Percentage Calculator

How it works

Percent means “per hundred”. A% of B = A ÷ 100 × B. A as a percent of B = A ÷ B × 100. Percentage change from A to B = (B − A) ÷ A × 100. Increasing B by A% multiplies it by (1 + A/100); decreasing multiplies by (1 − A/100).

The three percentage questions

Almost every percentage problem is one of three questions. The calculator above handles all three, plus increasing or decreasing a number by a percentage:

“Percent” means “per hundred”, so every formula is just a way of scaling to or from 100. If you remember that 20% is the decimal 0.2 and the fraction 1/5, you can switch between the three forms freely.

How to calculate a percentage of a number

Divide the percentage by 100, then multiply by the number. 35% of 240: 35 ÷ 100 = 0.35, and 0.35 × 240 = 84. A useful fact is that the order does not matter — A% of B is the same as B% of A — so 8% of 50 is the same as 50% of 8, which is obviously 4.

How to work out what percent one number is of another

Divide the part by the whole and multiply by 100. If you scored 42 out of 60 on a test, 42 ÷ 60 = 0.7, and 0.7 × 100 = 70%. Make sure the “whole” is on the bottom: 60 is not 142.9% of 42 in this context, even though that division is also valid arithmetic. The percent to decimal converter turns the result into a decimal or a fraction.

Percentage increase and decrease

Percentage change compares a new value with an old one: (new − old) ÷ old × 100. A rent rise from $1,200 to $1,320 is (1,320 − 1,200) ÷ 1,200 × 100 = +10%. A fall from $1,320 back to $1,200 is (1,200 − 1,320) ÷ 1,320 × 100 = −9.0909% — not −10%, because the starting point changed. For more on this, including percentage difference, use the percentage change calculator.

To apply a percentage change, multiply by a factor: increasing by 15% means × 1.15; decreasing by 15% means × 0.85. 15% of 200 is 30, so 200 + 15% = 230 and 200 − 15% = 170.

Test scores as percentages

To turn a score into a percentage, divide the marks you got by the marks available and multiply by 100. Here are some common results:

How percentages map to letter grades varies between schools and courses, so check your own grading scale. A common US scale treats 90% and above as an A, 80–89% as a B and 70–79% as a C.

Reverse percentages: finding the original number

If a price after a 20% discount is $60, the original is not $60 + 20% ($72). The sale price is 80% of the original, so divide: 60 ÷ 0.8 = $75. The same applies to tax: if $108 includes 8% tax, the pre-tax price is 108 ÷ 1.08 = $100. Whenever you know the result of a percentage change, divide by the multiplier to get back to the start.

Percent vs percentage points

When a rate itself is a percentage, say “percentage points” for the difference. If an interest rate goes from 4% to 5%, it rose by 1 percentage point — but by 25 percent relative to where it started. News reports about interest rates, unemployment, polls and taxes often depend on this distinction.

Successive percentages do not simply add

A 10% rise followed by a 10% fall does not bring you back to the start: 100 × 1.10 × 0.90 = 99, a net 1% loss. Two 10% rises give 100 × 1.1 × 1.1 = 121, a 21% increase, not 20%. To combine changes, multiply the factors. Stacked discounts work the same way: “20% off, then an extra 10% off” is 0.8 × 0.9 = 0.72, a total of 28% off, not 30%. The discount calculator shows the sale price and savings for any discount.

Percentages, fractions and decimals

Every percentage can be written as a fraction and as a decimal. Knowing the common ones makes many calculations instant:

So 25% of a number is a quarter of it, and 33⅓% is a third. The fraction to decimal converter and decimal to fraction calculator handle any other value.

Percentages over 100% and negative percentages

A percentage can be larger than 100. 150% of 40 is 60 — one and a half times the number. A value that doubles has grown by 100%, and one that triples has grown by 200%. Percentage change can also be negative: a fall from 50 to 30 is −40%. A decrease can never exceed −100%, because that would take a positive quantity below zero, but an increase has no upper limit.

Using the % key on a phone or desk calculator

On many phone and desk calculators, typing 200 + 15 % = gives 230, because the % key first works out 15% of 200 and then adds it. Typing 200 × 15 % gives 30. Calculators do not all behave the same way, so test yours with an example you know before relying on it — or use the calculator on this page, which always shows the working.

Percentages in your head

Tips work the same way: 15% of a $64 bill is $6.40 + $3.20 = $9.60; 20% is $12.80.

Where you use percentages

• Shopping: discounts, coupons and sales tax.
• School and work: test scores, grades, attendance, completion rates.
• Money: pay rises, price changes, interest rates and inflation figures.
• Health and food: % daily value on nutrition labels, body-fat and hydration readings.
• Data: survey results, market share, battery and download progress.

For finance decisions involving interest or investments, use a dedicated tool or professional advice; this calculator does the arithmetic only.

Percentages in Excel and Google Sheets

• A% of B: =A1*B1 with A1 formatted as a percentage (or =A1/100*B1 if A1 holds 20).
• A as a percent of B: =A1/B1, then format as Percentage.
• Percentage change: =(B1-A1)/A1, formatted as Percentage.
• Increase by a percentage: =B1*(1+A1).

A frequent spreadsheet error is typing 20 into a cell formatted as a percentage, which Excel reads as 2,000%. Type 20% or 0.2 instead.

Common mistakes

• Using the wrong base for percentage change: always divide by the original value.
• Adding successive percentages instead of multiplying the factors.
• Reversing a discount by adding the same percentage back. Divide by the multiplier instead.
• Confusing percent and percentage points when the quantity is itself a rate.