Percentage Calculator

Results are rounded to 2 decimal places.

• Decimals you enter are not turned into the approximations most computers use. Every digit is kept, and rounding happens once at the end, so a value such as 3.5 does not make the last digit wobble.
• When you calculate by hand, turn the percentage into a multiplier and multiply once. A 20% increase is × 1.2, and a 20% decrease is × 0.8.
• Percent change is the amount of change (B − A) divided by the absolute value of the starting value (|A|). When A is positive, this is the same as B ÷ A − 1. 150 ÷ 120 = 1.25, so it is a 25% increase.
• In A is what % of B, if B is 0 you see “B can’t be 0 for this calculation”. In percent change, if A is 0 you see “A can’t be 0 when calculating percent change”.

Every result below was produced by this calculator. On screen it appears as a sentence, such as “From 60,000 to 63,000 is a 5% increase”.

Two discounts in a row

A 20% discount followed by a 10% discount leaves 72% of the original price, which is a 28% discount in total, not 30%. Decreasing 50 by 28% gives the same 36.

Tips and sale prices

On a restaurant bill of $84.50, an 18% tip is $15.21 and a 20% tip is $16.90. A $59.99 item at 15% off costs $50.99.

A pay raise and an interest rate change

A salary that goes from $60,000 to $63,000 is a 5% raise, worth $3,000 a year. When an interest rate goes from 3.5% to 4%, the rate itself grew by 14.29%, while the difference between the two rates is 0.5 percentage points.

Test scores

15 correct answers out of 18 is a score of 83.33%. Going from 72 points to 90 points is a 25% increase in the score itself. On a test out of 100, that is also a move from 72% to 90%, which is 18 percentage points.

How much cheaper than the list price?

An item with a list price of $129 that sells for $99 is 23.26% off.

• Decreasing and then increasing by the same percentage does not get you back. $50 decreased by 20% is $40, and $40 increased by 20% is $48, because the second percentage is taken from a smaller number. At 50% the gap is bigger: 50 decreased by 50% is 25, and 25 increased by 50% is 37.5, only 75% of where you started.
• A value that halved has to double to recover. From 100 to 50 is a 50% decrease, but from 50 back to 100 is a 100% increase. The percentage down and the percentage needed to get back up are not the same.
• Percent (%) and percentage points are different. When a rate goes from 3% to 4%, it rose by 1 percentage point, and it rose by 33.33% as a percent change. Use percentage points for the difference between two rates, and percent for how much a rate changed relative to where it started.
• Taking the tax rate off a price that includes tax does not give the price before tax. With a sales tax of 8.25% (rates differ by state and city, so this is only an example), $100 becomes $108.25. Decreasing $108.25 by 8.25% gives $99.32, not $100. To remove the tax, divide: 108.25 ÷ 1.0825 = 100. Put another way, $100 is 92.38% of $108.25. VAT works the same way: a price of 120 that includes 20% VAT is 100 before VAT, not 96.
• When the starting value is negative, the calculator divides by its absolute value. For values that can go below zero, such as profit and loss, going from −100 to −50 is an improvement of 50, so it is a 50% increase. Dividing by A as it is would give −50% and read as a decrease, which is why the absolute value is used. When the sign flips, as when a loss turns into a profit, the number gets large: from −100 to 50 is a 150% increase. Look at the difference in amounts as well.
• Rounded shares may not add up exactly. 1 is 33.33% of 3, so three of those shares add up to 99.99%, because each result is rounded to 2 decimal places.
• In A is what % of B, if B is 0 there is nothing to divide by, so you see the reason instead of a result.

Can I add two discounts together?

No. 20% off and then another 10% off leaves 72% of the original price. That is not the same as 30% off once, which leaves 70%. Use Increase or decrease A by B% twice, one discount at a time.

What does “decrease” mean in a percent change result?

It means the value went down. For example, from 150 to 120 is a 20% decrease. Instead of a minus sign, the calculator says “increase” or “decrease” to show the direction.

When do I use percentage points instead of percent?

Use percentage points for the difference between two rates. If unemployment goes from 3.5% to 4%, it went up by 0.5 percentage points. The same change as a percent change is a 14.29% increase, so mixing the two up makes a change look much bigger or smaller than it is.

Can I find the original price from a discounted price?

There is no calculation type for working backwards, but you can do it by hand: divide the discounted price by (1 − the discount). If a price is $40 after 20% off, the original price is 40 ÷ 0.8 = $50. To check, enter “Decrease 50 by 20%” and see that the result is 40.

How do I take sales tax or VAT out of a total?

Divide the total by 1 plus the tax rate. A total of $108.25 with 8.25% sales tax is 108.25 ÷ 1.0825 = $100 before tax, and the tax is $8.25. Decreasing the total by the tax rate gives a smaller number than the price before tax.

What if I need more than 2 decimal places?

This calculator shows results to 2 decimal places only. If you need a more precise value, use the formulas in the table above. The decimals you enter are kept in full while calculating, and only the result is rounded when it is shown.