Percentage Calculator

Five ways to ask a percentage question

Percent means “per hundred”: 15% is 15 out of every 100, or 0.15 as a decimal. Almost every percentage problem is one of five questions, and the calculator has a mode for each:

• What is X% of Y? A 15% tip on an $80 bill, or 20% of a class of 30.
• X is what percent of Y? You scored 42 out of 50 on a test and want it as a percentage.
• Percentage change from X to Y. Rent went from $1,200 to $1,290; how big was the rise?
• X is Y% of what number? The deposit of $450 is 15% of the price; what is the price?
• Increase or decrease by a percentage. Add 8% sales tax to a price, or take 25% off.

Pick the question, enter the two numbers, and the answer appears as you type. Open Show the working to see each step with your numbers, the same way you would write it out by hand.

Percentage formulas

Each mode is one short formula. X and Y are the two numbers you enter.

X, Y

the two numbers you enter

|X|

the size of X without its sign, so a change from a negative number keeps “increase” meaning up

1 + Y ÷ 100

the multiplier: a 15% increase multiplies by 1.15, a 15% decrease by 0.85

A percentage change from 0 has no answer, because it would mean dividing by zero. In that case the calculator shows the plain difference instead.

Worked example: one price, five questions

A price of 80 rises to 92. Here is what each mode says about it:

1. 15% of 80: 15 ÷ 100 = 0.15, and 0.15 × 80 = 12.
2. 12 is what percent of 80? 12 ÷ 80 = 0.15, and 0.15 × 100 = 15%.
3. Change from 80 to 92: 92 − 80 = 12; 12 ÷ 80 = 0.15, a 15% increase.
4. Back from 92 to 80: 80 − 92 = −12; −12 ÷ 92 = −0.130435, a 13.04% decrease — not 15%, because the starting value is now 92.
5. 12 is 15% of what? 15 ÷ 100 = 0.15, and 12 ÷ 0.15 = 80.
6. 80 increased by 15%: 80 × 15 ÷ 100 = 12, and 80 + 12 = 92 — or in one step, 80 × 1.15 = 92.

Common percentage mistakes

Percent versus percentage points

When the thing that changes is itself a percentage, there are two ways to describe the change. If an interest rate goes from 4% to 5%, it rose by 1 percentage point (5 − 4), but by 25 percent (1 ÷ 4 × 100). Both are correct; they answer different questions. News reports and loan documents should use “percentage points” for the simple difference, and it is worth checking which one a headline means.

Percentage changes don’t add up

Raising 100 by 10% gives 110; lowering 110 by 10% gives 99, not 100. Each percentage applies to a different starting value. Likewise a 50% fall followed by a 50% rise leaves you at 75% of where you began. To combine changes, multiply the multipliers: 1.10 × 0.90 = 0.99.

Working back to the original

To remove a percentage that was added — tax included in a price, a raise already applied — divide by the multiplier instead of subtracting the percentage. A price of 120 that includes 20% tax was 120 ÷ 1.2 = 100 before tax; taking 20% off 120 would give 96, which is wrong. The “X is Y% of what number?” mode does this when you enter 120 and 120%.