Percentage Calculator

This percentage calculator answers the six percentage questions people ask most: what is X% of a number, what percent one number is of another, the percentage increase or decrease between two numbers, how to add or take off a percentage, the percent difference between two values, and the original number when you know a part and its percentage. Every answer shows the formula and the working, so you can check it or learn the method.

What Is a Percentage?

"Percent" means "per hundred." 25% is 25 out of 100, which is the fraction 25/100 or the decimal 0.25. To turn a percentage into a decimal, divide by 100; to turn a decimal into a percentage, multiply by 100.

Percentage Formulas With Examples

1. What is X% of Y?

Result = X ÷ 100 × Y. What is 20% of 150? 0.20 × 150 = 30. Use this for tips, discounts and sales tax: 15% of a $64 restaurant bill is 0.15 × 64 = $9.60.

2. X is what percent of Y?

Percent = X ÷ Y × 100. 30 is what percent of 120? 30 ÷ 120 × 100 = 25%. This gives test scores: 42 correct out of 50 is 84%.

3. Percentage increase or decrease

Percent change = (new − old) ÷ |old| × 100. A price that rises from $80 to $100 has increased by (100 − 80) ÷ 80 × 100 = 25%. If it falls from $100 to $80, it has decreased by 20% – the base is different, so the percentages are not the same.

4. Increase or decrease a number by a percentage

New value = number × (1 ± percent ÷ 100). $250 increased by 15% is 250 × 1.15 = $287.50; decreased by 15% it is 250 × 0.85 = $212.50. A 20%-off sale on a $59.99 item costs 59.99 × 0.80 = $47.99.

5. Percent difference

When neither number is the "starting" value – comparing two prices or two measurements – use the percent difference: |A − B| ÷ ((A + B) ÷ 2) × 100. For 40 and 50 it is 10 ÷ 45 × 100 = 22.22%.

6. Finding the whole from a part

Whole = part ÷ (percent ÷ 100). If 45 is 30% of a number, the number is 45 ÷ 0.30 = 150. This finds an original price: an item that costs $68 after a 15% discount was originally 68 ÷ 0.85 = $80.

Common Percentage Mistakes

• Increases and decreases don't cancel. A 50% drop followed by a 50% rise leaves you at 75% of where you started: 100 → 50 → 75.
• Percent vs. percentage points. If a rate goes from 4% to 6%, that is a rise of 2 percentage points but a 50% increase.
• Stacked discounts. 20% off and then another 10% off is 28% off in total (0.8 × 0.9 = 0.72), not 30%.

Quick Mental Math Tricks

• 10%: move the decimal point one place left. 10% of $86.50 is $8.65.
• 5%: half of 10%. 20%: double 10%. 15%: 10% plus 5% – handy for tipping.
• X% of Y = Y% of X. 8% of 50 is the same as 50% of 8, which is 4.

For growth over many years, use the compound interest calculator; for price changes over time, the inflation calculator; and for grade averages, the GPA calculator.

GPA Calculator Compound Interest Calculator Inflation Calculator Date Calculator