**PERCENTAGE CALCULATOR**

**How to calculate percentage? – online calculator, examples and verbal tasks here**

**Percent calculator**

How to figure up percentage? The percent calculator on this page offers an online percentage calculation for free. Not only that you can calculate percentages quickly and easily with this calculator but you will also learn how the percentage is calculated. How? Because for each method, there is a calculation formula, mathematical procedure, examples and percentage verbal tasks into which your given values are entered automatically. Percentage mathematics is suddenly becoming understandable fun and a toy.

**Percentage %**

A percentage is a dimensionless unit corresponding to one hundredth, which is a mathematical term representing the number 0.01 (10^{-2}) in the decimal system or 1/100 (one-hundredth of the whole) in a fraction. It is easier to express a percentage in hundredths of a whole than with a fraction. An example may be the value of 30 %, which would otherwise be written as a fraction of 30/100. However, a percentage exceeding 100, for example, 120 % can also be expressed as a percentage.

**Use of a percentage**

A percentage is used not just for quantification in mathematics but also in many other fields such as physics, economics, technology, natural and social sciences, etc.

**Misunderstandings in a percentage**

Many people have trouble with how to count up percentages. Percentage calculation is not so complicated, but sometimes there are many misunderstandings that are caused by an inaccurate expression, exactly what or from what part of the basis the percentage calculation is done.

**Percentage and percentage points**

A good example of misunderstanding is the difference between a percentage and a percentage point. If we want to express a change in percentage (increase or decrease), it is always necessary to state clearly whether it is a change in the original basis or a change in the percentage value already mentioned.

For example, if we tell someone that a bank raises the original 10% interest on the loan by 5 % without giving more specific information, then we can imagine two completely different situations:

1 – Interest increases from 10 % to 10.5 % (5 % out of 10 is 0.5%, which we add to the original 10 %)

2 – Interest increases from 10 % to 15 % (we add 5 % to the original 10 %)

In this example, we probably want to say that interest (as in point 2) will actually increase to 15 %. However, in such a case, it would be correct to state that the interest rate increased by 5 percentage points rather than percent.

The percentage point is the arithmetic difference between two percentage values having the same basis. The notion of a percentage point was introduced precisely because of possible confusion and doubts and also because of the considerable simplification of the situation described.

If we wanted to use just percentage for our example above and omit the percentage point designation, we would have to provide a clear and precise basis (a) for points 1 and 2 or indicate the final percentage part (b) as follows:

1a – An interest will rise by 5 % on the original interest (from 10 % to 10.5 %)

1b – An interest will rise to 10.5 % (clearly stated the final interest rate)

2a – An interest will rise by 5 % of the loan amount (from 10 % to 15 %)

2b – An interest will rise to 15 % (clearly stated the final interest rate)

**Repeated increase and decrease in percentage value**

Another example of misunderstanding of percentage calculations and the importance of basis is a repeated change in values, i.e. increasing and/or decreasing (for example, prices of goods in a shop). If the price of a product rises from 100 by 20 % to 120 and then falls by 20 %, the resulting price will not be the original 100 but little less. Again, this is due to the fact that the basis is incorrectly given. The calculation of the % discount will not be calculated from 100 but from 120.

Likewise, the original price of 100 can be reduced by 50 % and then reduced again by 50 %, while the goods will not be free. The basis of the first discount is 100, while the basis of the second discount is 50.

**Per mille**

While a percentage is 1 hundredth of the total, per mille is 1 thousandth of the total. In other words, per mille is a tenth of a percent, a 10x smaller number than a percent. Per mille is marked similarly as a percentage (%), except that there are 2 zeros or circles under the slash (‰).

Per mille is not used as often as a percent. In per mille is specified, for example, alcohol in blood, ascent or descent of a railway line or a small numerical value that is better expressed in per mille. For example, 8 ‰ inhabitants = 8 inhabitants per every 1 000 inhabitants.

**Percentage calculator – examples and verbal tasks**

**1 – Calculating the percentage part**

**Example: ** What is 5 % of 300? (A=5, B=300)

- I will pay 5 % interest on the $300 loan. How many dolars will interest cost me? ($15).
- The school has 300 pupils, 5 % of whom will go on a trip. How many pupils will go? (15).
- A road with a horizontal distance of 300 meters has a height difference (ascent or descent) of 5 %. How many meters between its start and end is the elevation? (15 m).

**Formula:** A x B / 100

**Procedure:** 5 x 300 / 100 = 15

**In detail:**

- 100 % = 300
- 1 % = 300 / 100 = 3
- 5 % = 5 x 3 = 15

**2 – Calculating the percentage number**

**Example:** What percentage is 120 out of 500? (A=120, B=500)

- I will pay an interest of $120 on a loan of $500. What percentage is the interest? (24 %).
- The worker has the task of producing 500 products a day, but he is able to make 120 products only. To what % does he fulfill the plan? (24 %).
- A road with a horizontal distance of 500 meters has an elevation (height difference between start and end) of 120 meters. What is the percentage of ascending or descending roads? (24 %).

**Formula:** A / B x 100

**Procedure:** 120 / 500 x 100 = 24 %

**In detail:**

- Base = 500
- 1 of 500 = 1 / 500 basis
- 120 of 500 = 120 / 500 basis = 24 / 100 basis = 0,24
- 100 % x 0,24 = 24 %

**3A – Calculating the percentage difference (more than)**

**Example:** By what percentage is the number 75 higher than 25 ? (A=75, B=25)

- 25 children gathered on the playground last week. Now it was 75 children. How much % is it more? (200 %).
- Originally, the price in the store was $25 but now it is $75. How much did the goods get more expensive? (200 %).

**Formula:** (A – B) / B x 100

**Procedure: **(75 – 25) / 25 x 100 = 200 %

**In detail:**

- 100 % = 25
- 1 % = 25 / 100 = 0,25
- 75 / 0,25 = 300 %
- 300 % – 100 % = 200 %

**3B – Calculating the percentage difference (less than)**

**Example:** What percentage is 150 less than 200? (A=150, B=200)

- The gardener picks 200 apples per hour, the temporary worker 150 apples. How much % is it less? (25 %).
- From the original price of $200, the product was discounted to 150 $. How much % is the discount? (25 %).

**Formula:** (B – A) / B x 100

**Procedure: **(200 – 150) / 200 x 100 = 25 %

**In detail:**

- 100 % = 200
- 1 % = 200 / 100 = 2
- 150 / 2 = 75 %
- 100 % – 75 % = 25 %

**4A – Calculating the percentage difference (more than)**

**Example:** What percentage is 80 % more than 20 %? (A=80, B=20)

- The girl received 80 % of the votes in the competition and the boy got 20 %. What percentage of votes did the girl get more? (300 %).

**Formula:** A / B x 100 – 100

**Procedure:** 80 / 20 x 100 – 100 = 300 %

**In detail:**

- 80 / 20 = 4
- 100 x 4 = 400 %
- 400 % – 100 % = 300 %

**4B – Calculating the percentage difference in percent (less than)**

**Example:** What percentage is 20 % less than 80 %? (A=20, B=80)

- 20 % of drivers want a diesel car and 80 % want a petrol car. What percentage fewer drivers want a diesel car? (75 %).

**Formula:** 100 – (A / B x 100)

**Procedure:** 100 – (20 / 80 x 100) = 75 %

**In detail:**

- 20 / 80 = 0,25
- 100 x 0,25 = 25 %
- 100 % – 25 % = 75 %

**5A – Calculating the number by increasing the original number by XY percent**

**Example:** What will be the resulting number if we increase the number 1 000 by 20 %? (A=1 000, B=20)

- The worker receives a salary of $1 000 per week but has 20 % added on weekends. How much does he take at the weekend? ($1 200).

**Formula:** A x (B / 100 + 1)

**Procedure:** 1 000 x (20 / 100 + 1) = 1 000 x 1,2 = 1 200

**In detail:**

- 100 % = 1 000
- 1 % = 10
- 100 % + 20 % = 120 %
- 120 x 10 = 1 200

**5B – Calculating the number after reducing the original number by XY percent**

**Example:** What will be the resulting number if we reduce the number 1 000 by 20 %? (A=1 000, B=20)

- The worker gets a reward of $1 000 gross, but he gets 20 % less due to taxes. How much is the net reward? ($800).

**Formula:** A – (A / 100 x B)

**Procedure:** 1 000 – (1 000 / 100 x 20) = 1 000 – 200 = 800

**In detail:**

- 100 % = 1 000
- 1 % = 1 000 / 100 = 10
- 100 % – 20 % = 80 %
- 80 x 10 = 800

**6A – Calculating the original number when we know the % increase and the result (price increase)**

**Example:** The number 1 250 is the result of a 25 % increase in the original number. What was the original number? (A=1 250, B=25)

- Goods in the store have been increased by 25 % and now cost $1 250. How much did it cost originally? ($1 000).
- The number of employees increased by 25 % and the company now employs 1 250 employees. How many were originally there? (1 000).

**Formula:** A / (100 + B) x 100

**Procedure:** 1 250 / (100 + 25) x 100 = 1 000

**In detail:**

- 100 % + 25 % = 125 % = 1 250
- 1 % = 1 250 / 125 = 10
- 100 % = 100 x 10 = 1 000

**6B – Calculating the original number when we know the % reduction and the result (discount)**

**Example:** The number 1 125 is the result of a 25 % reduction in the original number. What was the original number? (A=1 125, B=25)

- We bought goods in the store at a 25 % discount and now it costs $1 125. How much did it cost originally? (1 500 $).
- The company has laid off 25 % of employees and now employs 1 125. How many people worked in the company originally? (1 500).

**Formula:** A / (100 – B) x 100

**Procedure:** 1 125 / (100 – 25) x 100 = 1 500

**In detail:**

- 100 % – 25 % = 75 % = 1 125
- 1 % = 1 125 / 75 = 15
- 100 % = 100 x 15 = 1 500

**7 – Calculating an unknown number when we know how much % corresponds to its part**

**Example:** 5 000 is 20 % of the original number. What was the original number (A=5 000, B=20)

- The man returned $5 000, which was 20 % of his debt. How much did he borrow? ($25 000).
- 20 % of the city’s population, 5 000 people, have a car. How many residents does the city have? (25 000).
- 20 % of the flowers grow from the seeds. How many seeds do we need to plant when we want 5 000 flowers? (25 000).

**Formula:** A / B x 100

**Procedure:** 5 000 / 20 x 100 = 25 000

**In detail:**

- 20 % = 5 000
- 1 % = 5 000 / 20 = 250
- 100 % = 100 x 250 = 25 000