\%\text{ change}=\frac{\text{new}-\text{old}}{|\text{old}|}\times100\%Variables
- old: original value
- new: later value
- % change: signed relative difference
How to use this formula
Measures relative increase or decrease from an original nonzero value.
Important notes
- The original value must be nonzero.
- A positive result is an increase; a negative result is a decrease.
Quick example
A change from 80 to 100 is a 25% increase.
Applicability, worked calculation, and verification
Domain and applicability
The original value must be nonzero; the sign distinguishes an increase from a decrease, and context determines whether percentage change is meaningful.
Units
- old and new values must use the same unit
- the final result is a percentage
Assumptions and domain checks
- The original value must be nonzero.
- For the Percentage Change Formula, every denominator must be nonzero, and the numerator and denominator must remain correctly grouped.
- Map every symbol to the modeled quantity and verify units, domain restrictions, and simplifying assumptions.
Do not use this formula when
- Do not use Percentage Change Formula when its variable definitions, domain restrictions, or structural assumptions differ from the problem.
Boundary and special cases
- For Percentage Change Formula, check zero, negative, and extreme input values before relying on the result.
- When using Percentage Change Formula, confirm that denominators, radicals, logarithms, and domain restrictions remain valid for the chosen values.
Equivalent and alternative forms
- Keep the canonical LaTeX form \%\text{ change}=\frac{\text{new}-\text{old}}{|\text{old}|}\times100\% for copying; rearrange only after preserving equivalence and domain restrictions.
Worked example
A value rises from 80 to 100. Percentage change = (100 − 80)/80 × 100% = 25%.
- Identify the original value as 80 and the new value as 100.
- Calculate the change: 100 − 80 = 20.
- Divide by the original value: 20/80 = 0.25.
- Multiply by 100% to report a 25% increase.
Independent verification
Applying a 25% increase to 80 gives 80 × 1.25 = 100, recovering the stated new value.
Common mistakes
- When copying Percentage Change Formula, keep the complete numerator and denominator grouped; a missing brace or parenthesis changes the result.
- Verify the result of Percentage Change Formula with a known case, inverse operation, dimensional check, or independent calculation before publishing it.
Continue the workflow
Use Percentage Change Formula in your own work
- Check the domainMatch the variables and assumptions to the problem before substituting values.
- Copy the exact notationPreserve grouping, signs, and exponents in
\%\text{ change}=\frac{\text{new}-\text{old}}{|\text{old}|}\times100\%. - Edit or convertOpen the expression in the LaTeX editor, then export it for your document or web page.
Review and verification
Last reviewed: 2026-07-26
Review method: Reviewed the notation, variable definitions, applicability conditions, worked workflow, and verification method for Percentage Change Formula.
Verified against: OpenStax Algebra and Trigonometry; NIST Digital Library of Mathematical Functions
Automated quality check: Passed the core formula indexing gate.
Formula references
- Algebra and Trigonometry 2eOpenStax, Rice University — Reviewed algebra, functions, sequences, trigonometry, and analytic geometry definitions and examples.
- Digital Library of Mathematical FunctionsNational Institute of Standards and Technology — Definitions, notation, identities, and reference material for mathematical functions.
Frequently asked questions
What is the Percentage Change Formula used for?
Measures relative increase or decrease from an original nonzero value.
Can I copy this formula as LaTeX?
Yes. Copy \%\text{ change}=\frac{\text{new}-\text{old}}{|\text{old}|}\times100\% or open it in the LaTeX editor.
What should I check before using it?
Confirm that each variable, unit, domain restriction, and assumption matches the problem.