Percentages & Everyday Math Calculators

Which calculator answers which question

Most percentage problems are one of four questions wearing different clothes. Find the sentence closest to yours and the tool that solves it directly, rather than converting the problem by hand first.

The formulas behind this category

Part = whole × percent ÷ 100

Percent = part ÷ whole × 100

Whole = part ÷ percent × 100

Percent change = (new − old) ÷ old × 100

Sale price = price × (1 − discount ÷ 100)

Net from gross = gross ÷ (1 + tax rate ÷ 100)

Tip = bill × tip% ÷ 100

Mean = sum of values ÷ count of values

Percent, percentage point, and percent change

These three are not interchangeable, and mixing them up is the single most common error in this category — including in published reporting. If a rate moves from 4% to 6%:

• it rose by 2 percentage points — the plain arithmetic difference;
• it rose by 50 percent — the relative change, 2 ÷ 4 × 100;
• writing “it rose by 2 percent” is simply wrong, and off by a factor of 25.

Use percentage points when both numbers are already percentages. Use percent change when you are comparing any two quantities — prices, weights, visitor counts — and want the size of the move relative to where it started.

Fractions, decimals and percentages side by side

The conversions worth knowing by heart, because they turn most mental percentage math into a one-step operation.

One more shortcut that surprises people: X% of Y always equals Y% of X. 18% of 50 is awkward; 50% of 18 is nine. The mental percentage guide works through more of these.

Where everyday percentage math goes wrong

Stacked discounts do not add up

“20% off, then another 10% at the till” is not 30% off. The second discount applies to the already-reduced price: 100 → 80 → 72, which is 28% off. Two discounts of a% and b% combine to 1 − (1 − a) × (1 − b), always less than their sum.

A percentage increase is not undone by the same percentage decrease

Add 50% to 100 and you get 150. Take 50% off 150 and you get 75, not 100. To reverse a p% increase you need a decrease of p ÷ (100 + p) × 100 — so undoing +25% takes −20%, and undoing +100% takes −50%.

Removing tax is division, not subtraction

With 20% VAT included, a $120 price is not $120 − 20% = $96. The tax was added to the net price, so you divide: 120 ÷ 1.20 = $100 net, $20 tax. Subtracting instead overstates the net figure on every invoice you touch.

Averaging percentages ignores the size behind them

A 90% pass rate in a class of 10 and a 50% rate in a class of 90 do not average to 70%. Weight by the group sizes: (9 + 45) ÷ 100 = 54%. The average calculator shows mean, median and mode together, which usually makes an outlier-driven mean obvious at a glance.

The formulas behind this category, and the published sources they come from, are listed on the methodology page.