Percentage Change Calculator | QuickCalculators.in

Percentage Change Calculator

Quickly determine the increase or decrease between two values.

Start Value (Old Value)

End Value (New Value)

Understanding Percentage Change

The Formula

The percentage change is calculated by taking the difference between the new and old values, dividing it by the old value, and then multiplying the result by 100.

$$\text{Percentage Change} = \frac{\text{New Value} – \text{Old Value}}{\text{Old Value}} \times 100$$

Where Old Value $\neq 0$.

Mathematical Model (Conceptual)

The model focuses on the **absolute change** and compares it relative to the **initial quantity**. This ratio defines the magnitude of the change.

Absolute Change ($\Delta$): $\text{New Value} – \text{Old Value}$. This tells us *how much* the quantity moved.
Relative Change: $\frac{\Delta}{\text{Old Value}}$. This is the change expressed as a fraction of the starting amount.
Percentage Change: $\text{Relative Change} \times 100$. This scales the relative change to a base of 100, making it easily interpretable.

If the result is positive, it represents a percentage increase. If the result is negative, it represents a percentage decrease.

General Percentage Questions

1. What is a percentage?

A percentage is a number or ratio that represents a fraction of 100.¹ It's a way of expressing a portion of a whole, and it's denoted by the symbol % (e.g., ²$50\%$ means 50 out of 100).³

2. What is the basic formula for calculating a percentage?

To find what percentage a part is of a whole, the formula is:

$$\text{Percentage} = \frac{\text{Part}}{\text{Whole}} \times 100$$

Example: To find what percent 15 is of 60: 4$(15 / 60) \times 100 = 25\%$

3. How do I find X percent of a number?

To find a percentage of a number, you convert the percentage to a decimal (by dividing by 100) and then multiply it by the number.5

$$\text{Result} = (\frac{X}{100}) \times \text{Number}$$

Example: To find 20% of 70: 6$(20 / 100) \times 70 = 0.20 \times 70 = 14$.7

📈 Percentage Change & Difference

4. What is the formula for Percentage Change (Increase or Decrease)?

Percentage Change calculates the relative difference between a starting (original) value and a new (final) value.⁸

$$\text{Percentage Change} = \frac{\text{New Value} - \text{Original Value}}{\text{Original Value}} \times 100$$

If the result is positive, it's a percentage increase.
If the result is negative, it's a percentage decrease.⁹

5. What is the difference between Percentage Change and Percentage Difference?

Percentage Change (or Increase/Decrease) uses the Original Value as the denominator (the baseline for the change).¹⁰ It is used for changes over time (e.g., price went from $A$ to $B$).
Percentage Difference uses the Average of the two numbers as the denominator.11 It is used when there is no clear "original" or "new" value, only a comparison between two numbers (e.g., comparing $A$ and $B$).$$\text{Percentage Difference} = \frac{|\text{Value}_1 - \text{Value}_2|}{(\text{Value}_1 + \text{Value}_2)/2} \times 100$$

🛍️ Real-World Applications

6. How do I calculate a Discount Percentage?

A discount is a percentage decrease from the original price.12

$$\text{Discount Amount} = \text{Original Price} \times (\frac{\text{Discount \%}}{100})$$

$$\text{New Price} = \text{Original Price} - \text{Discount Amount}$$

7. How do I calculate the Percentage of Marks obtained in an exam?

This is a standard "Part of a Whole" calculation:

$$\text{Percentage Score} = \frac{\text{Marks Obtained}}{\text{Total Maximum Marks}} \times 100$$

8. What if the new price is given after the discount?

If you know the discounted price ($Y$) and the discount percentage ($P$), you can find the original price ($X$):

$$X = \frac{Y}{1 - (\frac{P}{100})}$$

Example: A 13$\$40$ item is 14$20\%$ off.15 This means 16$\$40$ is 17$80\%$ (or 18$1 - 0.20$) of the original price.19 Original Price 20$=\$40 / 0.80 = \$50$

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