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Reference

What is the percentage formula?

One page to rule the four patterns you will see in school, shopping and spreadsheets.

There is not a single magic “percentage formula” printed on a stone tablet—there is a family of formulas that all come from the same idea: express a relationship out of 100. Once you recognise which story you are reading (slice of a pie, growth, shrinkage, or comparing two snapshots), you pick the right member of the family and avoid the classic trap of multiplying when you should add, or vice versa.

Bookmark this cheat sheet next to the percentage calculator so you can jump between Basic, Increase and Decrease modes without hunting through notes.

Spreadsheet apps hide these formulas behind built-in functions—understanding the raw algebra helps when your model breaks and you need to debug a rogue absolute reference.

Detailed explanation: the four core patterns

Question typeFormula (symbolic)Quick words
What is p% of N?(p ÷ 100) × NPercent of a number / slice
Increase N by p%N × (1 + p ÷ 100)Growth multiplier
Decrease N by p%N × (1 − p ÷ 100)Shrink multiplier
Change from old to new((new − old) ÷ old) × 100%Relative change

Markup, margin, commission and interest reuse these bones but rename the numerator and denominator—see the dedicated finance FAQs so vocabulary stays precise.

Keep a sticky note on your monitor with the four formulas until they become muscle memory—speed on exams and interviews comes from pattern recognition, not from rediscovering the multiplier each time.

Examples and real-world scenarios

  • Slice: 12% of 250 km driven ≈ 0.12 × 250 = 30 km.
  • Growth: 250 employees growing 8% → 250 × 1.08 = 270.
  • Shrink: $180 shoes with 35% off → 180 × 0.65 = 117 sale price.
  • Change: ARR from $1.2M to $1.5M → (0.3 ÷ 1.2) = 25% growth.
  • Slice (science): If 8 mL of a 250 mL buffer is additive, that additive is (8 ÷ 250) × 100% = 3.2% of the volume—always confirm whether the problem wants mass or volume percent.

Common mistakes and misconceptions

  • Using increase formula when the sentence says “of.” Re-read for the word “of” versus “more than.”
  • Adding percents that were measured on different bases. Always track the denominator.
  • Letting calculators hide structure. Write the formula name in the margin once—future you will thank present you.
  • Reusing increase shortcuts on “percent of” problems. If the wording includes “of,” pause before you multiply by (1 + p/100)—that multiplier belongs to growth stories, not slice stories.

Calculation tips and best practices

Convert every percent to decimal early, do all multiplications, convert back to percent only at the end if needed.

When tutoring, colour-code: baseline in blue, percent in green, result in black—visual separation reduces sign errors.

People also ask

Quick answers to the most-related questions for this topic.

Note: Percentage results are estimates for informational use only. Always verify critical financial, tax, or business calculations with a qualified professional.

Apply these formulas in the calculator

Open the on-site percentage calculator: Basic mode for “what is X% of Y”, Increase for growth, Decrease for reductions, and Basic or Decrease for sale prices. Compare with the discount, percent-off and percentage change FAQs linked throughout this library.

Open the calculator Percent of a number FAQ

Related FAQs

Keep learning — these questions cover closely-linked percentage topics.

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