign branches. The inverse chooses a positive starting value when possible; otherwise it returns a negative branch. Some final/rate pairs are indeterminate or have no real branch.

Common questions

What must I enter?

Choose the mode when available and enter its independent known quantities. Leave an unknown editable quantity empty to use a supported inverse.

How should I use the result?

Interpret the numbers within the stated mathematical assumptions. Available unit selectors convert quantities; display rounding does not replace the internal calculation.

References

Both forward variants use the absolute starting value. The captured signed branch divided by initial in one equation and selected an incorrect inverse for negative starts. The reverse start selects a positive valid branch when available, otherwise the negative branch; indeterminate and impossible pairs cannot produce a finite nonzero start.

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