Guide
Percentages made easy: mental maths tricks
You do not need a calculator for most everyday percentages. A handful of tricks gets you close enough to decide quickly, and the calculator can confirm the exact answer.
Find 10% first
10% is just moving the decimal point one place left: 10% of 86.40 is 8.64. From 10% you can build almost anything: 20% is double it, 5% is half of it, 15% is 10% plus 5%, 1% is moving two places.
Work out a tip in seconds
For an $86.40 bill: 10% is $8.64; double it for 20% = $17.28. For 15%, add half of the 10% ($4.32) to get $12.96.
Sale prices
"30% off $120": find 10% ($12), triple it ($36), subtract: $84. Or think of it as paying 70%: 7 x $12 = $84. Thinking in terms of what you pay (70%) is usually faster than thinking about what you save.
Flip the numbers
x% of y equals y% of x. So 8% of 50 is the same as 50% of 8 - which is 4. Pick the easier direction.
Percentage change
Change = (new - old) / old. From 40 to 50 is a rise of 10 on a base of 40, which is 25%. Remember the base is always the old number, so a rise from 40 to 50 (+25%) is not undone by a fall from 50 to 40 (-20%).
Common traps
- Two discounts of 20% do not make 40%; they make 36%.
- A "50% increase" followed by a "50% decrease" ends up 25% lower than you started.
- Percentage points and percent are different things: going from 3% to 4% is +1 point but +33% in relative terms.
Practice with the percentage calculator until these feel natural.