What is the formula for percentage?

Part ÷ whole × 100. 30 out of 200 is 15%, and entering 30 and 200 in "A is what percent of B?" gives the same result.

40. Enter 50 and 20 under "Increase or decrease A by B%" and "Decreased by 20%" shows 40; the discount itself, 10, comes from "What is B% of A?".

How do I calculate percent increase?

Subtract the starting value from the new value, divide by the starting value and multiply by 100. From 80 to 100 is 20 ÷ 80 × 100 = 25%.

How do I calculate percent decrease?

Subtract the new value from the starting value, divide by the starting value and multiply by 100. From 100 to 80 is a 20% decrease, shown as "Decrease" in the calculator.

If a price rises 20% and then falls 20%, is it back where it started?

No. 100 rises to 120, and 20% off 120 leaves 96, which is 4% below the start. The decrease is taken from the higher value.

What is the difference between percent and percentage points?

Percentage points are the plain difference between two percentages. Going from 10% to 15% is a rise of 5 percentage points, which is a 50% increase.

How do I find the original price before a discount?

Divide the sale price by (1 − discount rate). If 30% off gives 35, the original price was 35 ÷ 0.7 = 50.

How do I turn a test score into a percentage?

Divide the score by the maximum and multiply by 100. 68 out of 80 is 68 ÷ 80 × 100 = 85%.

How do I increase a number by a percentage?

Multiply it by (1 + percent ÷ 100). Raising 3,000 by 5% gives 3,000 × 1.05 = 3,150.

What is the percent change from 0?

It cannot be calculated, because you cannot divide by zero. The calculator shows no result in that case; describe the change as an amount instead.

Percentage & Percent Change Calculator

Find what percent of a number is, X as a percent of Y, percent increase or decrease, and a price after a discount, all on one screen as you type

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This percentage calculator puts four calculations side by side as cards: "What is B% of A?", "A is what percent of B?", "Percent change from A to B" and "Increase or decrease A by B%". Use it to work out a discount, a test score as a percentage, or how much sales or a share price rose or fell. There is no calculate button: results update as you type, and because all four cards stay on one screen you can check a share and a percent change with the same numbers without switching pages.

How to use

Pick the card whose title matches your question. Use "What is B% of A?" for a discount amount or a fee, and "A is what percent of B?" for a share or a completion rate.
In "What is B% of A?", enter 200 in "Number (A)" and 15 in "Percent (B)"; the line "15% of 200" shows 30.
In "A is what percent of B?", enter the "Part (A)" and the "Whole (B)". A score of 45 out of 60 gives 75%.
For percent change, enter the "Starting value (A)" and "New value (B)" under "Percent change from A to B". The result is labelled "Increase" or "Decrease", and the "Difference" between the two values appears below it.
For a sale price or a raised price, enter the amount and the percent under "Increase or decrease A by B%". With 20 you get "Increased by 20%" and "Decreased by 20%" at the same time.
Change any number and the result is recalculated at once, so you can compare scenarios quickly. The last numbers you entered are still there the next time you open the page.

How it works

The formulas are: B% of A = A × B ÷ 100; A as a percent of B = A ÷ B × 100; percent change = (B − A) ÷ A × 100; A increased by B% = A × (1 + B ÷ 100); A decreased by B% = A × (1 − B ÷ 100).
A "Starting value (A)" of 0 gives no percent change, and a "Whole (B)" of 0 gives no share; the result then shows a dash. A negative starting value is divided by its absolute value.
Percent results are shown to four decimal places and number results to six. Round money amounts yourself as needed.
The percent field accepts values above 100. For example, 150% of 200 is 300.
Everything is calculated in your browser, and the last numbers you entered are stored only in this browser on this device.

How to calculate a percentage: part ÷ whole × 100

A percentage expresses a part as if the whole were 100. To find what percent one number is of another, divide the part by the whole and multiply by 100: 30 out of 200 is 30 ÷ 200 × 100 = 15%. To go the other way and find a percent of a number, multiply the whole by the percent and divide by 100: 15% of 200 is 200 × 15 ÷ 100 = 30.

The most common mistake is swapping the part and the whole. If 30 of 40 students attend, attendance is 30 ÷ 40 × 100 = 75%, while dividing 40 by 30 gives a meaningless 133%. The "A is what percent of B?" card labels its fields "Part (A)" and "Whole (B)", so decide which number is the whole before you type.

Percent change formula and common mistakes

Percent change is (new value − starting value) ÷ starting value × 100. If monthly sales grow from 8,000 to 10,000, that is 2,000 ÷ 8,000 × 100 = a 25% increase; if they fall from 10,000 to 8,000, it is 2,000 ÷ 10,000 × 100 = a 20% decrease. The same two numbers give 25% or 20% depending on the base, and the base is always the starting value.

A rise followed by an equal percentage fall does not bring you back to the start. 100 rises 20% to 120, and 20% off 120 is 96, a net loss of 4%. Likewise, a stock that drops 20% needs a 25% gain to recover, from 80 back to 100; enter 80 and 100 under "Percent change from A to B" to see it.

When the starting value is positive, a decrease can never exceed 100%, but an increase has no upper limit. Going from 50 to 150 is a 200% increase, which means three times as much. Writing "tripled" as a "300% increase" is a frequent error, so keep "how many times" and "what percent more" apart.

How to calculate a discount percentage and the original price

If an item listed at 50,000 sells for 42,000, the discount is (50,000 − 42,000) ÷ 50,000 × 100 = 16%. Enter the list price and the sale price under "Percent change from A to B" and the "Decrease" shows −16. To apply a known discount, enter the list price and the percent under "Increase or decrease A by B%" and read a line such as "Decreased by 16%".

Stacked discounts do not add up. A 30% discount followed by an extra 10% takes 100,000 to 70,000 and then to 63,000, which is 37% off in total, not 40%. To find the original price from a sale price, divide by (1 − discount rate): 40,000 after a 20% discount was 40,000 ÷ 0.8 = 50,000. Adding 20% back to 40,000 gives 48,000, which is not the original price.

Percent vs percentage points

A percentage point is the plain difference between two percentages, while percent change compares the new rate with the old one. If a savings rate goes from 3% to 3.5% a year, it rose 0.5 percentage points, which is a 0.5 ÷ 3 × 100 ≈ 16.67% increase.

If a poll moves from 40% to 44%, that is a rise of 4 percentage points. Calling it a "4% rise" suggests it went up by 4% of 40, only 1.6 points. Entering 40 and 44 in the percent change card gives a 10% increase: that is the relative change, while 4 points is the difference between the two rates.

Questions and answers

What is the formula for percentage?: Part ÷ whole × 100. 30 out of 200 is 15%, and entering 30 and 200 in "A is what percent of B?" gives the same result.
What is 20% off 50?: 40. Enter 50 and 20 under "Increase or decrease A by B%" and "Decreased by 20%" shows 40; the discount itself, 10, comes from "What is B% of A?".
How do I calculate percent increase?: Subtract the starting value from the new value, divide by the starting value and multiply by 100. From 80 to 100 is 20 ÷ 80 × 100 = 25%.
How do I calculate percent decrease?: Subtract the new value from the starting value, divide by the starting value and multiply by 100. From 100 to 80 is a 20% decrease, shown as "Decrease" in the calculator.
If a price rises 20% and then falls 20%, is it back where it started?: No. 100 rises to 120, and 20% off 120 leaves 96, which is 4% below the start. The decrease is taken from the higher value.
What is the difference between percent and percentage points?: Percentage points are the plain difference between two percentages. Going from 10% to 15% is a rise of 5 percentage points, which is a 50% increase.
How do I find the original price before a discount?: Divide the sale price by (1 − discount rate). If 30% off gives 35, the original price was 35 ÷ 0.7 = 50.
How do I turn a test score into a percentage?: Divide the score by the maximum and multiply by 100. 68 out of 80 is 68 ÷ 80 × 100 = 85%.
How do I increase a number by a percentage?: Multiply it by (1 + percent ÷ 100). Raising 3,000 by 5% gives 3,000 × 1.05 = 3,150.
What is the percent change from 0?: It cannot be calculated, because you cannot divide by zero. The calculator shows no result in that case; describe the change as an amount instead.