Percentage Calculator

Welcome to the Percentage Calculator. Various percentages can be easily calculated here, including the following 9 cases

1. X is what percent of Y
2. What percent of X is Y
3. Percentage Increase
4. Percentage Decrease
5. Percentage Difference
6. Percentage Change
7. Plus What Percent
8. Minus What Percent
9. Percent Error

Read on to learn how each percentage is calculated.

The formula for X is what percent of Y is

P% = XY

Among them, X and Y are known numbers, P is to be calculated.

This is the most basic formula for percentage calculation, and all percentage calculations are inseparable from this.

To calculate the percentage, divide X by Y to get the decimal value, then convert the decimal to percent by multiplying by 100.

For example: 5 is what percent of 25? (5 out of 25 is What Percent?)

Calculation steps:

• Substitute the values into the formula: P% = 525
• Calculate the result of 5 divided by 25: 525 = 0.2
• Convert the decimal to percent: P% = 0.2 * 100 = 20%
• So, the percentage is 20%.

5 is 20% of 25.

Similar to above, only the numbers change position, the formula is

P% = YX

Here, X and Y are given numbers, and X is greater than Y. P is the result to be calculated.

For example: What Percent of 150 is 90?

Calculation steps:

• Put X = 150 and Y = 90 into the formula: P% = 90150
• Convert fraction to decimal: 90150 = 35 = 0.6
• Convert decimal to percent: P% = 0.6 * 100 = 60%
• So, the percentage is 60%.

60% of 150 is 90.

Percentage Increase

A percentage increase is a case of a percentage change, the formula is

P% = Y – XX

Here, X and Y are given numbers, and Y is greater than X. If Y is less than X, it means a percentage decrease.

For example: What is the percentage increase from 32 to 40?

Calculation steps:

• Substitute X = 32 and Y = 40 into the formula: P% = 40 – 3232
• Calculate the value of the expression on the right: 40 – 3232 = 832 = 0.25
• Convert decimal to percent: P% = 0.25 * 100 = 25%
• So, the percentage increase is 25%.

32 increased 25% is 40.

Percentage Decrease

The percentage increase corresponds to the percentage decrease, and its formula is the same as the percentage increase.

P% = Y – XX

Among them, X and Y are given numbers, and Y is less than X.

Typically, percentage decreases are expressed as negative numbers.

For example: What is the percentage decrease from 40 to 32?

Calculation steps:

• Substitute X = 40 and Y = 32 into the formula: P% = 32 – 4040
• Calculate the value of the expression on the right: 32 – 4040 = -840 = -0.2
• Convert decimal to percent: P% = -0.2 * 100 = -20%
• So, the percentage decrease is -20%.

40 decreased 20% is 32.

The percent difference is the calculation of the difference between two numbers, expressed as a percentage. The result is a positive number regardless of the order of the numbers. The formula for the percentage difference is

P% = |X – Y||X + Y|2 * 100

Here, X and Y represent two numbers.

For example: What is the percentage difference between 80 and 200?

Calculation steps:

• Calculate the absolute difference between these two numbers: |80 – 200| = 120
• Calculate the average of these two numbers: 80 + 2002 = 2802 = 140
• Calculate the percentage difference. Substitute the values from Step 1 and Step 2 into the formula. P% = 120140 * 100 = 67 * 100 = 85.7%
• So, the percentage difference is 85.7%

The percentage difference between 80 and 200 is 85.7%.

Percentage change is an umbrella term for percentage increase and percentage decrease. The formula for the percentage change is

P% = Y – XX * 100

Among them, Y represents the new value and X represents the old value.

Usually, if the percent change result is positive, it means a percentage increase. If negative, it means a percentage decrease.

For example: Apple’s price rises from $5 to $6, what is the percentage change?

Calculation steps:

• Calculate the difference between the new value and the old value: 6 – 5 = 1.
• Divide the difference by the old value. 15 = 0.2
• Convert decimal to percent: P% = 0.2 * 100 = 20%

Therefore, the percentage change is 20%. This means that the price has increased and the percentage has increased by 20%.

Another example: the price of the stock drops from $100 to $85, what is the percentage change?

Calculation steps:

• Calculate the difference between new value and old value: 85 – 100 = -15.
• Divide the difference by the old value. -15100 = -0.15
• Convert decimal to percent: P% = -0.15 * 100 = -15%

Therefore, the percentage change is -15%. This means that the price has dropped by a percentage of 15%.

X plus what percent is Y? This is an interesting question and one that is frequently encountered. For example, if you invested $500,000, and now you need to invest $600,000, what percentage should you add?

How to solve it?

Suppose the percentage is P%, so we can get an equation.

X + X * P% = Y

Simplify the equation.

X + X * P% = Y

X(1 + P%) = Y

1 + P% = YX

P% = YX – 1

P% = Y – XX

So, X plus what percent is Y formula is

P% = Y – XX

Among them, X is the initial value and Y is the final value.

For example: 50 plus what percent is 60?

Calculation steps:

• Calculate the difference between final value and initial value: 60 – 50 = 10.
• Divide the difference by the initial value. 1050 = 0.2
• Multiply with 100 to obtain the Percentage result. P% = 0.2 * 100 = 20%.

Thus, 50 plus 20% is 60.

If there is a plus percentage, there is a minus percentage.

X minus what percent is Y?

Let the percentage be P%.

X – X * P% = Y

X (1 – P%) = Y

1 – P% = YX

P% = 1 – YX

P% = X – YX

So, the formula for X minus what percent is Y is

P% = X – YX

Here, X is the initial value and Y is the final value.

For example: 30 minus what percent is 18?

Calculation steps:

• Calculate the difference between the final value and the initial value: 30 – 18 = 12.
• Divide the difference by the initial value. 1230 = 0.4
• Change the decimal to Percentage by multiplying with 100. P% = 0.4 * 100 = 40%.

Therefore, 30 minus 40% is 18.

Percentage error refers to the error expressed as a percentage. The percentage error formula is

P% = |Y – X|X * 100

Among them, Y is the observed value and X is the true value.

For example: a party where 50 people are expected to come, but only 40, so what is the percentage error?

Calculation steps:

• In here, the observed value is Y = 50, the true value is X = 40
• Calculate the absolute difference between two numbers: |50 – 40| = 10
• Divide the absolute difference by the true value. 1040 = 0.25
• Multiply by 100 to get the percentage error. P% = 0.25 * 100 = 25%

So, the percentage error is 25%.