Percentage Increase Formula

The percentage increase formula is the standard way to describe how much a value has grown, expressed as a percent of the starting value. Whatever the domain (prices, pay, attendance, server load, anything with a before-and-after), the same formula does the job.

The result is a single percentage. A small percentage means a modest increase, a large percentage means a substantial one, and 100 percent or more means the new value is at least double the old value.

The plain-English version reads like a recipe:

Subtract the old value from the new value, divide by the old value, then multiply by 100.

Three operations and one multiplication by 100. That is the whole thing. Every step is doing useful work, which the next sections explain.

The same formula in math notation:

Some textbooks use slightly different variable names.Final instead of new, initial or original instead of old. The math is the same; only the labels change.

Reading the formula from inside out:

• new value. The final number, after the increase.
• old value. The starting number, before the increase. Sometimes called the original value or the base.
• new − old. The amount of increase. The absolute number of units the value went up by.
• (new − old) / old. The increase expressed as a fraction of the original. A value of 0.25 means the new amount is one quarter larger than the old amount.
• × 100. Converts the fraction into a percentage. 0.25 becomes 25.

The numerator (new − old) measures the size of the change. The denominator (old) puts that change in context. The × 100 at the end is just a unit conversion.

Percentage increase answers a specific question: how much bigger is the new value, compared to where it started? The old value is the reference point, so it goes in the denominator.

Example: 50 grows to 80. The absolute change is 30. As a fraction of the old value, 30 / 50 = 0.6, or 60 percent. That answer is the right one when you want to describe the change relative to the starting point.

If you divided 30 by the new value (80) instead, you would get 0.375 or 37.5 percent. That number is also real, but it answers a different question (what fraction of the new value is the change?), not “how much did the value grow relative to where it started?” The convention for percentage increase is always to use the old value as the base.

Take an old value of 50 and a new value of 80.

1. Subtract the old value from the new value: 80 − 50 = 30
2. Divide by the old value: 30 / 50 = 0.6
3. Multiply by 100: 0.6 × 100 = 60

The percentage increase is 60 percent. For a longer step-by-step walkthrough with three more worked examples (price, salary, traffic), see How to Calculate Percentage Increase.

A coffee shop raises the price of a latte from $4.00 to $5.00.

((5.00 − 4.00) / 4.00) × 100 = (1.00 / 4.00) × 100 = 25

The price went up 25 percent.

For pricing-specific applications of the same arithmetic, the markup calculator applies a percentage to a wholesale cost to get a retail price, and the sales tax calculator adds a tax percentage to a base. Both run the percentage increase formula under the hood, just labeled for specific commerce contexts.

Someone gets a raise from $60,000 to $66,000.

((66,000 − 60,000) / 60,000) × 100 = (6,000 / 60,000) × 100 = 10

The raise is a 10 percent increase. The absolute change ($6,000) is the money in your pocket; the percentage (10 percent) is the comparison to where the salary started.

A website goes from 8,000 monthly visitors to 12,000.

((12,000 − 8,000) / 8,000) × 100 = (4,000 / 8,000) × 100 = 50

Monthly traffic is up 50 percent. The multiplier (1.5) tells you the same thing in a different way: the new traffic is 1.5 times the old traffic.

The two formulas are the same. The difference is convention:

• Percentage change is the umbrella term for any movement between two values. It accepts negative results.
• Percentage increase is the specific case where the new value is higher than the old. The result is positive.
• Percentage decrease is the specific case where the new value is lower. The result is negative, or you describe it without the minus sign.

Run the same formula either way; the sign of the answer tells you which direction you went. For a calculator tuned to the decrease case (a sale or markdown applied to a price), the discount calculator handles that directly.

A few traps that catch people, even when the formula itself is clear:

• Dividing by the new value. The denominator is always the old value. Going from 50 to 80 is a 60 percent increase (30/50), not 37.5 percent (30/80).
• Forgetting to multiply by 100. A result of 0.6 is a fraction. The percentage is 60.
• Adding multi-stage percentages. A 10 percent increase followed by another 10 percent increase is 21 percent total, not 20 percent. Each stage is calculated against a new base.
• Calling a negative result an increase. A negative answer means the new value is lower. That is a decrease.
• Trying to use the formula when the old value is zero. The denominator becomes zero, which is undefined. There is no baseline. Report the absolute change instead, or describe the move qualitatively.

Doing the formula by hand is fine for one calculation. For multiple values, edge cases like a negative starting point, or when you want a sanity check, the percentage increase calculator runs the formula and reports the percentage change, the absolute change, and the multiplier in one step.

For the full step-by-step procedure with three more worked examples and a short tour of common pitfalls, see How to Calculate Percentage Increase.

• Formula in words: subtract the old value from the new value, divide by the old value, multiply by 100.
• Formula in symbols: ((new − old) / old) × 100
• The denominator is always the old value (the reference point), not the new value.
• A positive result is an increase. A negative result is a decrease.
• An increase greater than 100 percent means the new value is more than double the old value.
• The formula breaks when the old value is zero. Report the absolute change instead.
• The percentage increase calculator runs the formula in one step and handles edge cases cleanly.