Math Calculators

Everyday arithmetic that is easy to do wrong under time pressure, usually because percentages do not behave the way intuition suggests.

The percentage mistakes worth knowing

Increases and decreases do not cancel. £100 plus 50 percent is £150; 50 percent off £150 is £75, not £100. Each change applies to a different base. To reverse an increase you divide by (1 + rate).

Discounts stack multiplicatively. Two successive 30 percent reductions leave you paying 0.70 × 0.70 = 49 percent of the original — a 51 percent total discount, not 60.

Finding an original price means dividing. An item at £70 after 30 percent off was £100, because 70 ÷ 0.70 = 100. Adding 30 percent back to £70 gives £91 and is the most common error the Discount Calculator exists to prevent.

Percentage points are not percentages. Moving from 10 percent to 15 percent is a rise of five percentage points but a 50 percent relative increase. Reporting one as the other is misleading.

The rest

The Percentage Calculator covers the general forms — X percent of Y, percentage change, and reverse percentages. The Tip Calculator handles bill splitting, where the convention in the United States is to tip on the pre-tax subtotal. The Age Calculator counts complete years elapsed, which is why you are still 29 the day before your 30th birthday. The GPA Calculator weights each grade by credit hours, so a poor result in a four-credit course moves your average twice as much as one in a two-credit course.