**Basic percentage calculator**

**What is**

**of**

**Add / subtract percentages**

**Add / subtract a percent:**

**Percentage change between two values**

**% increase / decrease between**

**and**

**V1 is what percent of V2?**

**is what percent of**

Above you will find the most used percentage calculators. Further on this page you will also find more specific calculators which show the calculation of discounts and percentage deviations and show the conversion from percentages to decimals or fractions.

__Formulas and examples__

In the following formulas, the letter P always shows the percent and the letter V indicates the value from which we calculate the percentage. If there are two values, we make the distinction between V1 and V2.

__1. Normal percentage calculation__

This calculation answers the question: what is P percent of V?

The formula for this is: (P/100)*V

For example, what is 15% of 160? According to the formula we calculate (15/100)*160 = 0.15*160 = 24

__2. Adding or subtracting a percentage__

This calculation answers the question: add P percent to V or subtract P percent of V.

First we deal with how we can add percentages. Add P percent to the value V.

To add percentages the formula is: V + (P/100*V)

For example: add 25 percent to 280. According to the formula we can deduce: 280 + (25/100*280) = 280 + (0.25*280) = 350

The procedure to subtract a percentage is more or less similar. How can we deduct P percent of V?

To remove percentages the formula is: V - (P/100*V)

For example: subtract 20% of 240. After applying the above formula we get: 240 - (20/100*240) = 240 - (0.2*240) = 192

__3. Calculating the percentage difference between two values__

To calculate the percentage difference between two values V1 and V2 we can use the following formula. V1 is the start value and V2 is the end value.

percentage difference = ((V2-V1)/V1) * 100

With a positive result, we have an increase in percentage.

With a negative result, we have a decrease in percentage.

For example: what is the increase in percentage between 45 and 79?

Subject to the application of the formula, we get: ((79-45)/45)*100 = 75.55%. So there is a percentage increase of 75.55%.

__Other calculators__

Here are some less common questions regarding percentages:

The number V1 is what percentage of the number V2?

The number V1 is the percentage of P% of what?

**V1 is what percent of V2?**

**is what percent of**

**V is P % of what?**

**is**

**% of what?**

__Formulas and examples for these extra calculators__

1. The formula in case you want to know the answer to the question: V1 is what percentage of V2 is as follows:

P = (100/V2)*V1

For example: 16 is what percentage of 88? If we fill in the formula, we get: P = (100/88)*16 = 1.14*16 = 18.18

So the solution is: 16 is 18.18 percent of 88.

2. The formula for the answer to the second question: V1 is P% of what is just as easy:

X = (V1/P)*100

For example: 24 is 9% of what? The formula gives us the following result: X = (24/9) * 100 = 2.66 * 100 = 266

So the solution to this question is: 24 is 9% of 266.

__Deviation in percentage__

We may need the deviation in percentages when we compare a theoretical value with a measured value.

**Percentage error between a measured value and theoretical value**

**Measured value:**

**exact value:**

We can use the following as a formula for this percentage deviation:

Deviation in percent = 100* | measured value - theoretical value |/ | theoretical value |

We take the absolute value both in the numerator and in the denominator.

__Converting percentages into decimal places or fractions__

Converting percentages into decimal numbers is easy if you keep in mind that 100% is represented as the number 1.

Consequently, 50% corresponds to the number 0.5. The percentage of 16% corresponds to 0.16, and so on.

We can use the following formula: decimal = percent / 100

Proposing percentages as fractions follows the same formula or method.

For example 35% corresponds to the fraction of 35/100.

We can then simplify the fraction by dividing the numerator and denominator by the same number. If we divide the numerator and denominator of 35/100 by 5, we get: 7 / 20. This is the simplest representation of this fraction since we can no longer divide the numerator and denominator by the same number.

To list the above clearly, we have created a useful table:

Percent | Decimal | Fraction |
---|---|---|

100% | 1 | 1 |

90% | 0.9 | 9/10 |

80% | 0.8 | 4/5 |

75% | 0.75 | 3/4 |

66% | 0.66 | 2/3 |

60% | 0.6 | 3/5 |

50% | 0.5 | 1/2 |

40% | 0.4 | 2/5 |

33% | 0.33 | 1/3 |

30% | 0.3 | 3/10 |

25% | 0.25 | 1/4 |

20% | 0.2 | 1/5 |

10% | 0.1 | 1/10 |

__Discount calculation__

To calculate what amount corresponds to a certain percentage discount, you must perform a normal percentage calculation.

The formula for this is: discount = (P/100)*V

Where P is the percent of the discount and V is the price.

For example: if you get a discount of 13% on a price of 65 dollar, what is the amount of this discount? Discount = (13/100) * 65 = 8.45 dollar. The final price will therefore be: 59.51 dollar.

However, if you receive a discount from a certain amount on a total price, what is the discount percentage applied?

You can use this formula: P = (100/V2)*V1

For example: you get a discount of 12 dollars on a total price of 88 dollars. The discount percentage is then equal to (100 / 88 ) * 12 = 13.64 %

__Examples in your daily life__

__1. Turnover tax__

When purchasing a certain product, the turnover tax is 8 percent. Suppose that this 8 percent corresponds to the amount of 16 dollars.

What is the original price on which the sales tax was levied?

Eight percent equals the fraction of 8/100. If we simplify the fraction 8/100 by dividing the numerator and denominator by 4, we get 2/25.

We can find the solution to the problem through the following equation: 8/100 * X = 2/25 * X = 16

This means that X = 200.

__2. Discount voucher for a certain amount__

Suppose you want to buy a product for 35 dollars . However, you have a discount voucher of 5 dollars.

What percentage will you save by using the discount coupon?

We can solve this through the comparison: P / 100 * 35 = 5

By working out this comparison we find: P = 500 / 35 = 14.29%

__3. Discount coupon of a certain percentage__

Suppose you want to buy a new refrigerator and this refrigerator costs 360 dollars. However, through a publicity campaign you could seize a discount coupon of 12 percent. How much money can you save by actually using this voucher?

We can find the solution through the following comparison: 12/100 * 360 dollar = 43.2 dollar

__4. Calculation of a tip__

After a nice meal in a local restaurant, you want to leave a tip for the friendly service. A tip of 9 percent of the bill seems like a good idea. Suppose the bill for the meal is 89 dollar, what should be the amount of your tip?

This comparison gives us the solution: 9/100 * 89 = 8.01 dollar

__5. Interest on a bond__

You still have an old bond of 5000 dollars which yields 4 percent per year. What amount can you dispose of after 1 year?

After 1 year we receive an interest of 4 percent on top of the invested amount of 5000 dollars.

We can make the following calculation: 5000 + 4/100 * 5000 = 5000 + 200 = 5200 dollar.

__6. Increase of percentage on a savings account__

Suppose you have an amount of 450 dollar in your savings account at the bank. After 1 year this amount has risen to 465 dollar.

What is the increase of percentage after 1 year?

percentage increase = ((V2-V1)/V1)*100 = ((465-450)/450)*100 = 3.33 %

__7. Decrease of percentage after a price reduction__

At the local furniture store an oak cupboard costs 420 dollar. However, the price drops to 360 dollar due to a closing sale.

What is the decrease of percentage between these two prices?

percentage decrease = ((V2-V1)/V1)*100 = ((360-420)/420)*100 = - 14.28 %

__8. Difference between measured and actual values__

Assume the measured value from a test is equal to 12.86 while the actual value is equal to 14.

What is the deviation in percentage?

We use the formula: 100*| measured value - theoretical value|/ |theoretical value| = 100*| 12.86 - 14 | / |14| = 8.14%

__9. Deviation after rounding__

Suppose a value of 5.2 is rounded down to 5. What is the percentage deviation due to rounding?

We apply this formula: 100*| measured value - theoretical value|/ |theoretical value| = 100 * | 5 – 5.2|/ |5.2| = 3.85 %