This Percentage Change Calculator uses the fundamental proportional ratio to solve for the original value, new value, change amount, or the percentage change, ensuring accurate analysis of data variation.
Welcome to the **Percentage Change Calculator**. This versatile mathematical tool allows you to find the relationship between an Original Value ($OV$), a New Value ($NV$), the Change Amount ($C$), and the resulting Percentage Change ($P$). This calculation is vital in finance, statistics, and business to measure growth, decay, profit margins, and variance. Simply input any three of the four required variables to solve for the missing one.
Percentage Change Calculator
Percentage Change Formulas
The core relationship is $NV = OV + C$ and $P = C / OV \times 100$.
1. Solve for Percentage Change (P):
$$ P = \frac{NV – OV}{OV} \times 100 $$
2. Solve for New Value (NV):
$$ NV = OV \times \left(1 + \frac{P}{100}\right) $$
3. Solve for Original Value (OV):
$$ OV = \frac{NV}{\left(1 + \frac{P}{100}\right)} $$
4. Solve for Change Amount (C):
$$ C = NV – OV $$
Formula Source: Investopedia – Percentage Change
Variables Explained
- OV – Original Value: The starting number or base figure.
- NV – New Value: The final number after the change has occurred.
- C – Change Amount: The absolute difference between the New Value and the Original Value ($NV – OV$).
- P – Percentage Change: The change amount expressed as a percentage of the Original Value. (Percentage)
Related Calculators
What is the Percentage Change?
Percentage change is a mathematical concept used to describe the degree to which a value has changed over time. It is particularly useful when comparing changes across different contexts or when evaluating the relative impact of a change, irrespective of the scale of the numbers involved. A positive percentage change indicates growth or increase, while a negative percentage change indicates decay or decrease.
The crucial element in calculating the percentage change is the denominator: the **Original Value (OV)**. The calculation measures how much the net change ($NV – OV$) represents relative to that starting point. If the Original Value is zero, the calculation becomes mathematically undefined or infinite, which requires specific handling.
In practical business applications, this metric is used to track sales growth, analyze stock price movements, report economic inflation, or determine year-over-year operational efficiency improvements.
How to Calculate Original Value (Example)
A stock increased by **15%** ($P$) over one year and reached a **New Value** ($NV$) of **$230.00**. You want to find its **Original Value** ($OV$).
- Determine the Missing Variable: Original Value ($OV$) is missing.
- Convert Rate: $P_{dec} = 15 / 100 = 0.15$.
- Apply Formula: $$ OV = \frac{NV}{\left(1 + \frac{P}{100}\right)} $$
- Substitute Values: $OV = \frac{\$230.00}{(1 + 0.15)} = \frac{\$230.00}{1.15}$.
- Calculate: $OV = \$200.00$.
- Result: The Original Value was **$200.00**. (The Change Amount $C$ is $\text{\$230.00} – \text{\$200.00} = \text{\$30.00}$).
Frequently Asked Questions (FAQ)
If $OV$ is zero, the percentage change formula results in division by zero, which is undefined. In such cases (e.g., revenue goes from 0 to 100), it’s typically reported as an “Infinite” or “N/A” percentage increase, and only the absolute Change Amount ($C$) is meaningful.
Can the Percentage Change (P) be negative?Yes. If the New Value ($NV$) is less than the Original Value ($OV$), the resulting Change Amount ($C$) is negative, leading to a negative Percentage Change ($P$), indicating a decrease or decay (e.g., a loss in value).
What is the difference between Percentage Change and Markup?Percentage Change measures change relative to the *Original Value*. Markup measures the profit relative to the *Cost* of the product. They use the same inputs but reference different base figures, leading to different percentages.
Is the Change Amount (C) necessary?The Change Amount ($C$) is mathematically dependent on $NV$ and $OV$ ($C=NV-OV$), but it is included here to allow users to solve for $OV$ or $NV$ when the absolute change is known instead of the percentage.