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Formula reference

The percentage formula, explained without the jargon

One formula, three rearrangements, and almost every real-world percentage problem covered.

The percentage formula is a single equation that splits into a family of related shapes — one for each question you might ask. "What percent is this of that?", "What is X% of this?", and "What is the percentage change between two values?" all share the same DNA. Memorising one formula plus three rearrangements covers the vast majority of percentage problems in everyday life.

This page walks through the headline formula first, then shows how the other shapes are just rearrangements of the same equation.

The Percent of a number formula

The formula is short:

(p ÷ 100) × N

Convert the percent to a decimal, then multiply by your number. 35% of 280 is 0.35 × 280 = 98.

When to reach for it: Use this whenever a sentence contains the word of: tips, sales tax slices, exam scores, commissions on revenue.

The four percentage formulas you actually need

Memorise these four and almost every problem becomes substitution:

  1. Percent of a number: result = (p ÷ 100) × N
  2. Percent one number is of another: p% = (part ÷ whole) × 100%
  3. Percentage increase: new = N × (1 + p ÷ 100)
  4. Percentage decrease: new = N × (1 − p ÷ 100)

Print the list, stick it to your monitor for a week, and the substitution becomes automatic.

Worked examples you can copy

Each example walks the same formula with different numbers so the steps stay familiar.

  • 25% of $1,200 → 25% × 1,200 ÷ 100 = 300.
  • 17.5% VAT on £64 → 17.5% × 64 ÷ 100 = 11.2.
  • 85 marks out of 100 = ?% → 85% × 100 ÷ 100 = 85.
  • 40% of an 8-hour shift → 40% × 480 ÷ 100 = 192.

Common mistakes to avoid

  • Multiplying by the raw percent (e.g. 8) instead of the decimal rate (0.08). Always divide by 100 first.
  • Treating "p% more than N" as "p% of N". They differ by the original N.
  • Reusing the wrong member of the formula family — increase, decrease, change and percent-of all live in the same neighbourhood.
  • Ignoring units. Percentages are dimensionless; both parts of a ratio must share the same unit.

Calculation tips & best practices

  • Write the formula at the top of your scratch paper, then plug in numbers. The visible formula prevents algebra slips.
  • Convert every percentage to a decimal before you do anything else.
  • Sanity-check magnitude: the result should be smaller than the whole when you take a percent of it.
  • Reverse the calculation as a check (a 25% slice times four should give back the whole).

People also ask

The questions readers most often pair with this topic.

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

Plug your numbers into the calculator

Open the calculator, pick the mode that matches the question (Basic, Increase, Decrease or Change), and let the formula do the substitution for you.

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