Percentage Calculator

Percentage formula and examples

In the formulas below, P always stands for the percent, and V stands for the value we're calculating the percentage of. When there are two values involved, we label them V1 and V2.

1. Basic percentage calculation
This calculation answers the question: what is P percent of V?
The formula: (P/100) × V

For example: what is 15% of 160? Plugging into the formula: (15/100) × 160 = 0.15 × 160 = 24.

2. Adding or subtracting a percentage
This calculation answers the question: add P percent to V, or subtract P percent from V.

To add a percentage, the formula is: V + (P/100 × V)

For example: add 25 percent to 280. Working through the formula: 280 + (25/100 × 280) = 280 + (0.25 × 280) = 350.

Subtracting a percentage works the same way. How do you take P percent off of V?
The formula: V − (P/100 × V)

For example: take 20% off of 240. Applying the formula: 240 − (20/100 × 240) = 240 − (0.2 × 240) = 192.

3. Calculating the percentage difference between two values
Our calculator uses the following formula to find the percent difference between two values, V1 and V2, where V1 is the starting value and V2 is the ending value.
percent change = ((V2 − V1) / V1) × 100

A positive result means a percentage increase.
A negative result means a percentage decrease.

For example: what's the percent increase from 45 to 79?
Applying the formula: ((79 − 45) / 45) × 100 = 75.55%. That's a 75.55% increase.

Other percentage calculators

Here are a couple of less common but still handy percentage questions:
V1 is what percentage of V2?
V1 is P% of what number?

Percent error

You'll need percent error (the deviation in percentage terms) any time you're comparing a measured or estimated value against the actual, accepted value — a common step in science class labs and quality-control checks.

Converting percentages to decimals or fractions

Converting a percentage to a decimal is easy once you remember that 100% is the same as the number 1.
So 50% is 0.5, 16% is 0.16, and so on.
The formula: decimal = percent / 100

Turning a percentage into a fraction follows the same logic.
For example, 35% is the fraction 35/100.
From there you can simplify by dividing the numerator and denominator by the same number. Dividing 35/100 by 5 gives you 7/20 — the simplest form of that fraction, since you can't divide the top and bottom by anything else.

Here's a quick reference table:

Discount calculation / Percent off

Figuring out how much a percentage discount takes off a price is just a basic percentage calculation — our calculator above handles it in one step.

The formula: discount = (P/100) × V, where P is the discount percentage and V is the original price.

For example: a store is running 13% off a $65 item during a Black Friday sale. How much do you save? Discount = (13/100) × 65 = $8.45. Your final price at checkout comes out to $56.55.

Sometimes it works the other way — you know the dollar amount you saved and want to know what percentage discount that represents.
You can use this formula: P = (100/V2) × V1

For example: you save $12 off a $88 total. The discount percentage is: (100/88) × 12 = 13.64%.

How to use our percentage calculator in everyday life: examples

1. Sales tax
Say your state charges 8 percent sales tax, and that 8 percent works out to $16 on a purchase.
What was the sticker price before tax?
Eight percent is the fraction 8/100, which simplifies to 2/25.
We can solve for the answer with this equation: 8/100 × X = 2/25 × X = 16.
That means X = $200.

2. Using a dollar-off coupon
Say you're buying something that costs $35, and you have a $5-off coupon.
What percentage discount does that coupon actually give you?
We can solve this with the comparison: P/100 × 35 = 5.
Working it out: P = 500/35 = 14.29%.

3. Using a percentage-off coupon
Say you're shopping for a new refrigerator that costs $360, and during a Memorial Day sale you find a coupon for 12 percent off. How much would you save by using it?
We can solve this with: 12/100 × $360 = $43.20.

4. Calculating a tip
After a good meal at a restaurant, you want to leave a fair tip for the server. In the U.S., 18–20 percent is the standard tip on the pre-tax total. Say the bill comes to $89 and you decide on 18 percent — what should the tip be?
The math: 18/100 × 89 = $16.02.

5. 401(k) employer match
Say your employer matches 4 percent of your salary in your 401(k), and your annual salary is $50,000. How much does your employer contribute for the year?
We calculate 4 percent of the salary: 50,000 + 4/100 × 50,000 = 50,000 + 2,000 = $2,000 in matching contributions on top of your own.

6. Growth in a savings account
Say you have $450 in a savings account. After a year it's grown to $465.
What's the percentage increase over that year?
percentage increase = ((V2 − V1)/V1) × 100 = ((465 − 450)/450) × 100 = 3.33%.

7. A price drop during a clearance sale
An oak dresser at the furniture store is normally $420, but it's marked down to $360 for a clearance sale.
What's the percent change between the two prices?
percentage decrease = ((V2 − V1)/V1) × 100 = ((360 − 420)/420) × 100 = −14.28%.

8. Batting average and rounding
A baseball player's true batting average works out to .1286 (or 12.86 when scaled to 100), but it's commonly reported rounded to .140 (14 when scaled to 100).
What's the percent error introduced by rounding?
Using the formula: 100 × |measured value − actual value| / |actual value| = 100 × |12.86 − 14| / |14| = 8.14%.

9. SAT/ACT score percentile rounding
Say a student's raw percentile score of 5.2 gets rounded down to 5 on a score report. What's the percentage deviation caused by that rounding?
Using the same formula: 100 × |measured value − actual value| / |actual value| = 100 × |5 − 5.2| / |5.2| = 3.85%.