Percentage Calculator

What do you need?

A — percent

B — value

15% of 80 = 12

12 = 80 × 15 ÷ 100

Computed in your browser with standard floating-point arithmetic, so very long results round on the last digit. For tax or invoice figures that have to reconcile exactly, check them against your source of record.

The five percentage questions

Almost every percentage problem is one of these. The formulas are short enough to memorise:

Percentage formulas
Question	Formula	Example
What is A% of B?	`B × A ÷ 100`	15% of 80 = 12
A is what percent of B?	`A ÷ B × 100`	12 of 80 = 15%
Percent change A → B	`(B − A) ÷ \|A\| × 100`	80 → 92 = +15%
Increase B by A%	`B × (1 + A ÷ 100)`	80 + 15% = 92
Decrease B by A%	`B × (1 − A ÷ 100)`	80 − 15% = 68

The two mistakes almost everyone makes

A percentage increase and decrease do not cancel out

Take 100, add 20% to get 120, then take 20% off: you land on 96, not 100. The second percentage is calculated from the larger number, so it removes more than the first one added. This is why a stock that falls 50% needs to rise 100% to recover.

Stacked discounts multiply, they do not add

“30% off, plus an extra 20% at checkout” is not 50% off. It is 0.70 × 0.80 = 0.56, so you pay 56% — a 44% discount. The discount calculator works this out for you.

What the % key does on a calculator

This is where calculators quietly disagree with each other. On most physical calculators — and in CalcBoard — 100 + 10% gives 110, because the % is read as “10% of the number on the left”. But 200 × 10% gives 20, because in a multiplication the % just means “divide by 100”.

Same key, two different behaviours, depending on the operator in front of it. That is the Casio convention, it is deliberate, and it catches people out constantly — the full explanation is here.

Percentages that need to be exact

Tax, interest, and invoicing are the cases where a rounding error in the twelfth decimal place eventually becomes a cent that does not reconcile. Browser calculators — including this one — use floating-point arithmetic, where 0.1 + 0.2 famously comes out as 0.30000000000000004.

CalcBoard computes in exact decimal instead, and lets you save a rate as a named variable: type tax=0.0825 once, then use subtotal*tax in any panel, in any mode, for as long as you like.

Frequently Asked Questions

How do I calculate a percentage of a number?

Multiply the number by the percentage and divide by 100. For 15% of 80: 80 × 15 ÷ 100 = 12. On a calculator you can usually type 80 × 15% directly.

How do I work out percentage change?

Subtract the original from the new value, divide by the original, and multiply by 100. From 80 to 92: (92 − 80) ÷ 80 × 100 = 15% increase. A negative result is a decrease.

Why doesn't a 20% increase then a 20% decrease get me back to where I started?

Because the second percentage is taken from a bigger number. 100 + 20% = 120, and 20% of 120 is 24, so you land on 96. The two percentages are of different bases.

Is 30% off plus 20% off the same as 50% off?

No. They multiply: 0.7 × 0.8 = 0.56, so you pay 56% of the original — a 44% discount, not 50%.

Why does 100 + 10% give 110 on a calculator?

Most calculators, CalcBoard included, treat % after a plus or minus as a percentage of the left-hand number. So 100 + 10% adds 10% of 100. After × or ÷, the same key simply divides by 100, so 200 × 10% is 20.

Percentages that stay exact

Exact decimal arithmetic, saved tax rates, and a second panel to check your work. Free to download.

Download Free on App Store