Everyday Math Calculators
Percentages, tips, discounts, sales tax and area.
Five calculators for the arithmetic that comes up constantly and still catches people out. Stacking 20% off and then 10% off is 28% off, not 30%, and that class of mistake is what these pages exist to prevent.
All 5 everyday math calculators
Percentages have four operations, not one
Most percentage confusion comes from treating one operation as though it were another. There are four distinct questions, and each has its own formula.
| Question | Formula | Example |
|---|---|---|
| What is X% of Y? | Y × X ÷ 100 | 15% of $80 is $12 |
| X is what % of Y? | X ÷ Y × 100 | 12 of 80 is 15% |
| Percent change | (new − old) ÷ old × 100 | 80 to 92 is +15% |
| Removing a percentage | total ÷ (1 + rate) | $107.25 at 7.25% tax is $100 |
Undoing a percentage is a division
This is the single most valuable line on the page, and it catches people repeatedly. If a percentage was added to a smaller base, removing it means dividing, never subtracting the same percentage back off.
Take a $107.25 receipt that includes 7.25% sales tax. The pre-tax price is 107.25 ÷ 1.0725 = $100.00. Subtracting 7.25% of the total instead gives $99.47, which is 53 cents wrong on a small receipt and hundreds of dollars wrong on an invoice. The same shape appears when pricing to a margin: to make 30% margin on a $70 cost you divide by 0.70 to get $100, not add 30% to get $91.
Stacked percentages multiply
Two discounts applied one after the other do not add. Twenty percent off then a further ten percent off leaves 0.80 × 0.90 = 0.72 of the price, which is 28% off, not 30%. Half price twice is 75% off, not free. The second discount is taken on the already-reduced price, so it is always worth less than its headline suggests, and the gap widens as the discounts get larger.
Tips, tax and the order they are applied
Whether a tip is calculated before or after sales tax changes the total, since tipping on the tax-inclusive figure adds a tip on money that was never for service. Custom varies and neither is wrong, but the tip calculator is explicit about which base it used so you can see the difference rather than guess at it. Splitting a bill adds one more wrinkle: rounding each share up individually collects slightly more than the total, which is usually the intention.
Square footage is the gateway to everything else
The square footage calculator sits in this category but feeds most of the site. Area is length × width for a rectangle, πr² for a circle, and a sum of rectangles for anything awkward. Once you have it, the material coverage chart turns it into a materials order for almost any product, which is the step where most projects actually go wrong.
Everyday Math Calculators: common questions
How do I remove sales tax from a total?
Divide by 1 plus the rate. A $107.25 total including 7.25% tax is 107.25 ÷ 1.0725 = $100.00. Subtracting 7.25% of the total instead gives $99.47, and the error grows with the amount.
How do two stacked discounts combine?
They multiply rather than add. Twenty percent off then ten percent off leaves 0.80 × 0.90 = 0.72 of the price, so 28% off rather than 30%. Half price applied twice is 75% off, not free.
Should I tip before or after tax?
Custom varies and neither is wrong, but tipping on the tax-inclusive total adds a tip on money that was never for service. The tip calculator states which base it used so the difference is visible rather than hidden.
What is the difference between percent and percentage points?
A rise from 5% to 6% is one percentage point but a 20% increase. Mixing the two is a common way for a modest change to be reported as a dramatic one, or the reverse, so state which you mean.