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Percentage calculator

Pick the question you are really asking, fill in two or three numbers and read the answer as a sentence, with the formula and the steps underneath. It covers 20% of 150, how much something went up or down, the price before a percentage was added, two discounts in a row, and a tip split between friends. You can type 1.5 or 1,5. Everything is worked out in your browser and nothing is sent anywhere.

Results are rounded once, at the end, half away from zero (0.125 becomes 0.13). Pick 0 to 8 decimals.

Type 1.5 or 1,5, negative numbers are fine. A single comma or dot is a decimal mark. A lone 1,234 is ambiguous (1.234 or 1234?), so it is not guessed: write 1234 or 1.234. Thousands separators work when there is also a decimal part, such as 1,234.5 or 1 234,5. Up to 60 characters.

What is X% of Y?

For example, 20% of 150.

20% of 150 is 30.

Formula

Y × X ÷ 100

Steps

  1. 1. 20 × 150 = 3000
  2. 2. 3000 ÷ 100 = 30

This result is exact. Divisions in the steps are shown rounded. The answer is worked out from the exact values and rounded only once.

X is what percent of Y?

For example, 30 out of 150.

30 is 20% of 150.

Formula

X ÷ Y × 100

Steps

  1. 1. 30 ÷ 150 = 0.2
  2. 2. 0.2 × 100 = 20

This result is exact. Divisions in the steps are shown rounded. The answer is worked out from the exact values and rounded only once.

Percentage change from A to B

How much a value went up or down, as a percent of where it started.

From 80 to 100 is an increase of 25%.

Formula

(B − A) ÷ |A| × 100

Steps

  1. 1. 100 − 80 = 20
  2. 2. 20 ÷ 80 × 100 = 25
  • Percent and percentage points are different. If A and B are themselves percentages, for example a rate that moved from 80% to 100%, the gap is 20 percentage points (a plain subtraction). The relative change is 25%.
  • Going back from 100 to 80 takes a change of -20%, not the same percent: each is measured against a different starting value.

This result is exact. Divisions in the steps are shown rounded. The answer is worked out from the exact values and rounded only once.

X is P% of what?

Find the whole when you know a part and its percent.

30 is 20% of 150.

Formula

X × 100 ÷ P

Steps

  1. 1. 30 × 100 = 3000
  2. 2. 3000 ÷ 20 = 150

This result is exact. Divisions in the steps are shown rounded. The answer is worked out from the exact values and rounded only once.

Add or take off a percentage

Price with a percentage added (such as a sales tax or VAT rate you enter yourself) or taken off, and the way back to the price before.

Both directions: adding is Amount × (1 + P ÷ 100), and getting back to the amount before is Amount ÷ (1 + P ÷ 100).

Enter the rate yourself. This page does not know any tax rates and does not give tax advice.

100 plus 20% is 120.00. The added 20% is 20.00.

Formula

Amount × (1 + P ÷ 100)

Steps

  1. 1. 1 + 20 ÷ 100 = 1.2
  2. 2. 100 × 1.2 = 120.00
  • Careful: taking 20% off 120 gives 96.00, not 100.00 (it is off by 4.00). A percentage applies to the amount it is taken from, so adding a percent and taking the same percent off do not cancel out.

This result is exact. Divisions in the steps are shown rounded. The answer is worked out from the exact values and rounded only once.

Discount, with a second discount stacked

Leave the second discount empty for a single discount.

100 with 20% off, then 10% off, is 72.00. You save 28.00, which is 28% off in total.

Formula

Price × (1 − D1 ÷ 100) × (1 − D2 ÷ 100)

Total off = 100 − (1 − D1 ÷ 100) × (1 − D2 ÷ 100) × 100

Steps

  1. 1. 100 × (1 − 20 ÷ 100) = 80.00
  2. 2. 80.00 × (1 − 10 ÷ 100) = 72.00
  • 20% off and then 10% off is 28% off in total, not 30%. The second discount applies to the already reduced price, so it is worth 2 percentage points less.

This result is exact. Divisions in the steps are shown rounded. The answer is worked out from the exact values and rounded only once.

Tip and split a bill

Tip on the bill, then each person’s share.

A bill of 86.4 with a 18% tip comes to 101.95 (tip 15.55). Split between 3, each person pays 33.98.

Formula

Total = Bill × (1 + Tip ÷ 100); share = Total ÷ People

Steps

  1. 1. 86.4 × 18 ÷ 100 = 15.55
  2. 2. 86.4 + 15.55 = 101.95
  3. 3. 101.95 ÷ 3 = 33.98
  • Each share is rounded to the decimals chosen above, so the shares together differ from the total by -0.012 (negative means they fall short). Round up if the shares must cover the bill.
  • The tip and total are calculated exactly and rounded only for display.

Rounded to 2 decimals (half away from zero). Divisions in the steps are shown rounded. The answer is worked out from the exact values and rounded only once.

Percentage error

How far a measurement is from the accepted value.

A measured 9.7 against an accepted 9.81 is an error of 1.12%.

Formula

|Measured − Accepted| ÷ |Accepted| × 100

Steps

  1. 1. 9.7 − 9.81 = -0.11
  2. 2. 0.11 ÷ 9.81 × 100 = 1.12
  • Signed error: -1.12%. A negative sign means the measurement is lower than the accepted value.

Rounded to 2 decimals (half away from zero). Divisions in the steps are shown rounded. The answer is worked out from the exact values and rounded only once.

Ratio to percent

Turn a ratio such as 3 : 2 into shares of the whole.

A ratio of 3 : 2 is 60% and 40% of the whole.

Formula

A ÷ (A + B) × 100 and B ÷ (A + B) × 100

Steps

  1. 1. 3 + 2 = 5
  2. 2. 3 ÷ 5 × 100 = 60
  3. 3. 2 ÷ 5 × 100 = 40
  • Compared with each other, 3 is 150% of 2.

This result is exact. Divisions in the steps are shown rounded. The answer is worked out from the exact values and rounded only once.

How it works

  • •Choose the card that matches your question. Each one has its own boxes and starts with an example, so you can see the answer shape before typing your own numbers.
  • •Read the sentence at the top of the result, for example "20% of 150 is 30". Below it are the formula and the steps, so you can check the arithmetic or copy the method into a spreadsheet.
  • •Numbers are read as exact decimals rather than as floating-point numbers, so 0.1 + 0.2 is exactly 0.3. The answer is rounded once, at the end, half away from zero, to the number of decimals you choose (0 to 8).
  • •Zero and negative values get a plain explanation instead of a wrong answer: dividing by zero, a percent change from a starting value of 0, a discount above 100% and similar cases are all named.
  • •The add-or-take-off card shows the formula forward and in reverse, and warns when the two do not cancel out. You enter any rate yourself; the page has no tax rates and gives no tax advice.

Questions

Why is 20% off and then 10% off not 30% off?
The second discount applies to the price that is left after the first, not to the original. On 100, 20% off leaves 80, and 10% off 80 leaves 72, so you paid 28% less in total. The discount card shows the total and how far it is from the sum of the two.
Why does taking 20% off a price with 20% added not give the original?
Because the percent is taken from a different amount each time. 100 plus 20% is 120, and 20% of 120 is 24, so taking it off leaves 96, not 100. To get back to 100 you divide 120 by 1.2. The add-or-take-off card has a mode for exactly that, such as finding the price before a percentage was added.
What is the difference between a percent and a percentage point?
A percentage point is the plain difference between two percentages, a percent is a change relative to the starting value. If a rate goes from 4% to 5%, it rose by 1 percentage point, which is a 25% increase. The percent-change card shows both when your two numbers are read as percentages.
How does it avoid rounding errors, and is anything uploaded?
It reads what you type as an exact decimal and calculates with whole numbers, so the answer never carries float noise such as 0.30000000000000004. Results are rounded once at the end. All of this runs in your browser; nothing you type is sent or stored, and reloading the page resets the boxes.

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