Percentage Calculator

What is a percentage?

A percentage is a way of expressing a number as a fraction of 100. The word comes from the Latin "per centum," meaning "by the hundred." Percentages make it easy to compare proportions and express parts of a whole.

Common percentage calculations

What is X% of Y?

$$\text{Result} = \frac{X}{100} \times Y$$

Example: What is 25% of 200?

$$\frac{25}{100} \times 200 = 50$$

X is what percent of Y?

$$\text{Percentage} = \frac{X}{Y} \times 100$$

Example: 50 is what percent of 200?

$$\frac{50}{200} \times 100 = 25\%$$

Percent change

$$\text{Percent Change} = \frac{\text{New} - \text{Original}}{\text{Original}} \times 100$$

Example: Change from 80 to 100:

$$\frac{100 - 80}{80} \times 100 = 25\% \text{ increase}$$

Converting percentages

To decimal

Divide by 100 (move decimal 2 places left):

• 25% = 0.25
• 7.5% = 0.075
• 150% = 1.50

To fraction

Put over 100 and simplify:

• 25% = 25/100 = 1/4
• 50% = 50/100 = 1/2
• 75% = 75/100 = 3/4

Quick mental math

Finding 10%

Move the decimal one place left:

• 10% of 250 = 25

Finding 5%

Half of 10%:

• 5% of 250 = 12.5

Finding 1%

Move decimal two places left:

• 1% of 250 = 2.5

Building other percentages

Combine these to find any percentage:

• 15% = 10% + 5%
• 22% = 20% + 2% = (2 × 10%) + (2 × 1%)

Common applications

Discounts

Original price minus the discount:

$$\text{Sale Price} = \text{Original} \times (1 - \frac{\text{Discount}}{100})$$

$80 item with 25% off:

$$\$80 \times (1 - 0.25) = \$60$$

Tax calculations

Add tax to the base price:

$$\text{Total} = \text{Price} \times (1 + \frac{\text{Tax Rate}}{100})$$

$50 with 8% tax:

$$\$50 \times 1.08 = \$54$$

Interest rates

Simple interest:

$$\text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time}$$

Grade calculations

$$\text{Grade \%} = \frac{\text{Points Earned}}{\text{Total Points}} \times 100$$

Percentage increases vs. decreases

A 50% increase followed by a 50% decrease does NOT return to the original value:

• Start: $100
• 50% increase: $150
• 50% decrease: $75

This is because the second percentage is calculated on the new amount.

Percentage points vs. percent change

These are different:

• Percentage points: The absolute difference (8% to 10% = 2 percentage points)
• Percent change: The relative change (8% to 10% = 25% increase)

Common percentage equivalents

Fraction	Decimal	Percentage
1/2	0.5	50%
1/4	0.25	25%
1/5	0.2	20%
1/10	0.1	10%
1/3	0.333...	33.33%
2/3	0.666...	66.67%