Percentage Change Calculator

What Is a Percentage Change?

Percentage change indicates whether a value has increased or decreased compared to its original value. The calculation is done by first subtracting the original value from the new value, then dividing the result by the original value, and in the end multiplying the result by 100.

There are 2 possible results that can be outputted, a positive number, which means an increase, and a negative number, which indicates a decrease. This approach is widely used for understanding growth or loss in fields like data analysis, sales, and finance. An example can be a sales increase from 400$ to 500$ the 100$ difference shows a 25% increase.

Why Percentage Change Is Important

Percentage change is a crucial method because it shows relative increase or fall rather than just absolute numbers. It helps make it easier to compare results, spot changes over time, and make smart decisions in finance, work, and everyday situations. Percentage change makes data easier to understand and act upon by clearly displaying both the size and direction of change, going beyond raw numbers.

Because change is represented as a percentage, it becomes more easier and clearer to spot whether the difference is major or minor. For example, an increase indicates significant growth or minor change. Additionally, percentage change makes it possible to fairly compare values of various sizes, track trends over time, and promote wiser choices in areas such as budgeting, discounts, economic research, and investment

Percentage Change Formula

The percentage change formula compares the difference between two values with the original value. A positive result is an increase, and a negative result is a decrease. The image below shows the formula which also is used in our percentage change calculator, and the next section walks through it step by step.

How to Calculate Percent Change (Step-by-Step)

To calculate percentage change between two numbers, follow the simple steps below:

1. First, we find the amount of change by subtracting the original value (start) from the new value.
2. Then, we divide the amount of change by the original value.
3. Finally, convert the decimal number to a percentage by multiplying by 100 and adding the % sign.

Keep in mind

• A positive result means an increase.
• A negative result means a decrease.
• In the second step, never divide by the new value.

Percentage Change Examples

The examples below use the same formula and steps. In each one, the result shows how big the change is compared with the original value, and a positive result means an increase while a negative result means a decrease. Enter the numbers into the percentage change calculator above to check that you get the same result.

Why the Order Matters In Percentage Change

When we calculate the percentage change, the order is important because the starting value changes depending on which direction we are calculating. Every percentage change is calculated in relation to the starting value, reversing the order changes the overall percentage. From the formula, we see that the original value is in the denominator and determines how big or small the change feels.

So, when a price goes from $100 to $150 is a 50% increase, but if we reverse it back from $150 to $100 is a 33.33% decrease. Besides, the change is 50 unit for the both ways, the base is different for both of them.

How to Find the New Value After a Percentage Change

When you need to find the new value after a percentage change, which can be either an increase or decrease, you can use the formula, New value = Original × (1 + change ÷ 100). The steps and examples below will show you how to use the formula and find what you need.

Steps:

1. First, we convert the percentage into a decimal number by dividing the percentage by 100.
2. Then, we need to choose the multiplier for an increase we add the decimal (1 + decimal), and for a decrease, we subtract the decimal (1 – decimal).
3. Finally, we multiply the original value by the multiplier in the second step, and we get the new final value.

Percentage Increase vs Percentage Decrease

Percentage increase and decrease are both related and covered by percentage change using the formula given in the image above. Depending on the output from the formula, when a positive result is calculated, it means an increase, and when it is a negative result, it means a decrease. The negative result, or percentage decrease, is also usually written as a positive percentage decrease (e.g., -30% = 30% decrease).

The key difference between percentage increase and decrease is the direction of change that whether it goes up or down. To make it simpler to remember, and when percentage increase and decrease happen related to percentage change, keep in mind the note below:

Keep in Mind

Percentage increase: it happens when the new value is bigger than the original value, the percentage change is positive (for example, going from 10 to 15 is a 50% increase).

Percentage decrease: it happens when the new value is smaller than the original value, the percentage change is negative (for example, going from 15 to 10 is a 33.33% decrease).

Absolute Change vs Percentage Change

Absolute change is a simple difference between two values, the new value and the original value, and it tells whether the amount has increased or decreased in real units. On the other hand, percentage change indicates the size of the difference between the new and original value that is expressed as a percentage.

The same absolute change can mean very different things. For example, going from 10 to 20 and going from 100 to 110 are both change of 10, but in percentage change the first is 100% increase and the second only 10%. In cases when both values are percentages, the absolute change is measured in percentages points. For example, an interest rate rising from 4% to 5% is a 1 percentage point increase.

Percentage Change vs Percentage Difference

The percentage difference displays the differences between the two values without indicating an increase or decrease, compares them without a start or end, and utilizes the average of both as the base. On the other hand, percentage change needs and uses a starting value and an ending value so it can indicate how much a value has gone up or down over time, and also uses a base value.

You have to use percent change for situations like before and after or going from old to new, and percentage difference when comparing 2 similar values at the same time. For example, from 50 to 80 the percentage change is 30 ÷ 50 = 60%, an increase. The percentage difference between 50 and 80 is 30 ÷ 65 = 46.15%.

When Not to Use Percentage Change

Percentage change can be misleading in some situations, below we have listed some of the situations.

• When the starting value is zero, the result is undefined because you can’t divide by zero.
• In cases when the starting value is very small, for example, going from 2 to 6 is a 200% increase it sounds like a huge rise, but actually it is only 4 units change.
• The starting values are negative, results can be difficult to interpret. In these cases, you can show the absolute change too.
• If you are comparing percentages, we can use percentage points for the gap between the two rates.
• Changes can use different base values, in these cases, don’t add percentage changes together.

Common Mistakes to Avoid

When calculating percentage change, one of the most common mistakes is dividing by the incorrect number, such as using the new value instead of the original one. Other ones can be forgetting to multiply by 100, adding more percentage change incorrectly, mistaking percentage points for percentage change, and forgetting to consider whether the outcome is positive or negative. You have to keep in mind that you always divide by the original value to convert into a percentage, and to clearly indicate if it is an increase or decrease. Since division by zero is undefined, changes from zero cannot be stated as a percentage.