Percentages appear everywhere - sales tax, discounts, tips, investment returns, and grade scores. These shortcuts let you calculate them in seconds, in your head.

The Core Swap Trick

x% of y = y% of x

This sounds odd but it’s mathematically true. And it makes hard problems easy:

  • What is 8% of 25? → What is 25% of 8? → 2 ✓
  • What is 4% of 75? → What is 75% of 4? → 3 ✓

Finding 10% and Building From It

10% of any number is just the number divided by 10 (move the decimal point left once).

  • 10% of 340 = 34
  • 5% = half of 10% → 5% of 340 = 17
  • 15% = 10% + 5% → 15% of 340 = 51
  • 20% = double 10% → 20% of 340 = 68
  • 1% = 10% ÷ 10 → 1% of 340 = 3.4

Quick Tip Calculations

For a restaurant bill:

  • 20% tip: double the 10% you calculated
  • 18% tip: 10% + 5% + 3% (which is close to 10% × 0.3)
  • 15% tip: 10% + 5%

Calculating Discounts

“30% off $80” → 30% of 80 = 24, so you pay $56.

Fast method: 100% − 30% = 70%. 70% of 80 = 56. Done.

Percentage Change Formula

(New − Old) ÷ Old × 100 = % Change

If a stock goes from $120 to $150: (150 − 120) ÷ 120 × 100 = 25% increase

Reverse Percentages

If a price after 20% increase is $240, what was the original?

Original = $240 ÷ 1.20 = $200

Not $240 − 20% (which would give $192 - a common mistake!).

Try the Calculator

For complex calculations, use our Percentage Calculator.