Calculating Percentage Increase: Formula, Calculator & Examples

Using Variables:

Two-Step Method:

Step 1: Calculate the increase: \(\text{Increase} = \text{New} - \text{Original}\)
Step 2: Calculate percentage: \(\%\text{ Increase} = \frac{\text{Increase}}{\text{Original}} \times 100\)

📊 Results:

\(\text{Increase} = 960 - 800 = 160\)

\(\text{Proportion} = \frac{160}{800} = 0.2\)

\(0.2 \times 100 = 20\%\)

\[\%\text{ Increase} = \frac{\text{New} - \text{Original}}{\text{Original}} \times 100\]

\[\%\text{ Increase} = \frac{13{,}800 - 12{,}000}{12{,}000} \times 100\]

\[\%\text{ Increase} = \frac{1{,}800}{12{,}000} \times 100\]

\[\%\text{ Increase} = 0.15 \times 100 = 15\%\]

Answer: The stock price increased by 240%

💡 Note: This is more than a 100% increase! The stock more than tripled in value (it's now 340% of the original: 100% + 240% = 340%). Percentage increases can definitely exceed 100%.

The formula for percentage increase is: Percentage Increase = ((New Value - Original Value) / Original Value) × 100. In simpler terms: subtract the original value from the new value, divide by the original value, then multiply by 100 to get the percentage. For example, if a value increases from 50 to 75: \(\frac{75-50}{50} \times 100 = \frac{25}{50} \times 100 = 50\%\) increase. Always remember to divide by the original value (the starting point), not the new value.

To calculate percentage increase between two numbers: (1) Find the difference by subtracting the smaller (original) from the larger (new) number. (2) Divide this difference by the original (smaller) number. (3) Multiply by 100 to convert to percentage. Example: From 40 to 52: Difference = 52 - 40 = 12; Proportion = 12 ÷ 40 = 0.3; Percentage = 0.3 × 100 = 30% increase. The key is always using the original/starting value as the denominator.

Percentage increase specifically refers to when a value goes up (positive change) - the new value is greater than the original. Percentage change is the general term that includes both increases (positive) and decreases (negative). If you calculate and get a positive result, it's a percentage increase. If you get a negative result, it's a percentage decrease. The formulas are identical: \(\frac{\text{New} - \text{Original}}{\text{Original}} \times 100\), but "percentage increase" implies the answer will be positive. Some people use "percentage change" as the umbrella term for both.

Yes! Percentage increase can definitely exceed 100%. A 100% increase means something doubled (became twice as large). A 200% increase means it tripled (became three times as large), and so on. Example: If a stock goes from $10 to $40, the increase is \(\frac{40-10}{10} \times 100 = 300\%\) - it's now four times its original value. Think of it this way: the original value is 100% of itself. If it increases by 150%, the new value is 250% of the original (100% + 150%). There's no upper limit on percentage increase!

You divide by the original value because you want to know how much the value changed relative to where it started. The original value is your baseline (100%). If a price goes from $50 to $75, you're asking "What percentage of the original $50 did it increase by?" Answer: $25 is 50% of $50, so it's a 50% increase. If you wrongly divided by $75 (the new value), you'd get 33.3%, which doesn't represent the true growth from the starting point. The original value is always the denominator in percentage change calculations.

In Excel or Google Sheets, use this formula: =((New_Value - Original_Value) / Original_Value) * 100. If your original value is in cell A1 and new value in B1, type: =(B1-A1)/A1*100. For example: A1 = 50, B1 = 75, formula gives 50 (representing 50%). You can also use: =(B1/A1-1)*100 which is mathematically equivalent. To format as percentage automatically, use =(B1-A1)/A1 and apply percentage formatting (no need to multiply by 100 when using percentage format). Both programs handle percentage calculations the same way.

If the original value is zero, percentage increase cannot be calculated using the standard formula because division by zero is mathematically undefined. Think about it: you can't calculate "what percentage of zero" something is. In practical terms, if something goes from 0 to any positive number, it's an infinite increase or "undefined increase." This situation often appears in business when a new product line starts from nothing. Instead of percentage, report the absolute change: "increased from 0 to 100 units" rather than trying to calculate a percentage.

Yes! A 50% increase is exactly the same as multiplying by 1.5 (or 150%). When something increases by 50%, the new value is 150% of the original, which equals 1.5 times the original. Example: $100 increased by 50% = $100 × 1.5 = $150. The general rule: to increase a value by x%, multiply by \((1 + \frac{x}{100})\). So: 20% increase = multiply by 1.2; 75% increase = multiply by 1.75; 100% increase = multiply by 2.0; 200% increase = multiply by 3.0. This shortcut is very useful for quick mental calculations!